The preparation of dispersions : conference, Veldhoven, 1991,October 14-16 : preprintsCitation for published version (APA):Lavèn, J., & Stein, H. N. (Eds.) (1991). The preparation of dispersions : conference, Veldhoven, 1991, October14-16 : preprints. Stichting Chemische Congressen XII.

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I

J c . 9 1

Preprints of the Conference

THE OF

PREPARATION DISPERSIONS

Veldhoven, The Nether lands

1 9 9 1 , October 1 4- 1 6

lA CIS conference I Event 4 3 9 of the EFChE

Editors: J.Laven, H.N.Stein

Preprints of the Conference

THE OF

PREPARATION DISPERSIONS

Veldhoven, The Netherlands

1 9 9 1 , October 1 4- 1 6

lA CIS conference I Event 4 3 9 of the EFChE

Editors: J.Laven, H.N.Stein

iii

This conference is organized by the "Stichting Chemische Congressen XII", a foundation owned by the Royal Netherlands Chemical Society.

The conference is held under the auspices of the European Federation of Chemical Engineers and the International Association of Colloid and Interface Scientists.

The purpose of the conference is to stimulate discussions between investigators who study model systems and those who experience the fulJ complexity of dispersions in practical applications.

This book contains preprints of the invited papers by Gosele, Garrett, Walstra, Jeelani and Hartland, and Vanderhoff, together with 18 other, contributed papers.

After the conference these papers will be published in a special issue of Chemical and Engineering Science.

H.N. Stein, J. Laven

iv

SCIENTIFIC COMMITTEE

H.N. Stein W.G.M. Agterof W.M. Brouwer R. Buscall B. Dobias D. Langbein A.E. Nielsen D. Thoenes P. Walstra

(Technical University Eindhoven, NL), Chairman (Unilever Research Vlaardingen, NL) (Akzo Research Centre, Deventer, NL) (ICI Runcorn, GB) (Universitat Regensburg, D) (Battelle Institut Frankfurt, D) (University of Copenhagen, DK) (Technical University Eindhoven, NL) (Agricultural University Wageningen, NL)

ORGANIZING COMMITTEE

H.N. Stein W.G.M. Agterof A. Eshuis G. Frens J. Laven D. Thoenes

(Technical University Eindhoven, NL), chairman (Unilever Research Vlaardingen, NL) (Technical University Eindhoven, NL) secretary (Technical University Delft, NL) (Technical University Eindhoven, NL) treasurer (Technical University Eindhoven, NL) vice chairman

Correspondence adress: Secretary: Dr. A. Eshuis,

Technical University Eindhoven, Building FT 1.34, Laboratory of Chemical Process Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. phone: 040 - 472199 telefax: 040 - 442576

CONTENTS

1. W. Gosele (Ludwigshafen, D) Precipitation so as to obtain easily separated solids.

2. Z. Sadowski (Wroclaw, PL)

3

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

The Influence of the sodium oleate adsorption on the behavior of calcite suspension.

S.G.J. Heijman, H.N. Stein (Eiruilwven, M.,) Preparation of oxide dispersions which are stabilized both sterically and electrostatically.

H. Strauss, H.P. Heegn, I. Strienitz (Freiberg, D) Effect of PAA adsorption on stability and rheology of Ti02 dispersions.

V.N. Kislenko, A.A. Berlin, M.A. Moldovanov (Lvov, USSR) Intensification of suspension flocculation by partially hydrophobized polyacrylamide.

M. Kawaguchi, Y. Ryo (Mie, JAP) Rheological Properties of silica suspensions in aqueous cellulose derivatives solutions.

P.R. Garrett (Bebington, GB) Recent developments in the understanding of foam generation and stability.

P.J.M. Baets and H.N. Stein (Eirullwven, M.,) The influence of solid particles on CT AB films .

P. Walstra (Wageningen, M.,) Principles of emulsion formation.

W.J. Tjaberinga, A. Boon, A.K. Chesters (Vlaardingen, M.-) Model experiments and numerical simulations on emulsification under turbulent conditions.

R.A. de Bruijn, (Vlaardingen, M.-) Tipstreaming of drops in simple shear flows.

P.H.M. Elemans, H .L. Bos (Geleen, M.,) and J.M.H. Janssen, H.E.H. Meijer (Eiruilwven, M.,) Transient phenomena in the dispersive mixing.

J.M.H. Janssen, G.W.M. Peters, H.E.H. Meijer (Eindhoven, M.,) An opposed jets device for studying the breakup of viscoelastic drops and threads.

v

page

11

19

29

39

53

61

65

77

93

103

111

121

VI

page

14. S.A.K. Jeelani, S. Hartland {ZUrich, CH) Separation of dispersions. 131

15. F. Groeneweg, F. van Voorst Vader, W.G.M. Agterof (Vlaardingen, NL) The dynamic stability of W/0 emulsions from vegetable oil. 147

16. W.Q. Zhao, B.Y. Pu, S. Hartland (ZUrich, CH) Measurement of drop size distribution in liquid/liquid dispersions by encapsulation. 157

17. F.I. Liaschenko, A.M. Romaniukha, N.N. Zaiets, E.V. Radzievski, M.A. Al'tshuler (Kiev, USSR) Stable oil dispersions of grafite: preparation, testing and application. 167

18. V.A. Pryamitsyn, V.P. Glinin, G. Kotov (Leningrad, USSR) The creation of dispersions by the electro-hydraulic effect. 169

19. J.W. Vanderhoff (Bethlehem, USA) Recent advances in the preparation of latexes. 177

20. F.K. Hansen (Oslo, NOR) The function of surfactant micelles in latex particle nucleation. 193

21. B. Vincent (Bristol, GB) The preparation of colloidal particles having (post-grafted) terminally-attached polymer chains. 201

22. M. Leca (Bucharest, RUM) Cataphoretically applicable film-forming disperse systems. 209

23. P.A. Ruining, C. Pathmamanoharan, A.P. Philipse, H.N.W. Lekkerkerker (Utrecht, NL) Preparation of (non-)aqeous dispersions of colloidal boehmite needles. 219

PRECIPITATION TO OBTAIN EASILY SEPARATED SOLIDS

ABSTRACT

W. GOSELE

BASF, Dep . ZET, D-6700 Ludwigshafen Germany

1

A large number of precipitation reactions have been optimized in order to minimize the cost of solid-liquid separation. This paper presents the methods applied and derives some general rules from the results. The difference between precipitation and crystallization is explained by the very low solubility of most precipitates, and some of the strongest effects on filterability are explained by enhanced agglomeration on existing particles.

KEYWORDS Precipitation from Solution, Solid-Liquid Separation.

~ /I\

/

Fig. 1: Precipitation of more or less easily separated solids

2

DEFINITION OF THE PROBLEM

It is often necessary to optimize precipitation processes so that the solids can be separated as easily as possible, see Fig. 1. A slurry which is easy to filter is indicated here by very large particles, but particle size alone is not sufficient to characterize a suspension.

The filter resistance depends, for example, both on the particle size and on the porosity of the filter cake. Figure 2 [Gosele 1986] shows the usual range of filter resistance as a function of particle size and porosity E. The two straight lines are calculated by the equation of Karman and Kozeny for spherical particles at very low and very high porosities. The low porosity of 26% corresponds to the closest possible packi ng of spheres, and the high porosity of 90% corresponds to filter cakes with a residual moisture of 90% by volume. Such a high porosity is not unusual with filter cakes of fine particles like pigments. As a rule, pigments in industrial filter presses have particle sizes between 0,1 and 0,5 ~m and filter resistances between 1014 and 1015 m- 2 • If the resistance is more than 1015 m- 2 , the filt­ration is too time-consuming for most industrial processes.

aH

m-2

(1) finished pigments (_) 1015 c C\S ....... (j)

"(j) 14 spherical particles (1)

a: 10 (Karman and Kozeny) ~

£= 0.26 (1) :::! 1013 u:::

E = 0.90

1012 0.1 1 10 100 ~m

mean diameter

Fig. 2: Filter resistance as a function of particle size and porosity E

Figure 2 illustrates an important aspect: The same particle size can give very different filter resistances, depending on the porosity of the filter cake. Since this porosity is known only after the filtration, filter resistances are determined by direct measurement and cannot be calculated from granulometric data.

Figure 3 shows a typical arrangement for the measurement of filter resistances. The suspension is placed in a filter and filtered with a constant gas pressure. The filter resistance of the cake can then be calculated from the quantity of filtrate, the correspon­ding time and the cake thickness.

Balance

3

Fig. 3: Measurement of the filter resistance

OPTIMIZING THE PRECIPITATION

What is precipitation?

Precipitation is very similar to crystallization, but the methods to optimize each operation are rather different. Comparison of precipitation and crystallization is instructive, Fig. 4 [Gosele et al. 1990]:

CRYSTALLIZATION

Evaporation

Cooling

Vacuum= Evaporation+Cooling

PRECIPITATION

Reaction

Displacement

Fig. 4: Usual ways of crystallization and precipitation

Crystallization always starts from a saturated solution of the substance to be crystallized. It is obtained either by evapo-

4

ration or by cooling, or by applying vacuum. The effect of applying vacuum can be considered as a combination of evapor­ation and cooling.

In contrast to this, precipitation starts when two liquids are brought together. The solid particles are formed either by a chemical reaction between the two liquids, or by displacement of dissolved substance from the solution. The basic difference between precipitation and crystallization, however, does not appear in these definitions. This difference is a consequence of the fact that most precipitates have very low solubilities compared to crystallized substances.

A simple experiment shown on the overhead projector will demonstrate the obvious characteristics of precipitation. Two drops of aqueous solutions of calcium nitrate and of sodium carbonate are brought together. They react according to the equation:

At first we see only a gel-like substance. The solid particles appear several minutes later. This phenomenon can be observed with many precipitations, and Fig. 5 summarizes some of them. Various inorganic salts have been precipitated, and the process of solidification has been observed. The positions on the graph depend on the solubility of the precipitated solid (horizontal axis) and on the concentration (vertical axis). Different

Concentration mol/1

0,1

0,01

• Crystals o transient gels "" permanent gels

Relative supersaturation 0 = c I c* --

Relative solubility c* ID.c

Fig. 5: Observations during formation of solids

5

symbols indicate if crystals were formed immediately, or if a gel-like substance appeared, as in our experiment. Crystals were formed only when the relative solubility of the solid was >0,001, which means that more than 1/1000 of the solid to be formed was soluble in the surrounding liquid. This amount of dissolved substance was evidently necessary for mass transport during crystallization. At lower solubilities crystallization was not possible, and gel-like substances were precipitated instead and subsequently became the final solid product.

Precipitated solids typically have very low solubilities. Thus the particular feature of precipitation is that intermediate forms of matter are produced, as shown in Fig. 6. The influence of these forms with unknown properties explains why precipita­tion has to be treated in a much more empirical way than crys­tallization. To optimize precipitations, tests are necessary in a laboratory installation like that depicted in Fig. 7. Impor­tant parameters to be varied are concentrations, pH, tempera­ture, flow rate and stirrer speed.

Precipitation

Fig. 6: The particular feature of precipitation compared to crystallization

Solutions

r- - ----- - ---------------------------1 I I

I : I I

Suspension

Fig. 7: Precipitation test installation

6

Some typical results

A statistical analysis of the results from a large number of different precipitations is shown in Fig. 8. We counted how often a certain parameter had a beneficial (positive) effect on the filterability of the precipitate . The parameters are listed in the order of decreasing probability of a beneficial effect.

• inoculation

• contin. operation

• recycle

• lower concentr.

• higher temp.

• less precipitating agent

• slower stirring

Percentage of cases observed

0 20 40 60 80 100%

~ ~

~ • longer residence ~

time ~t:_CLL.CLL.CLL.CLL.-.t:>eo.:~-=---------'

~ positive effect

m optimum

~ negative effect

0 noeflect

Fig. 8: Factors affecting the filter resistance

Filter Resistance (relative)

1,0 111~====----- detergent _____ ..,..fertilizer

0,5

inter= mediate

insectizide

animal feed additive catalyst catalyst

· herbizide catalyst

0 ~-----------------.-----

Batch Continuous

A B

batchwise continuous

Fig.9: Filter resistance from batchwise and from continuous precipitations

As an example of the importance of these effects, Fig. 9 shows the difference between pre cipitates from batchwise and from continuous operations. Depending on the substance, the partic l e s from continuous precipitation h ad up t o 1/l Oth o f the fi lter

7

resistance of particles from batchwise precipitation. We explain this by the larger particle size: in the continuous precipita­tion there are always many solid particles on which the newly formed solid substance can agglomerate.

This is depicted in Fig. 10 and 11 for precipitation by reaction. The horizontal axis shows the mixing ratio of the two reacting solutions A and B, and the vertical axis shows the concentration S of solids formed from these mixtures. The theoretical amount of solid can be calculated from the stoichio­metry of the reaction and is represented by straight lines. A proportion, depending on the solubility, of this theoretical amount of solid will remain dissolved, so that the real amount of solid is somewhat smaller. The mixing takes place on straight lines between the mixture M and the incoming solution A or B.

It is important for the formation of large particles that the amount of solids to be formed is small compared to the amount of solids already present, so that the newly formed solids can agglomerate on existing particles. The two graphs in Fig. 10 and 11 show that the ratio of newly formed solid substance to solid particles already present will always be smaller in a continuous operation than in a batchwise reaction. This explains why continuous precipitations produce bigger particles than batchwise precipitations; and of course these bigger particles make smaller filter resistances, as shown in Fig. 9.

(/)

c 0

~ c <D (.) c 0 (.)

(/)

:!2 0 (/)

A

0

M

stoichiometry 8

B

Ratio B/A

Fig. 10: Concentration of solid as a function of mixing ratio. In batchwise precipitation, the concentrations are described by a straight line between the incoming liquid B and the momentary mixture M.

8

(/)

c .Q ~ c Q) () c 0 ()

(/)

:Q 0 (/)

A

0

M

newly formed solids

Ratio B/A

A B

B

Fig. 11: Concentration of solid as a function of mixing ratio. In continuous precipitation, the concentrations are described by two straight lines between the incoming liquids A and B and the final mixture M.

The possibility of agglomeration on existing particles depicted in Fig. 10 and 11 seems in fact to be one of the most important and generally valid parameters if we wish to produce large particles. Graphs like Fig. 10 and 11 are therefore helpful to describe the best way of mixing in order to produce easily separated solids.

Unfortunaltely these graphs cannot be used to predict the particle size and the rate of agglomeration quantatively: The horizontal axes of Fig. 10 and 11 show different compositions of the solution. This means that the pH values and zeta potentials are also different, and thus the rates of agglomeration between the newly formed solid and the existing particles differ along the horizontal axes. Since we know much too little about the local zeta potentials and their influence on agglomeration, it is not possible to quantify the the size of agglomerates from such graphs.

9

FUTURE PROSPECTS, UNANSWERED QUESTIONS

In industrial practice we are particularly concerned by the fact that it is even not always possible to scale up from laboratory findings to large scale. Several times we found clear contra­dictions between the results from small and large scale tests. They could be explained by the existence of different mixing zones in large vessels, as shown in Fig. 12 [Gosele and Kind 1991]. When we reproduced these zones in the laboratory with an arrangement of three different vessels, we got approximately the same results on the small and the large scale.

Our next goal is therefore to find out why and when these contradictions between small and large scale arise, and how we can identify the "difficult cases".

Production Plant Miniplant

Fig.12: Mixing zones in a large vessel and their reproduction in laboratory scale

REFERENCES

Gosele, W. (1986). Grenzflachenprobleme bei der Fest/Fltissig­Trennung. Chem.-Ing.-Tech. 58 (1986), 3, S. 169-175.

Gosele, W., W. Egel-Hess, K. Wintermantel, F. Faulhaber and A. Mersmann (1990). Feststoffbildung durch Kristallisation und Fallung. Chem.-Ing.-Tech. 62 (1990), 7, s. 544-552.

Gosele, W. and M. Kind. (1991). Versuche zum Einflu~ der Vermischung auf die Qualitat eines kontinuierlich gefallten Produktes. Chem.-Ing.-Tech. 58 (1986), 3, S. 169-175.

10

11

THE INFLUENCE OF THE SODIUM OLEATE ADSORPTION ON THE BEHAVIOR

OF CALCITE SUSPENSION

Z. SADOWSKI

Department of Inorganic Chemistry and Metallurgy, Technical University of Wroclaw, 50-370 Wroclaw, Poland

ABSTRACT

The effect of sodium oleate (SOL) on the behavior of calcite suspension has been investigated. The stabilit~9 of ~lute calcite suspension dramatically increased at 3 10 kmol/m of SOL. It was a good correlation with the vertical part of the adsorption isotherm of SOL on the calcite surface. The hindered settling technique has been used for the concentrate calcite suspension tests. The maximum of mean equivalent Stokes radius corresponded with the flocculation of mineral suspension. Also, the Bingham yield values received the maximum at the flocculation area of calcite suspension. The spherical agglomeration of calcite suspension has been r~ilized

9at the

high surfactant concentration region (3 10 kmol/m )_ The specific resistance of calcite cakes has been also investigated. The results showed that the specific resistance of the calcite cake created by the mechanical agitation was higher than for the cake made by flocculation.

KEYWORDS

Calcite suspension; stability; hindered rheological measurements; spherical agglomeration; and sodium oleate adsorption.

INTRODUCTION

settling; filtration

The behavior of fine particle suspensions is a major problem in the mineral processing (Fuerstenau,19BO). Many ores must be deslimed before flotation and the slimes are currently discarded. Thus, the better knowledge of basic principles governing dispersion and agglomeration of fine particles at the present of surfactants (collectors) has a significant affect on the development the new methods such as selectiv coagulation, selective flocculation, oil agglomeration and carrier flotation (Subrahmanyam et al., 1990). The stability of mineral suspensions can be analyzed from both an energy standpoint and a kinetic standpoint (Hunter, 1987). The changes in the mineral suspension stability brought about by the surfactant addition are the consequence of the

12

adsorption and orientation of surfactant molecules in the adsorbed layer. In the presence of surfactants which adsorb at surface hydrophobicity will be altered. This phenomenon has an effect on both the oil agglomeration and filtration process (Sadowski,1990). The sediment volume of coarse suspensions basically depends on both the particles shape and the particles interactions. This reciprocal action in the presence of adsorbed surfactant molecules on the mineral surface is mainly the hydrophobic interaction (Xu et al.,1990). The energy of hydrophobic association would be modified by the surfactant adsorption. The subject of the present oleate on the stability, rheology and filtration of

MATERIAL AND METHODS

Materials

steady is the influence of sodium hindered settling, sedimentation,

calcite water suspensions.

Iceland spar variety of calcite crystals purchased from Wards Natural Science Establishment, Inc., were used. The mineral lumps were crushed and ground dry to minus 40 ~m in a porcelain mill. Particle size analyzer Sentigraph 5000D was apply to the particle size distribution determination. It was shown that 80% of calcite particles have a diameter less than 20 ~m. The specific surface area was me~sured by the nitrogen adsorption method (BET), it was 2.822 m /g. Sodium oleate was pure grade and was supplied from T.Baker Chemical Co.

Adsorption isotherms

The adsorption isotherm was determined at the room temperature. 1g of calcite powder was dispersed in the sodium oleate solution of known concentration. The pH was adjusted at the vicinity pH 10. The equilibration time for the surfactant adsorption was about 8 hours. After centrifugation, the residual concentration of surfactant in the supernatant was determined. The SOl (sodium oleate) concentration was determined by the reaction with buffered copper(II) triethylenetetramine reagent. The complex was extracted into an isobutanol-cyclohexane mixture. After the phase separation, the concentration of copper complex in organic phase was determined spectrophotometrically (Fowler,1968).

Suspension stability

The stability of calcite suspension was achieved by the sedimentation method, using an Andreasen pipette. Th~ calcite suspension, contained 1g of calcite powder in 530 em of the solution, was placed in the pipette and shaking. 10 cm9 samples of suspension was taken from a constant depth in the pipette at 0.0 min. and 5.0 min. elapsed time. The stability was calculated from the relation : Stability (%) = 100 M<l=!S/ M<l=O> where M is the mass of the samples taken from the pipette at these two times.

13

Hindered settlin~ sedimentation

The sedimentat~on studies were carried out in graduated stoppered 50 em cylinders. Six calcite suspensions with a progressively increasing concentration of solid phase were prepared and placed in the cylinders. Suitable quantity of sodium oleate solution was added to the each suspension. pH of suspension was adjusted by the sodium hydroxide solution addition. The suspensions were mixed by turning the cylinder end-over. Immediately after the mixing cylinders were put in a vertical position the height of the interface between clear liquid and the suspension was visually observed and recorded as a function of time. The settling curves were constructed as the plot of logQ versus the solid concentration, where Q is the speed of interface movement . They were prepared for the different concentrations of sodium oleate. The extrapolation of the sedimentation curve to the zero solid concentration value permited the equivalent stokes radius calculated.

Rheolo~ical studies

Rheological measurements were performed in Rheotest No 2 rotational viscometer with a rotating inner cylinder. Dispersions were prepared by mixing calcite with sodium oleate solutions of varied concentration . In all experiments carried out, the calcite powder volume concentration was kept constant at 0.48 vlv . The range of shear rates_fo which the dispersions were subjec ted was 10 - 760 sec . The results of the rheological measurements were graphically presented and the Bingham yield values were obtained from the rheological curves by extrapolating these curves to the zero shear rate.

Spherical agglomeration experiments

Agglomerat ion took place at room temperature in a teflon c ylindrical vessel about 100 cm9 capacity. Agitation was provided by a central 3 em diameter turbine impeller with six flat blades, operated 2 em from the bottom of the container . n-Heptain from Loba Chemie Austria was used as an agglomerating liquid. 2 g of the calcite powder was used in each experiment. The hydrophobic properties of the calcite surface were controlled by an addition of the adequate amount of sodium oleate into the suspension.

Filtration ~

A specially designed apparatus was used for the rate of filtra tion determination. The equipment consisted with a 10-liter vacuum reservoir fitted with a filtration unit, manometer and vacuum pump. Details of this equipment were described elsewhere (O'Gorman et al., 1974). The amount of filtrate collected in a graduated cylinder were measured as a func tion of filtration time. The obtained results were treated according to the filtration theory equation : p t I ~ v = a c v I 2

whe r e : p is the pressure difference applied to the filter ~ is the viscosity of the filtrate at the temperature

of filtration test v is the volume of filtrate a is the specific resistance of the cake at pressure (p)

14

The values of o were calculated from the slope of linear plots pt/.uv versus v.

RESULTS AND DISCUSSION

The settling behavior of mineral suspensions depends primarily on the solid concentration and the degree of agglomeration. The stability of dilute calcite suspensions where the mineral particles behave as free individual particles is presented in the Figure 1. The major effect of the sodium oleate addition was a permanently decreasing of the stability with the increasing of surfactant concentration. ~en the surfactant concentration obtained the value of 3 10- kmol/m9 the dramatic stability increase was observed. The rapid increase in the stability of calcite suspension corresponded with the nearly vertical part of adsorption isotherm (Figure 1). 1oor-~--.-------.---.-------.---0=~~~~

so CALCITE 8

N E

pH 9.7-10.0 " 0

60 6 E

U"\

~ ' 0 0

.c ~ :J5

"' ~ Vl

40

20

4

2

Sodium O!eat~ Concentration , kmoljm3

Fig. 1. Stability of ~alcite suspension ~and f::'\ adsorption of soddium oleate on ~ite ~

:.:: Cl. '-0 VI "C <{

The shape of adsorption isotherm was attributed to the calcium oleate precipitation (Rao et al . , 1988/ 89, Rao et al., 1990) and the possibility of calcium oleate adhesion to the homoginies hydrophobic layer of early adsorbed oleate anions. High stability of calcite suspension should be explained by the strong electrostatic interaction. As it is know from the literature (Matijevic et al., 1966, Nemeth et al., 1971), the

15

metal soap particles were negatively charged and the zeta potential of calcite particles covered by calcium oleate was -60 mV (Nemeth et al., 1971). The hindere settling technique has been used to the study of aggregation stability of mineral suspensions in early author's work (Sadowski et al . , 1980). The mean equivalent Stokes radius could be an important parameter for the description of the mineral suspension behavior.

Ill QJ ~ 0

VI

..... c: QJ

-ro > ·s o­QJ

..... c: QJ L.. ro a. a. ro

60

40

"0 ~ 10 ro "5 u

10 LJ

s 1 o-4

Sodium Oleate ConcentrCJtion , kmoljm3

Fig. 2 . Effect of sodi~leate concentration on th~quivalent Stokes radius~and Bingham yield values~

As can be seen in the Figure 2, the maximum oj equivalent Stokes radius was at the vicinity of 5 10-

4 kmol/m of sodium

oleate. There was a good correlation with the strong flocculation which was observed for the dilute calcite suspensions in the presence of surfactant (Fig.1). Mineral dispersions in which the attractive forces between the dispersed particles were strong, generally showed the Bingham rheological behavior (Heertjes et al., 1977). Figure 2 also shows the variation of the yield values (T~) with the sodium

oleate concentration. Two models have been introduced by Hanter (Hunter et al 1976, Firth et al., 1977) which can be used to interpret the rheological results in the presence of surfactant. The floc rupture model (Firth et al., 1977, Hunter et al., 1983)

16

assumed that the major contribution to the excess energy dissipation comes from the need to provide energy from the shear field to separate contacting particles. Under these conditions the extrapolated yield values should be correlated with the energy needed to the floc rupture. This approach may be used to explain the maximum observed in Figure 2 (curve 1). The decrease of the yield values at a higher sodium oleate concentration should be correlated with the strong electrostatic repulsion between the calcite particles covered by the c alcite oleate layer.

100

V):~ a~le

CAL C IH l O.S eo

., ~

60 ., ~ £

~ >-., ., >

~ 0.4 0 ..

·;;; a:

~

0.2 20 ., "' "'

S:r.1!un: Oleate C o··:: e."ltra~ion, ~m:;i / m3

Fig. 3. ~ect of sodium oleate concentration on~e~covery ~and the resistance of calcite cakes~~

Spherical agglomeration of salt-type minerals was a process which the agglomerates were produced in a liquid such as water by addition of both sodium oleate and immiscible bridging liquid. In this process it was important that the hydrophobicity of surface was sufficient to bring the particles together through the bridging liquid (Kawashima et al., 1986). The curve 1 in the Figure 3 shows the recovery of calcite as a function of sodium oleate concentration. As can be seen, the re~~very ~creased and reached the value of 100 % at 3 10 kmol/ m of sodium oleate. At this concentration of surfactant the spherical agglomeration occured. These results suggested that the agglomeration action of the liquid bridge might be stronger than the electrostatic interaction due to the calcium oleate adsorption. At a higher surfactant concentration, a future facility of the surface wetting by the bridging liquid was observed. The furnicular state was received and mineral paste was obtained Most of the liquid filtration operation follow the mechanism of cake filtration. The classical theories of filtration rely on the empirical correlation of experimental measurements of the specific cake resistance and permeability (Tiller et al., 1980). A new, micro-structure point of view was used for the filtration data interpretation (Tadros et al., 1980, Venkatadri

17

et al., 1984). According to this concept the interaction between particles is correlated with both permeability coefficient and the specific cake resistance (Cross et al. 1985). The Figure 3 shows that the specific resistance of the calcite cake was changed as a function of the surfactant concentration (curves 2 and 3). In the first case (curve 2) the filtration cakes were made by the calcite particles with out both a mechanical agitation and bringing liquid. In the second case (curve 3) the filtration cakes were created with the oil agglomeration products. Generally, both curves possessed the same character, which can be suggested that the structure of filtration cakes became progressively more open as the surfactant concentration increased. The minimum of the specific cake resistance good correlated with the spherical agglomerates formation. It should be noted that the specific resistances of the calcite cake created by the mechanical agitation with an immiscible liquid were higher than only flocculated suspensions. It can be explained by the differences in the sediment consolidation. This specific relationship, however, will be the target of the future works.

CONCLUSION

From the presented experimental generalizations appear to be valid :

data the following

1. The stabilization and destabilization of calcite suspensions are strong depend on the sodium oleate concentration. 2. The hindered settling technique permits estimate the size of aggregated particles. 3. The calcite suspension in the presence of sodium oleate exhibited pseudo plastic flow behavior which can be characterized by a Bingham yield value. 4. The agitation of calcite suspension with organophilic liquid (n-heptane) at the high level of surfactant concentration gives both the spherical agglomeration and mineral paste. 5. The agglomerating character of calcite particles can be determined by the rate at which the filtrate pass through the bed of solid.

REFERENCES

Cross, M, W.H. Douglas and R.P. Fields (1985). Optimal design methodology for composite materials with particulate fillers. Powder Technology . .4_3, 27-36.

Firth, B.A. and R.J. Hunter (1976). Flow properties of coagulated colloid suspension. ~ Colloid Interface ~ 51, 243 - 256.

FowJ~r. E .W. and I.W. Steel (1968). National Inst. of Metallurgy, Johannesburg, Report 443.

Fuc:rstenau, D.W. (1980). Fine particle flotation. In: Eine. particle processing (P. Somasundaran, Ed.) AIMM, New York, GG9-705.

Heertjes, P.M .. and C.I. Smits (1977). The influence of adsorbed layers on the rheological behaviour of titanium dioxide dispersions, Powder Technology. 17, 197-205.

18

Hunter, R.J. and B.A. Firth (1976). Flow properties of coagulated colloid suspension. II The elastic floc model. ~ Colloid Interface ~ 51, 266-275.

Hunter, R.J., R. Matarese, and D.N. Napper (1983). Rheological behaviour of polymer flocculated latex suspension. Colloids Surfaces. ~ 1-13.

Hunter, R.J. (1987). Foundation QL colloid science. Clarendow Press, Oxford , pp 395-449.

Kawashima, Y., T. Hanada, H. Takeuchi and H.Takenaka (1986). Spherical agglomeration of calcite carbonate dispersion in aqueous medium containing sodium oleate . Powder Technologv . .4.6_,_ 61-66.

Matijevic, E., J. Leja and R. Nemeth (1966). Precipitation phenomenon of heavy metal soaps in aqueous solutions. 1. Calcium oleate. ~ Colloid Interface ~ 22, 419-429.

Nemeth, Rand E. Matijevic (1971). Precipitation and electron microscopy of calcium and barium oleate soaps. Kolloid = Z ~ ~ Polymere. ~. 497-507.

O'Gorman, J.V. and J.A. Kitchener (1974). The flocculation and de- wate ring of kimberlite clay slimes. Inter ~ Mineral Processing. ~. 33-49.

Rao, K. H., B.M . Antti and E . Forssberg (1988/89) . Mechanism of oleate interaction on salt-type minera ls (part I). Colloids Surfaces .3_4, 227-238.

Rao, K. H. , B.M. Antti and E. Forssberg (1990). Mechanism of oleate interaction on salt- type minerals (part II). Inter J Mineral Processing. ~ 59-79.

Sadowski, z. and J. Laskowski (1980). Hindered settling a new method of the i.e.p. determination of minerals. Colloids Surfaces ~. 151-159.

Sadowski, z. (1990). Report of investigati on No.18/90. Technical University of Wroclaw.

Subrahmanyan , T . V. and E. Forssberg (1990) . Fine particles pr oc essing: she ar flocculation and c arrier flotation, a review . Inter ~ Mjneral Processing. JQ, 265-286.

Tadros, M. E. and I . Mayes (1980). Effect of particle propertie s on filtration of aqueous suspension. in Eina particle processing vol. 2 (P. Somasundaran, Ed . ), AIMM, 1583- 1593.

Tiller, F.M., J . R. Crump and F. Ville (1980) . A revised approach to the theory of cake filtration. in partic les processing vo l. 2. (P . Spmasundara n, Ed.), 1549-1582.

Eine. AIMM

Venkatadri , R., S.H. Chiang, G.E . Klinz i ng and J.W. Ti erney (1984) . A fundamenta study of filtration and dewatering of fine coal . QQal Preparation. ~ 71-92.

Xu , Zhenghe an d Roe-Hoan Yoon (1990) . A study of hydrophobic c oagulation. ~ Colloid Interfac e ~ ~ 427- 434.

PREPARATION OF OXIDE DISPERSIONS WHICH ARE STABILIZED BOTH STERICALLY AND ELECTROSTATICALLY.

ABSTRACT

S.G. Heijman and H.N. Stein,

Laboratory of Colloid Chemistry Eindhoven University of Technology,

P.O. Box 513, 5600 MB Eindhoven, The Netherlands.

19

TiO dispersions prepared in the presence of polyacrylic acid (PAA) may be ste¥ically stabilized, electrostatically stabilized, or stabilized by both mechanisms simultaneously, depending on PAA and electrolyte concentrations. Very stable suspensions are obtained when both sterical and electrostatical stabilizations occur.

PAA adsorption is especially pronounced at low pH, when TiO and PAA are oppositely charged. Larger amounts of PAA are effectively a8sorbed as neutral molecules since the large concentration of anionic groups near the TiO surface cause a large negative electrical potential which exerts a str~ng attraction on H+ions.

The thickness of the PAA layer was found to be about 3 nm at pH=6 in 0.01 M KNO solutions.

3

KEYWORDS

TiO dispersions; polyacrylic acid; stabilization by polyacrylic acid ads~rption.

INTRODUCTION

In order to improve the quality of water based paints, so called dispersing agents are used to optimize the dispersion process of the oxide pigments in water. As dispersing agents polyacrylic acid (= PAA) has proved to enhance the gloss and the opacity of the dry paint film. Polyacrylic acid is a water soluble polymer with carboxylic acid groups. The polymer is therefore negatively charged depending on the pH. With adsorbed charged polymers in theory two stabilization mechanism are possible: First, steric stabilization caused by the steric hindering of the loops and tails of the polymers adsorbed on the oxide surface; second, enhanced electrostatic stabilization due to increase of negative charge on the surface as a result of the adsorption of the charged polymer. The aim of our research is to investigate the relative importance of both mechanisms for the dispersion process of oxide pigments in water. The results of the experiments suggests that both mechanisms are important and that there is a positive influence of the thin polymer layer on the electrostatic stabilization .

20

EXPERIMENTAL

Material

TiO : prepared by hydrolysis of TiCl (Berube et al., 1968). Pol§acrylic acid: a. ex Jansen Chimica (H . W. 2000);b. ex Servo FX 508 (H.W. 11000).

Methods

pH titrations were performed using a Philips PHM 84 Research pH meter, and an ABU 80 autoburette with conventional glass and calomel electrodes. Zeta potentials were measured by electrophoresis using a Malvern Zetasizer 3. PAA equilibrium concentrations in solution were calculated from total organic carbon content measurements.

Adsorption of the polyacrylic acid on the titanium dioxide surface.

For both stabilization mechanisms it is important to investigate the amount adsorbed of the polymer as a function of pH and electrolyte concentration . The pH is a very important parameter in the adsorption process because the charge of both the oxide as well as the polyme r vary with the pH. The concentration of the indifferent electrolyte i s i mportant because it is of influence on the mutual repulsion of the charged groups on the polymer chain and on the Coulomb interaction of the charged groups on the surface and the charged groups of the polymer.

0.1

(\J

E ...__ ·.pigment ~ .... c (!)

E 01

0.0 a. (!) 01 Iii ..c u

- 0 . 1 2 3 4 5 8

Fig. 1. Titration curves of polyacrylic dioxide

• charge of polyacrylic acid

• charge of titanium dioxide

• charge of titanium dioxide

' charge of titanium dioxide

9

acid and

in 0,01 in 0,001 in

1340

0

-1 340 10

t ltanium

H KNO H KNO

M KNO 3 0,01 in 0,1 M KNO 3

3

OJ ...__

u "'§ u ro

u >. u ro >-0 Q.

(!) 01 Iii ..c u

21

1. The influence of the pH: The adsorption of the polymer is stimulated when charges on the TiO and on the PAA are of opposite sign whereas the ads orption is limited when2 both charges become negative . In figure 1 the charges of separate t i tanium dioxide and polyacrylic acid are plotted as a function of the pH. The charges are measured by comparing an acid/ base titration of the species with a titration of an electrolyte solution. The charge of polyacrylic acid varies from almost zero at pH 3 to about 90% of the theoretical maximum charge at pH 11 . The hydroxyl groups on the titanium dioxide surface can be either negatively charged at a high pH or positively charged at a low pH. At pH 5.7 the oxide surface is not charged (point of zero charge, PZC). As aspected from these considerations the amount adsorbed at a low pH is larger than at a higher pH (see figure 2) .

2. The influence of the electrolyte concentration : According to Lyklema (1987) the increase of indifferent electrolyte can either increase or decrease the amount adsorbed of the charged polymer . There are two opposing influences : First the mutual repulsion of the charges on the chain is decreased, so the polymer behaves at high salt concentrations as an uncharged polymer rather than as a charged polymer. Uncharged polymers adsorb in larger amounts compared to charged polymers, so the adsorption is increased. The second effect of the electrolyte concentration is the effect on the interaction between surface groups and negative carboxylic acid groups: the coloumbic attraction between positive and negative groups decreases with increasing electrolyte concentration and as a consequence the amount adsorbed is decreasing at higher salt concentrations . In our case the influence on the mutual repulsion of the carboxylic acid groups is the most important effect of the electrolyte concentration because the amount adsorbed is increasing with the salt concentration (see figure 3).

(\J

E ....... 9 "D (1J .0

0 (j) u (Q

+-' c ::J 0 E (Q

1.5e-03 ,--------------.....,

1.0e-03

I 5.0e-04

1

---· ,---------

O.Oe+OO --------o----+-----+---....J 0.000 1.200

equilibrium cone. (mol / 1

Fig. 2. Adsorption isotherms of polyacrylic acid on titanium dioxide, in 0,01 M KN0

3 solutions

• pH 6 . 5; l' pH 5. 3; • pH 4 . 2;

22 1.5e-03

(\J

E -· -..... -..9 ~--'0

l.Oe-03 0

Q) I .0 ,__ I

0 I (f) 0 0 '0

ro ....... S.Oe-0 4 0 c :J 0 E ro

o.oe ... oo 0 .000 1.200

e qui l ib r ium cone. (g/1)

Fig. 3 . The influence of the elec trolyte concentration on the adsorption of PAA, pH=5.3. The lines represent the same experiments as shown in more detail in fig . 2, f or comparison. • 10-1 H KNO

3 0

1000 r---------------------------------------------

10 0

10

0 .1 0.01

Fig . 4.

0

0 . 1

0

• 0

elec t r o ly te c o ne. (mo l/ 1)

10

Stability as a function of the electrolyte concen tration at daffe r ent polyacryli c ac id concentra tions at pH=6. 0 (g/m ) .

• 0; [j. 2 . 8 *10-5

;

Y 2 . 2 •10- 4;

• J . s•1o-4

;

4 . 9 *10- 4

s. 9•10- 4

3. Stability measurements: The stability of an oxide dispersion can be followed by measuring light-transmission as a function of time. From these measurements we can calculate a stability factor W, which is defined as: the coagulation rate of the dispersion divided by the coagulation rate in the absence of any kind of stabilization.

23

If the stability factor W is measured as a function of the electrolyte concentration we find for low polyacrylic acid concentrations a graph typical (Lyklema et al., 1987) for electrostatic stabilization: At electrolyte concentration above 0 . 15 M KNO the stability fact or indicates that at these concentrations there is no s{abilization at all . At lower electrolyte concentrations the stability is increasing (W higher) as a result of the increasing electrostatic repulsion. With increasing polyacrylic acid concentrations, stability factors significantly larger than 1 are obtained even at electrolyte concentrations of 0 . 4 M. But even in this polyacrylic acid concentration range, the log(W) versus log(c) graph turns upwards with decreasing c values (figure 4). Under these circumstances, the stability significantly surpasses the values found for electrostatic stabilization. This indicates that under these circumstances, both sterical and electrostatic stabilization occur simultaneously, and act synergistically. Almost the same results are obtained with a polyacrylic acid copolymer used in the paint industry to stabilize pigment dispersions for water based paints (figure 5) . The concentration mentioned is the initial concentration calculated per square meter of specific s urface of the oxide . In this experiment it is not possible to give an equilibrium concentration because the amount adsorbed is changing with the pH .

1000r--------------------------------------------,

100

10

0.1 0.01

Fig. 5

L

0.1

electrolyte cone. mol/1

Stability as a function of the electrolyte concentration at different concentrations SERVO FX 508 (g/m2

) at pH=6.0 . .. 0 · ! 3:2·10-4

;

<> 1 .2·10-4

;

• 4. 7.10-4.

24

4. Electrostatic stabilization: For the electrostatic stabiliza tion the zeta potential is a better parameter than the surface charge because the surface charge is by definition only the charge of the surface groups and does not include the charge of the adsorbed species. In our case it is possible that at a low pH the surface charge of the oxide is positive whereas the overall charge of the particle is negative as a consequence of the adsorption of the charged polyacrylic acid. The zeta potential is an overall parameter and is therefore directly related to the stability of the particle (Hornet al., 1990). In figure 6 the zeta potential is plotted as a function of the pH at different polyacrylic acid concentrations . The zeta potential is measured in the suspension used to measure the adsorption isotherms of figure 2. Because the equilibrium concentrations are measured, the zeta potent ial can in this case directly be compared with the amount adsorbed . Comparing these two measurements a striking difference is observed between the shape of the adsorption isotherm and the shape of the zeta potential vs . equilibrium concentration curve: the zeta potential reaches a constant value at low concentrations whereas the amount adsorbed is still increasing at higher concentrations. In order to explain these differences we calculated the total charge on the surface by adding together the surface charge and the charge of the adsorbed polymer. Because of electroneutrality this charge should be also charge in the diffuse l ayer surrounding the particles:

0 (J = -(J -(J

dlff TIO PAA 2

a0 then is the charge in the diffuse layer if the charges o~lffTiO and PAA would not change during adsorption.

2

> E

ro ro .... c 2 0 Q.

2 (J) N

20

0

- 20

-40 \. II. L-.

1--

- 60 0 .00

J.

~

0 .50

equll ibrrum cone. g/1

Fig . 6 Ze ta potential ve r sus equilibrium PAA concentration in 0,01 M KN0

3 solutions a t • pH=4. 2; T pH=S . 3; • pH=6.5.

25

0 . 10

0.00 ------~~------'----~----' 0.00 0.20 0.40

equrlrbnum cone. PA (g/1)

Fig. 7 Charges behind the electrokinetic slipping plane. pH=5.3; [KNO ] = 0.01 M.

• •

a0 calculated on the assumption of absence of dlff charge changes during adsorption .

a0 calculated from the zeta potential . dlff

We compared this calculated charge in the diffuse layer with the charge behind the electrokinetic slipping plane (calculated from the zeta potential). As expected we observe a large difference between the two calculated charges: a

0 is still increasing while the charge calculated from the zeta potenti~lffeaches a constant value (figure 7). The discrepancy between the two calculated charges is a consequence of the assumption that the charge of the polymer as well as the charge of the oxide does not change during the adsorption process . This is in fact not true. We can measure the change in charge caused by the adsorption by measuring the acid consumption after addition of the polyacrylic acid and keeping the pH constant (pH-stat experiment).

a dlff

-a -a +0' TI0

2 PAA pHstat

If we use the result of the pH-stat measurements in the calculations of the diffuse charge, the calculated charge is of the same magnitude as the charge calculated from the zeta potential (figure 8) . The conclusion of these measurements is that although the amount adsorbed is increasing at higher equilibrium polymer concentrations the net charge of the particle reaches a maximum value and is not changing any more. The additional amount of polymer is therefore effectively adsorbed as a neutral polymer. This can be effected either by adsorption of undissociated PAA, or by simultaneous adsorption of PAA anions and an equivalent amount of H+ ions . The latter alternative is the most likely one : a large amount of adsorbed PAA anions would lead to a large negative potential near the surface, which exerts a strong attraction on H+ ions.

26

(\J

E f'-

I 0

2)

>-.:=

..0 ro <])

E (jj a.

I< E Q ilJ Ol

l <J

0.2 ,------------------,

0.1

r 0.0 ----~---'----~----'

0 .0 0.2 0.4

equilibrium cone. PA {g/1)

Fig . 8. Charges behind the electrokinetic slipping plane. pH=S.3 ; [KNO )=0 . 01 M.

3.00

2.50

2.00 0.001

Fig . 9

• cr0

taking into account charge changes during dlff adsorption .

e cr0

calculated from the zeta potential dlff

0 .01 0.1

e lectrolyte cone. <moi/D Hydrodynamic permeability of a packed bed of titanium dioxide as a func tion of the electrolyte concentration pH=S . S, PAA: 0 . 5 g/1.

27

5. Sterical stabilization: The hydrodynamic layer thickness of an adsorbed polymer gives an indication of the extension of the loops and the tails of the polymer and is therefore an indication for the sterical stabilization of a dispersion . The hydrodynamic layer thickness can be obtained from measurements of a parameter which is dependent on the total volume of the solid fraction of the dispersion. With oxide particles the viscosity of the dispersion or the sedimentation velocity of the particles may be suitable measurements. But in our case the expected hydrodynamic layer thickness is small compared to the size of the oxide particles and the particles are not spherical. Therefore we measured the thickness of the adsorbed layer by measuring the hydrodynamic permeability of a column packed with titanium dioxide as a function of the electrolyte concentration (figure 9). The porous plug was previously flushed with 0.5 g/1 polyacrylic acid solution until the permeability became constant. The amount adsorbed resembles the amount adsorbed at an equilibrium concentration of 0.5 g/1 PAA. Using the Blake-Kozeny equation (Bird et al., 1960) we calculated a hydrodynamic layer thickness of 3 nm in 0 . 01 M KNO and at pH=6. This is a thin layer compared to layers of adsorbed unchar~ed polymers on oxides (Pandoe et al., 1987).

CONCLUSIONS

The electrostatic stabilization is enhanced by the adsorption of charged polyacrylic acid molecules on the oxide surface. But at rather low polymer concentrations the zeta potential reaches a constant value and the total charge of the particle is not changing anymore . As the amount adsorbed is still increasing the polymer is adsorbed as an uncharged molecule and is not increasing the electrostatic stabilization. The polymer molecules form a hydrodynamic layer on the oxide surface of about 3 nm at pH 6 and 0.01 M KNO . But this rather thin layer increases the stability of the dispersion sigfiificantly.

REFERENCES

Berube, Y.G . and de Bruijn, P . L. Adsorption at the Rutile-Solution Interface , 1. Thermodynamic and Experimental Study, J . Coll.Int. Sci. 27 (1968) 305 .

Bird, R. B., Stewart, W.E., Lightfoot, E.W. Transport Phenomena, J. Wiley & Sons, Inc. 1960, p. 199.

Horn, R. G. and Swith D.T. Measuring Surface forces to explore Surface Chemistry : Mica, Sapphire and Silica, J. Non-Crystalline Solids 120 (1990) 72-81.

Lyklema, J. and fleer, G.J . Electrical contributions to the effect of the electrolyte colloid stability, Colloid and Surfaces, 25 (1987) 357-368 .

Pandou, A.M. and Siffert B, Polyethylene Glycerol adsorption at the TiO H0

2 interface, Colloids and Surfaces, 24 (1987) 159-172. 2

Overbeek, J.Th.G. in: H.R. Kruyt (ed. ), Colloid Science I, p. 320, Elsevier Publ. Co. 1952.

28

EFFECT OF PAA ADSORPTION ON STABILITY AND RHEOLOGY OF Ti02 DISPERSIONS

H. STRAUSS, H. HEEGN and I. STRIENITZ

Forschungsinstitut fUr Aufbereitung Abteilung Werkstoffe Chemnitzer StraOe 40

9200 Freiberg, Deutschland

ABSTRACT

The specific modification of the interfacial properties of finely dispersed TiOz-powders by adsorbing surface-active substances (polyacryl1c acid) causes a change of dispersity and flow behaviour of Ti0 2-suspensions. Without polyacrylic acid the pH value mainly determines the state of charge and, consequently, the granulometric and rheological properties of the system. Addition of a polyelectrolyte leads to a higher content of fine grains and a lower viscosity of high­concentrated Ti0 2-suspensions. It turned out that an effec­tive improvement of the properties of the solid suspensions investigated depends on definite amounts of polyacrylic acid and definite pH ranges as well.

KEYWORDS

T1D 2-suspension; interfacial properties; polyelectrolytes; adsorption; dispersity; flow behaviour

INTRODUCTION

For producing high-efficiency ceramics highly disperse sol­ids are mostly used. However, processing of these solids is getting more and more difficult with increasing dispersity. Interfacial properties and interaction of the particles with each other as well as with the surrounding medium are of great importance to the highly disperse state of solids. These processes can be of such a great weight that they become decisive to preparation of slurries.

Methodical modification of interfacial properties of such finely dispersed solids by adsorbing surface-active sub­stances is therefore very important to science and practice. At this surface properties such as wetting behaviour, adhe­sive forces, agglomeration etc. can be changed.

On the other hand it is also possible that the adsorption layer itself has a decisive effect on the properties, for

29

30

instance on the stabilization of dispersions or on the flow behaviour (rheology) of concentrated dispersions.

The present work contributes to fundamental knowledge of the connection between the properties of highly disperse solids interacting with selected organic additives and those of ceramic slicks. Furthermore, the results obtained provide the necessary basis for the intended application of works in the field of high-temperature solid state reactions. In this way improved production methods and a better quality, espe­cially that of ceramic materials, can be obtained.

EXPERIMENTAL

Materials

Ti0 2 was the model substance selected for the investiga­tions. It is a very fine powder Cx 50 0.2 ~m) with a specific surface (BET) of 6.7 m2 /g ana a density of 4.26 g/cm 3

•

Polyacrylic acid (Scopacryl LW 301, BUNA AG) was used as surface-active reagent.

This product is a solution of polyacrylic acid (PAA) in water (dry residue = 50 %). The mean molecular weight is 10.000 g/mol corresponding to about 140 functional groups.

Methods

For the investigation of adsorption isotherms, 20 g of Ti0 2 were added to 50 ml of H20 , the pH value was adjusted and then a definite amount of polymer solution of the same pH value was added during agitation. Agitation was continued under constant conditions (for an hour) up to the adjustment of equilibrium. After decanting the supernatant solution centrifugation was carried out. The content of PAA not adsorbed was determined by acid-base titration under con­stant conditions (constant pH difference and calibration).

Zeta potential measurements to get information on the state of charge at the solid-liquid interface were carried out by means of a microelectrophoresis device (ZETASIZER 3, Malvern Instruments). Strongly diluted solid-PAA-suspensions (in 10 -3 M KNO 3) were used.

To characterize the state of dispersion achieved under dif­ferent conditions the particle-size distribution was meas­ured by means of a sedimentation centrifuge of the type SA-CP 3 (Shimadzu). A well defined sample preparation was succeeded by using dilute Ti02-PAA-suspensions which were agitated up to the adjustment of equilibrium. Each suspen­sion was subjected to an ultrasonic treatment (1 min, 100 W) immediately before measurement. A sample dispersed with

CALGON (sodium hexametaphosphate) under the same conditions was used as reference standard.

Rheological measurements were carried out by means of the rotational viscosimeter Rheotest 2 (MLS PrUfgeratewerk Medingen) with the cylindrical measuring system KS 1 at a temperature of 20 • C. The required sample amount of 25 ml was filled into the cylindrical measuring system and, fi[st of all, thermostated for 10 min at low shear rate of 3 ~. Then, the shear rate was gradually increased at first and afterwards decreased again, where shearing stress was recorded every 30 s. This measuring cycle must be strictly observed because disper­sions show a non-Newtonian behaviour with a flow behaviour dependent on the history of the system (energy input, time, temperature and others). For comparing

1discussions, viscosi­

ty at a shear gradient of 0 = 145.8 s- is taken usually.

RESULTS AND DISCUSSION

Surface Charges

If a disperse oxide is added to an aqueous medium equilib­rium reactions will occur which cause charges on the surface and the formation of the so-called electrochemical double layer at the solid/liquid interface. In highly dispersed systems, properties of this electrochemical double layer have an essential influence on the interaction of the parti­cles with each other (stability) as well as with the sur­rounding medium (e. g. adsorption) because of the increasing content of surface in relation to the volume. For oxides, in particular, the following reactions are predominant:

OH -S-O S-OH~==~

I. e., the surface hydroxyl groups are protonated (positive surface charges) or deprotonated (negative surface charges) in dependence on the pH value of the dispersion and the polarity of the bond. Therefore, the hydroxyl ions and the protons are characterized as potential decisive ions.

The determination of the surface charge of the Ti02 used as a function of the pH value is realized by measuring the zeta potential that can be determined by relatively simple means (Bernhardt, 1990; Jacobasch, 19BB; Sonntag, 1977). Figure 1 shows the results of the zeta potential measurements in the system Ti0 2/PAA.

It can be recognized that the presence of PAA decreases the electrophoretic mobility and the zeta potential resp. and shifts the point of zero charge (PZC) of the system to low pH values. This effect may be attributed to the electro­static interaction of the anionic polymer with the particle surface and occurs particularly within the acidic pH range.

31

32

Whereas the zeta potential curve for TiOz shows positive values in the range above the PZC and negative values below the PZC that is characteristic of oxides the zeta potential values are constant over a wide pH range in the presence of polyacrylic acid . Therefore, a direct connection between the adsorbed amount of PAA in dependence on the pH value of the system and the zeta potential cannot be stated.

.--,----~ 40 !, mV

'20

.~-----

- -- · ~

\ -- - --- ------ -

0

~ eTiOz

I--- - Ofi02/PAA 13,5-wt OJo)_ '\

~--20

-40

~ ......_____. -60

4 5

Fig. 1: Effect of the acid addition dispersions in

-- -

6 7 8 9 10 pH

pH value and the polyacrylic on the zeta potential of TiOz­

lo-3 rv1 KN03

That's why it has to be pointed out that even small amounts of the polymer cause a charge reversal of particles and that a further increase of the PAA concentration influences no longer the zeta potential values. Accordingly, a polymer molecule is able to compensate several TiO z surface charges.

If the state of charge saturation is reached the charge conditions of the system remain stable independent of possi­ble further adsorption processes. They are only determined by the electrical properties of the polyacrylic acid.

Adsorption Investigations

In aqueous systems the diss~ci~tion behaviour of polyelec­trolytes and, consequently, the total charge of the polymer are to be considered as pH dependent. At low pH values the

dissociated content of COOH-groups decreases, and so does the surface charge of the polymer, whereas the content of dissociated acid groups increases at high pH values.

If charged polymers are adsorbed on oxides the electrostatic interaction will represent the primary adsorption mechanism, i. e. polyelectrolytes should be adsorbed to a much higher extent in the case of carrying counterions to the solid ad­sorbent. Therefore, the interaction of solid and polymer and the resulting adsorption depend strongly on the nature of the dispersion medium.

Results of the adsorption investigations in the system Ti0 2 /PAA at different pH values are shown in fig. 2. The shape of the adsorption isotherms shows an increasing con­tent of adsorbed polymers up to a plateau with increasing initial concentration of PAA.

Relation between the adsorbed amount of PAA at the of the adsorption isotherms and the pH value of the is shown in fig. 3.

plateau system

According to the corresponding literature (Cesarano et al, l9B5, l9BB; Gebhardt and Fuerstenau, l9B3; Lopatin, 1961) it was found that below the pH value of the isoelectric point the plateau value decreases with increasing pH value. This result supports the assumption that electrostatic forces influence the adsorption process in the observed pH range essentially. At the isoelectric point of the oxide (pH 6.1) it can be expected that the effect of this interaction has become weak. Only small amounts of PAA are adsorbed as shown by the results obtained within the pH range of 6 - 7. At high pH values (pH B; pH 10), however, the plateau value increases again.

Because the oxide particles carry mainly negative surface charges at this pH range, it can be concluded that besides the electrostatic interaction other forces exist which pref­erably become effective in the alkaline medium and cause a different adsorption mechanism.

A computer program (Heegn, 1991) for the qualitative and quantitative evaluation of sorption processes in aqueous systems was created. Considering general thermodynamic reac­tion equations the surface of the solid is regarded as reaction component which is in a metastable equilibrium with the surrounding medium.

By introducing a dissociation degree of the surface of the solid depending on the pH value in relation to the specific surface and the solid mass, the solid component being effec­tive in the equilibrium can be calculated. In relation with the known pH values of the surface-active substance an actual description of sorption is possible.

The dependence of the sorption on the pH value which is shown in figure 3 was calculated theoretically by using the equation system presented.

33

34

1.------.------,-------,------,,-------, CADIZ mglm oa~---t~~~==~E;~

pH=8

2 4 6 8 cA I gil

Fig. 2: Adsorbed amount of PAA as a function of the initial concentration of PAA and the pH value

02

~

~ ( ------calculated values

\ I (

\ I a measured values

0,6

0,4

I

I PZC 2 4 6 8 10 12 pH

Fig. 3: Adsorbed amount of PAA (plateau value) as a function of the pH value

Properties of Dispersion

To characterize the dispersion state of the system inves­tigated the granulometric characteristics of the TiD2 suspensions were determined as a function of pH value and PAA addition. The results obtained are shown in table l. The given measuring data

Table 1: Particle size distribution in depen­dence upon the pH value and the PAA addition

system pH value

TiD 2 + CALGON

TiD 2 4

TiD 2 + PAA CPAA= 0,4 g/1

TiD 2 + PAA C PAA = 3 g/1

Ti02 + PAA C PAA = 5 g/1

6 8

10

4 6 8

10

4 6 8

10

4 6 8

10

passage in % at l J.l m

90

71 61 89 89

87 87 87 87

62 45 76 65

35 45 85 40

represent the particle size percentage below l J.lm.

Considering the results obtained by the zeta potential meas­urements it follows:

Without adding polyacrylic acid the well dispersed solid content (fine grains) of the system is a function of the pH value and of the state of charge of the oxide particle connected with it. That means that a considerably higher content of fine grains is found in the pH range below the PZC (pH 4) and above the PZC (pH 8; pH lD) than at the PZC, because of the existing positive and negative surface charges of Ti02 particles (and, in connection with it elec­trostatic repulsion and stabilization resp.).

35

36

Adding polyacrylic acid (CPAA = 0.3 g/1) causes a qualita­tive improvement of the granulometric result. Within the whole pH range no differences in the shape of the particle size distribution curves are observed.

If, however, the PAA concentration is increased the state of dispersion is getting worse and the differences within the pH range investigated are considerable. Consequently, an optimum dispersion can only be achieved by adding definite amounts of polymer, which have to be exactly determined for each system, and by adjusting definite pH ranges. An "over­dose" can have negative effects on the dispersion.

Generally, it can be said that a specific modification of the dispersion state of Ti02 - suspensions is possible . How­ever, a more comprehensive discussion of the problem intro­duced requires further investigations, e. g. on the stabili­zation of the system tested.

Rheological Investigations

The effect of polyelectrolytes on the flow behaviour of oxide dispersions is shown in Figure 4.

A suspension containing 60 wt % of solid content and 2.5 wt % of added PAA (related to the solid content) was investigated at a shear gradient of 0 = 145.8 s-1 The dependence on the pH value of the viscosity compared to the behaviour without adding PAA is shown in fig.4 . In the neutral pH range a considerable influence of PAA is noticed whereas at pH values of ~ 2 and ~ 10 only small differences of the viscosities are observed.

The viscosity of the suspension without PAA addition has an obvious maximum at pH values of 6 ... 7 . This is the range of the isoelectric point of Ti02(pHpz c = 6.1). Since Ti02 particles have not repulsive surface charges a skeletal structure can form within the suspension causing high visco­sities.Because of the positive surface charges, which have a dispersing effect, the viscosities in the acidic pH range are considerably smaller. Within the basic range the repul­sive effect of the surface charge of TiD 2 particles is not so strong, the viscosity compared to pHpzc is decreased only to the half, therefore.

Between pH 2 and pH 10 a strong decrease in viscosity occurs by addition of polyacrylic acid. At that low values of the acidic dispersion without polyelectrolytes were measured nearly up to pH 8 . These results of the rheological measure­ments correspond with the measurements of the zeta poten­tial. The viscosity in pH ranges with large potential is lower than at the isoelectric point. The added polyelectro­lytes cause a shift of the PZC of the system and also influ­ence the viscosity.

10 000 .----.------..,.-~I mPas

1000~--+-~~---+---~~~~~~--~

10 --- - ---+---+---1

2 4 6 8 10 12 pH

Fig. 4: Effect of the pH value and polyacrylic acid addition on the viscosity of Ti02 suspensions (60 wt %)

The effect caused by the polyelectrolytes cannot only be reduced to an effect of sorption because e. g., at the PZC of TiD 2no or a very low sorption was found. Nevertheless a strong influence on zeta potential and on rheology by PAA mentioned above was observed.This effect could be explained by the fact that the solid particles are coated by the polyelectrolyte molecules. This coating structure determines the behaviour of the whole system. The bonding of the solid particles, however, must be very weak because the amount of adsorbed PAA detected by the method of residual concentra­tion determination (centrifuge the solid off a solution) is very small. A marked sorption minimum was found in the range of pH PZC·

It is essential for the use of polyacrylic acid that consi­derably larger solid contents can be taken at comparable viscosities. The flow curves of Ti02-suspensions with solid contents of up to 80 wt % and PAA contents of 2.5 wt % (related to the solid content) compared with a suspension with 60 wt % of solid content without PAA are shown in fig. 5. Investigations on the influence of the reagent concentra ­tion at 80 % solid content showed that the amount of reagent could be reduced down to 0.5 wt % without essentially effect on the flow behaviour. Below this limit, however, the viscosity strongly increases such that a further processing is not possible.

37

38

10000~---------.----------.----------.

v mPos --t---------'----j

60% only Ti02

--t--======t====75% 100 f-------

500 1000 1500

Fig. 5: Influence of the shear rate, the solid concentration ( wt %) of Ti0 2 and the addition of PAA ( 2.5 wt %) on the viscosity

RE FERENCES

Be rnhardt, C. (1990). Granulometrie: Klassi e r- und Sedimen­tationsmethoden. Dtsch. Verl. f. Grundstoffindustrie, Leip­zig. Cesarano, J. and I. A. Aksay (19B5). Interaction between polyelectrolytes and oxides in aqueous suspensions. Surface and colloid science in computer technology, symp. Po t sdam, 73 - 86 Cesarano, J., I. A. Aksay and A. Bleier (19BB). Stability of aqueous ~-A1 2 0 3- s uspension s with polymethacrylic acid . ~ Am. Ceram. Soc . , 7la 250 - 255. Gebhardt, J. E. a n D. W. Fuerstenau, ( 1983). Adsorption of polyacrylic acid at oxide / water interfaces . Colloids and Surfaces, 7, 221 - 231. Heegn, H. (1991) . unpublished results. Jacobasch, H. J . (1 988). Characterization of polymer sur­faces by means of electrokinetic measurements. Progr. Colloid & Polymer Sc., 77, 40 - 48. Lopa tin, G. (1961). The adsorption of polymethacrylic acid fr om solution. Ph. D. Th es i s , Polytechnic Institute of Brooklin. Sonntag, H. (1977). Lehrbuch der Kolloidwissenschaften. Dtsch. Verl. d. Wissenschaften, Berlin

INTENSIFICATION Ol.i' SUSPENSION l.i'LOCCULATION BY PARTIALLY HYDROPHOBIZATED POLYACRYLAJ.IIDE

V .N.KISLENKO, Ad.A.BERLIN and M.A.MOLDOVANOV

Department of General Chemistry, Polytechnieal Institute, Lvov, 290646, USSR

ABSTRACT

39

Influence of chemical modification of polYacrylamide by diffe­rent nature reagents onto sedimentation rate of production suspensions has been investigated. Mathematical model of floc­culation kinetics has been developed and equations, describing changing of particles quantity in the system and of particles quantity in aggregate according to time have been presented. Rate constants of floes formation have been found.

KEYWORDS

Modified po!yaorylamide,: flocculation kinetics; mathematical model.

CHEMICAL MODIP'ICATION Ol.i' POLYACRYLAMIDE

Use of polymer flocculants allows to intensifY the process of separation of systems solid - liquid. The most wide spread flocculent became po!yacrylamide (PAA), being accessible and possessing definite universal effect on different suspensions. Besides, while choosing floceulants for specific suspensions,

there appears the necessity of PAA efficiencY increase by ita directed chemical modification.

Influence of po!yacr,ylamide chemieal modification on the sepa­ration process of industrial suspensions of sulfur concentrate and floatation wastes of sulfur production (lime - sulfur sus-

40

pension) with polydisperse solid phase content 25o-300 and so­roo g/1 respectively, with the size of solid phase particles in the range of (0.4- 2.5)•ro-7 m with the prevalence of fine­disperse fraction, as well as of floatation tails of coal en­riching mill with solid phase content 65-85 g/1 and particles sizes (0.2 - 6)•ro-8 has been investigated in the present article. Sedimentation rate of flocculated suspensions has been defined by Dorr method on rectilinear section of sedimentation curve (error didn't exceed 8%).

Influence on polyacrylamide efficiency as flocculent of diffe­rent methode of chemical modification: varying of content in carbo:xyl groups of PAA, changing its hydrophilic-lipophilic balance (.by radical grafting of acrylatee and treatment bY non­radical reagents), as well as partial erose-linking of PAA mac­romolecules has been investigated. Increase of anion groupe content in PAA has been attained by two ways: radical acrylami­de copolymerization with acrylic acid and partial alkali ~dro­lyeie of commercial polyacrylamide. carboxYl groupe content was being varied up to I5% from the total number of functional groups. Testing of the received reagents during clearing of sulfur concentrate suspension has delivered that sedimentation rate of the solid phase hasn't been considerably changed as compared with the initial PAA. On the other hand, it may be expected that monomers grafting onto polyacrylamide will allow to increase the molecular mass of polymer, to ohange its func-­tional composition and hydrophilic--lipophilic balance depending on the nature of the monomer used and the reagents concentration. At grafting of water soluble monomers onto polYacrylamide, acry­lic acid for example, high viscous products, dissolving in water very well, are formed. But their efficiencY as flocculants apPeared to be somewhat lower, than that of the initial polyac­rylamide. Grafting of insoluble in water monomers, methyl acry­late (Korostyleva et al., 1975), in particular, leads to disper­sions formation, viscosity of which is somewhat lower than that of the initial PAA. At the same time, their efficiency as floc­culants doesn't reduce, and in some cases it even rises a little. At the same time, a considerable efficiency increase hasn't been observed, maybe, as a result of polYmer chaine destruction under the action of peroxide initiator, applied at graft polymeriza-

tion. That's why it was interesting to study the influence of

41

PAA molecular mass increase (by its partial cross-linking by nonradical reagents) and of hYdrophobization degree of po!yac­rylamide macromolecules on the efficiencY of polymer as a floc­culant • . Epichloro.b,ydrin and fonnald'ehyde as a cross-linking reagent, and epoxidated higher fatty acids and alkylamines with hydrocarbon radical CrG - c20 as a hydrophobizated agent have been used. Treatment of PAA by these reagents doesn't lead to its destruction.

Carried out investigation delivered that at sedimentation of flocculated lime-sulfUr suspension with high concentration of particles, polyacrylamide, modified by epoxid·ated higher fatty acids is more effective flocculant, and at sedimentation of floatation tails of coal enriching, PAA, modified by alkylami­nes and partially cross-linked by formaldehyde, are more effec­tive. This, to our opinion, is connected with changing of hydrophilic-lipophilic balance of the polYmer.

Fig.I illus.trates the influence of modification degree of com­mercial polyacrylamide on sedimentation rate of flocculated suspensions. As it is seen on it, such dependence is of extreme kind for polYacrylamide modified by thin cross-linking, as well as for bydrophobizated polyacrylamide. This is stipulated bY the fact, that at small degree of polYacrylamide modification bY epoxidated fatty acids or alkYlamines, favourable shifting of hydrophilic-lipophilic balance takes place, while its fUrther increasing brings to partial loss of solubility in water. Simi­lar picture is being watched in case of cross-linking of polY­acrylamide by epichlorohydrin and formaldehyde.

Curves of suspensions sedimentation rate change with the growth of floceulant expenditure are presented in fig.2. During floc­culation of floatation tails of coal enriching (curves I-3) and sulfUr concentrate (curves 4-6) flocculant expenditure is con­siderably higher, than at floatation waste sedimentation. The biggest sedimentation rate of sulfur concentrate suspension is being observed at flocculant expenditure of about I50 g/t. Further increase of flocculent dose may promote suspension stabilization, encumbering its separation, evidently, as a result of formation of protective po~er film around the par­

ticles of solid phase.

42

4 2.0

s.o './)

" ~ <'C 1.5 ~ ...,_

~

/.0 0 10 20 30

X,%

Pig. Io Influence of polYacrylamide modification degree by epoxidated higher fatty aoids (I), alk;ylamines ( 2), epy chloroeydrin (3) and fonnaldehyde (4) on sedimentation rate of floatation wastes of sulfUr production at floceulant expend! ture 60 g/t ( I, 3) and of floatation tails of coal enriching at flocculent expenditure 75 g/t (2,4).

At floatation waste suspension sedimentation, acceleration of suspension sedimentation is being watched firstlY for the in­vestigated floceulants at their relativelY amall dosage. PUr­ther increase of flocculant expend! ture does-n't practicallY influence the sedimentation rate of suspension.

Analogous curves have been observed during flocculation of other suspensions, as silver iodide sol (Baran et al., I980) or polystyrene latex ( Soloment~eva et al., I980) by poly(me­teylvinYlpyridine).

MATHEMATICAL MODEL OP PLOCCULATION KINETICS

Working out mathematical model, describing adequatelY kinetics

of flocculation, furthers studying its mecbaniam and control

43

6 3

VI 2S " ~ ~

'> • 2 ~

C) .., .

.... IS ~ ~ 1 ::.

s

0 {0() 200

Fig. 2. Dependence of sedimentation rate of floata­tion tails of coal enriching (I-3) and of flocculated sulfur concentrate (4-6) on flocculant expenditure: commercial polyac­rylamide (I, 4), PAA thin cross-linked by formaldehyde (2), PAA modified bY alkYlami­nes (3), PAA thin erose-linked bY epychloro­hydrin (5) and PAA modified by epoxidated higher fatty acids (6).

the process of suspension clearing.

Kinetics of flocculation process in general case may be des­cribed by the s.ystem of differential equations (Neesae at al., 1985), taking into consideration aggregates interaction with one another with different number of initial particles in them and with different fraction of surface covered by flocculant, floc break-up at Q1drodynamic action and adsorbtion of floccu­lant macromolecules by particles from: solution. Unfortunately,;, Solving of suoh a task is connected with serious difficulties, because of the absence of information about aggregates distri­bution according to sizes and fraction of surface covered by po!ymer, about kinetic constants values. That is why simpli­fied models with averaged values of above mentioned parameters are worth to be mentioned. For example, if it is assumed, that

44

equilibrium state at flocculant adsorbtion by particles is reached quickly enough, and floc break-up doesn't pl~ a consi­derable role, it is particles aggregation that must determine the rate of the whole process. In such a case, kinetics of flocculation in the initial period of time, when fraction e of particles surface covered by flocculent ma,y be considered con­stant, may be described by the equation (Healy at al., I964) 1

2 -d.N/dt = e(I - e)KN

Integration of the equation (I) under initial condition

(I)

( 2)

brings to the linear dependence of the average number of ini ti­al particles in aggregate on time. But it is possible to obser­ve. experimentally such linear dependence only in the ver.t first sections of kinetic curves (fig.), curve I; fig.4, curves I-5).

T/rne) ;,

0 0,4 0,8

2

It 4

~ 3 .3 N

~0

2 I 2

f

0 I 2 -r.

h '<me,

Fig. 3. Changing of the value N0

/N (I) and z (2) in time in the process of flocculation of sil­ver iodide sol by polY (methyl vinyl pyridine) with molecular mass 9.3·Io5 and concentrati­on 0.25 mg/1. Experimental data taken from (Baran at al.,. I980),: curve I is calculated according to the equation (I6)·

45

22 " 6 240

18 (60

>-/If

80

~ '-... 0 ~0 10

6

2

40 80 120

Pig. 4. Changing of the value N0/N (I-5) andY (6)

in time in the process of polystyrene latex flocculation by poly(meteylvinylpyridine): 0

0 = 0.09I (I), 0.9I (2), O·I8 (3), 0.68 (4),

0.36 (5). Experimental data taken from (Solomentseva at al., I980), ere marked by points. curves I-5 are calculated according to the equation (I5).

Further on, the process vividlY decelerates, and on the deep stages kinetic curves come out onto plateaus.

If floc break-up doesn't play a significant role, then the rea­son of such a state of affairs may be the changing of aggregate surface fraction, covered by flocculant in the course of the process. Really, at particles aggregation as a result of con­tact of covered-by-flocculent surface section of one particle with free-from-flocculent surface section of another particle, the fEaction of covered-by-flocculant surface of the formed aggregate must differ from that of initial particles. If it is assumed in the first approach, that every floc is formea bY the chain of initial particles, then its surface area may be found by the formula:

(3)

46

If in the initial particle or in already formed floc

e < I/2 (4)

then free !rom !locculant surface prevails in it, and in case

e > I/2 (5)

covered with !locculant surface is prevailing, area of which in both cases is marked as Fpr• Let introduce a concept of fracti­on of prevailing surface S, which under condition (5) is defin­ed by ratio:

s = e (6)

and under condition (4):

s = r- e (7)

For the goven floc

( 8)

Herewith

( 9)

From the expressions (3), (8), (9) it follows that prevailing surface fraction of the floc, compos~d of i particles:

( IO)

According to (IO) Si(i=I) = S0

that corresponds to the initial condition.

First, let's examine simple and obvious case of floc !ormation !rom two initial particles (i=2). Then from (IO) we shall get:

~ = (2S0 - c)/(2- 2c) (II)

Aggregates concentration, having formed in the system up to the

moment o~ time t and consisting o~ two initial particles, is determined by the expression:

(I2)

Herewith number o~ initial particles le~t in the volume unit o~ the system:

( I3)

Hence, average fraction o~ prevailing surface of particles of the system in the moment of timet:

( I4)

47

It is worth to be mentioned, that function (I) possesses the property of ~etry to the operation of substitution into it of the expresSions (6) or (7) under the condition (5), as well as under the condition (4). That's w~, for simpli~eation of succeeding considerations let us use the equation, received from (I) as a result of such substitution and the further transformation:

(I5)

Integrating the equation (I5) at substitution into it the exp­ression (I4) at the initial condition (2), the following equ­ation will be received:

N0

/N=( 2S0 -s2 ) /(S

0 ... s2 )+ (S

0-S2 ) -I{ ( I-S

0)-Iexp[-K(S2-S

0)N

0 t]-r}- I

( I6) As is seen from ~ig.3, concentration of particles in the system in section o~ coming out of kinetic curve onto plateau doesn't practicallY change. Expression ( I7), got from ( I6) at the con­dition t __. = corresponds to this section of curve:

ern

Average su~ace ~raction o~ particles, corresponding to contact segment may be found from the equation (II) and (I7):

48

Rate constant of floes formation may be defined by the equation got by transformation (I6):

(I9)

EvidentlY, suoh kinetic model must be fit for the description of processes, completing with the formation of stable floes by aggregation of two initial particles, for example, for the des~ cription of flocculation kinetics of silver iodide sol by poly­(methylvinylpyridine), because approximately twofold lowering of particles concentration is being observed as a result of it ( fig.3, curve I).

As is seen from fig.3 (curve 2), experimental data in the equ­ation (I9) coordinates lie down on the straight line with cor­relation coefficient 0.965 (which exceed the critical value 0.878 for significance level o.o5). BY tangent of slope angle of straight line value K = r.5·ro-I0 sm3/min, and by intercept on ordinates axis value S

0 = 0.94 have been found. The latter

agrees with experimental value s = o.aa (Baran at al., !980), 0

which testifies in favour of correctness of the suggested kine-tic model. Found rate constant value of floes formation allowed to calculate from the equation (I6) the dependence N

0/N on time

for flocculation process of silver iodide sol by poly(metnyl­vinylpyridine). Pig.3 illustrates the agreement of calculated curves with experimental data.

Examined mechanism of aggregates formation from two initial particles may be transferred onto the processes, concluded by floes formation, composed of arbitraXY number of particles. In

this case it is necessar.y to take into consideration that ex­

perimantally found number of initial particles in floc n=N0/N

is an averaged value. It may be assumed, that this discrete value has Poisson's distribution with parameter ). , herewith probabilities of its separate values may be defined (Muller~

al., I979) by a formula:

p{k, .A )=exp(- A) .J..k/k! {k=O,I,2, ••• ) (20)

In our case k=i~I . where i is number of particles in separate floccule, ). =n-I.

From the expressions (IO) and (20) average prevailing surface fraction of floc, composed of n particles may be defined by a formula:

s =L p(i-I; .A )Si i

( 2!)

As has been shown above, at deep stages of flocculation, its kinetic curves come out onto the plateau, where function (!5)

becomes equal to zero. This is possible under condition:

S- I (22)

The said allows to define with the help of computer the value c for the given kinetic curve, using average number n=N0 /N

49

in the section of coming out of the curve onto plateau and equalling the expression (2I) to I taking into account the co~ ditions (22): c = 0.37. Integrating the equation (I5) at the initial condition (2), the following dependence will be received

N0/N s s-I(!-S)-I d(N

0/N) = N

0Kt y (23)

I

Por experimentally found values n=N0

/N of the given kinetic curve of flocculation taking into account the above found value c by fonnulas (20), (2!) and (IO) it is possible to calculate the values S and accomplish with the help of computer numerical integration of the left part of the equation (23). This allows to determine rate constant value of floc formation K. As is seen from fig.4 (curve 6), experimental data of flocculation kinetics

of polystyrene latex by poly(methylvinYlpyridine) in the equa­tion (23) coordinates lie down on the straight line, going through the beginning of coordinates. calculated correlation coefficient value 0.901 (which prevails ita critical value 0.56I for significance level O·OI) confirms this. B1 tangent of

Slope angle of straight line value K=5·6·ro-II am3 /min for the

50

investigated process of flocculation has been found. Found· rate constant value of floes formation allowed to determine by the equation (!5) the dependence N /Non time for flocculation of

0 polYstyrene latex at different values of the initial surface fraction of particles, covered by poly(metbYlvinylpyridine). Fig.4 (curves I-5) illustrates the agreement with experimental data of calculated in such a way kinetic curves, that corrobo­rates adequacY with experiment of the suggested model of floc­culation kinetics.

NOTATION

c average surface fraction of the particle corresponding to contact segment.

F0 contact segment area of the given particle with the nei~ bouring one in fioc to which joining of the third partic­le is impossible.

Pf surface area of the floc. F

0 surface area of initial particle.

Fpr prevailing surface of the particle. i the number of initial particles in the given floc. K rate constant of floes formation. n an averaged value of initial particles number in floc• N number of particles in the volume unit. Ni number of floes containing i initial particles. N

0 initial number of particles in the volume unit.

N average concentration of particles in section of coming out of kinetic curves onto plateau.

S fraction of prevailing surface of the particle. Si prevailing surface fraction of the floc containing i

initial particles. S0 prevailing surface fraction of the initial particle. t time 0 fraction of particle surface covered by floc~ant.

REFERENCES

Baran, A.A., Tusunbayev, I.K., Solomentseva, r.M., Deryagin, B.

V. and K.B.Musabekov (I980). Study of qydrophobic sols floc-

51

culation by water soluble polYmers with the stream ultramic­roscopy. colloid J. (USSR), 42, II-I9·

Heaiy, Th. and v.K. La Mer (I964). The energetics of floccula­tion and redispersion by polymers. J. Coll. and Int. Sci., _TI, 323-332.

Koroatyleva, R.N. and S.I. Trakhtenberg (!975). Mathematical planning of experiment at investigation of methylacrylate graft copolYmerization onto polYacrylamide. J. Appl. Chem. (USSR), 48, 2759-276!.

Muller, P.H., Neumann, p. and R. Storm (I979). Tafeln der mathe­matiaohen Statiatik. VEB Fachbuchverlag, Leipzig.

Neesse, T., Ivanaakaa, A. and K· Muhle (I985). Ein phyaikalisch begrundeter Modellanaata !Ur die Stabilitat von Teilchenr aggregaten bei der Flockung. In: Freiberger Forsohungahefte, A, N 720, s. r-ro6.

Solomentseva, I.M., Tusunbayev, I.K., Baran, A.A. and KoB• Mu­sabekov (I980). Study of po!yatyrene latex flocculation by

cationic polyelectrolitea with the stream ultramicroscopy method. Ukr. Chim. J. (USSR), 46, 928-933 •

52

RHEOLOGICAL PROPERTIES OF SILICA SUSPENSIONS IN AQUEOUS CELLULOSE DERIVATIVES SOLUTIONS

M. KAWAGUCHI and Y. RYO

53

Department Engineering, 514 JAPAN

of Chemistry Mie University,

for Materials, Faculty of 1515 Kamihama-cho, Tsu Mie

ABSTRACT

The rheology of the silica suspensions in aqueous solutions of hydroxypropylmethylcellulose (HPMC) was investigated as a function of sili c a content, HPMC concentration, and HPMC molecular we i ght. Most silica suspensions showed rheopexy behavior after the silica suspensions were subjected to the highest shear rute. Only the low molecular weight HPMC gave silica suspensions with low silica content characterized by Newtonian flow. For most silica suspensions there wer~ some frequency ranges where the G" value exceeds the G' value. On the other hand, for the silica susp~nsions with the highest silica contents in the solution of high molecular weight HPMC the G' values we re larger than the G" values in the entire frequency rauge.

KEYWORDS

Rheology; silica suspension; HPMC; shear stress; shear rate; storage modulus; loss modulus.

INTRODUCTION

Fumed silica such as Aerosil is well-characterized and widely used as an adsorbent for polymer adsorption experiments (Kawaguchi,1990). When Aerosil silica is mixed with water the resulting silica slurry is sedimented due to silica aggregation (Iler,1978). It is expected that mixing aqueous polymer solutions with the silica slurry yields a stable silica suspension reinforced by polymer adsorption. Then, the resulting silica suspension shows a well response to some rheological measurements such as steady state shear stress­shear rate measurement (relative large deformation) and oscillatory measurement (small deformation). Their rheological responses should strongly depend on the silica content, the adsorbed amounts of polymer chains, and the polymer's molecular weight.

54

Thus, an investigation of the rheological behavior of silica suspensions by changing the added amounts of silica as well as polymer and the molecular weight of polymer leads to understanding the stability of silica suspensions by adsorption of polymer chains. In this paper, the rheological properties, such as viscosity and storage and loss moduli of the silica suspensions in aqueous solutions of hydroxypropylmethylcellulose (HPMC) were studied as functions of concentrations of silica and HPMC samples having different molecular weights. The rheological measurements of the silica suspensions were carried out using a coaxial cylinder rheometer.

EXPERIMENTAL

Three HPMC samples were kindly supplied from Shin-Estu Chemical Co., Ltd. They were purified by precipitation of their aqueous solutions into acetone and freeze-dried from their aqueous solutions. The molecular weights of the samples were determined from the intrinsic viscosity

measurements in 0.1 N aqueous NaCl solution at 25.0 ±0.05 °C using an Ubbelohde viscometer (Kato et al., 1982). The molecular characteristics, such as molecular weight (Mw), degree of substitution (DS) of methyl group, and molar substitution ( MS) of hydroxypropyl group are summarized in Table 1.

Table 1. Molecular Characteristics of HPMC

Codes DS MS

65SH-50 107 1.8 0.15

65SH-400 321 1.8 0.15

65SH-50000 2670 1.8 0.15

The nonporous Aerosil 130 silica was used after being cleaned by the procedure described in a previous paper (Kawaguchi et al., 1980)

Silica slurry was prepared by dispersing the silica powder in water by mechanically shaking and ultrasonic irradiation. An aqueous HPMC solution with known concentration was added to the resulting silica slurry and the mixture, hereafter called as silica suspension was mixed well by mechanically shaking for 1-2 weeks and by further ultrasonic irradiation to obtain a homogeneous mixture. The amounts of added silicas and HPMC are expressed as weight percent in the final mixtures. To prevent the degradation of HPMC in aqueous solution by bacteria, a preservative, NaN 3 , is added to keep its concentration of ca. 0. 02 wt%. The media were solutions of

HPMC at concentrations of 0.5-2.5%. The silica contents in the silica suspensions were 2.5, 5.0, and 7.5%.

Steady state shear stress a- shear rate y (steady flow) measurements and oscillatory (dynamic) measurements were performed by using a coaxial cylinder geometry on a MR-3 Soliquid Meter (Rheology Co. Kyoto, Japan). The steady flow measurements were carried out in the shear rate range 0. 01-

148 s- 1 and the dynamic measurements were performed in the

frequency (w) range 0.031 to 12.4 s- 1 . The temperature of

the sample chamber was maintained at 27 ± 1°C. Stability of the silica suspension should be mainly governed by the adsorbed amount of HPMC. The silica suspensions which are not observed any flocculation over one week after preparation were subjected to the rheological measurements.

RESULTS AND DISCUSSION

All HPMC solutions used in the dispersed media show Newtonian flow, whereas most of the silica suspensions show non­Newtonian flow. After subjecting silica suspensions at the

highest shear rate 148 s- 1 to destroy their structures, the silica suspensions showed rheopexy behavior except for the silica suspensions in aqueous 65SH-50 solutions. Above the

shear rate = 20 s- 1 no silica suspension shows rheopexy. The steady flows of the 2. 5 and 5. 0% silica suspensions in aqueous 65SH-50 solutions strongly show a near-Newtonian behavior (Kawaguchi et al., 1991), in contrast the 7.5% silica suspension shows non-Newtonian flow and there is observed the yield stress in its flow curve. Such a non-Newtonian flow was observed for the 7.5% silica slurry, whereas the 2.5 and 5.0% silica slurry showed weak responses for the steady shear stress-shear rate measurements.

Figure 1 shows the shear rate dependence of the stresses at the steady flow for the 2.5, 5.0, and 7.5% silica suspensions in aqueous 2. 0% 65SH-400 solution. The log-log plot of a against Y for the 2.5% silica suspension can be almost fitted on the straight line with a slope of 0.8. In contrast, the 5.0 and 7.5% silica suspensions have the respective yield shear stress in their flow curves. The yield stress increases with an increase in the silica content. This means that the silica suspension at the higher silica content is more strongly aggregated, which is attributed to the gelation character of fumed silica suspended in water.

Above the yield shear stress the shear stresses for the respective silica suspension tend to increase with an increase in shear rate along with a straight line. Similar flow behavior was observed for other silica suspensions (Kawaguchi, et al. , 1991). As a result, the slope of the straight 1 ine is almost the same at the same silica content, irrespective of the HPMC concentration. Such a slope decreases with an increase in silica content. The higher HPMC concentration is, the higher the shear rate at which the stresses first deviate

55

56

from such a straight line is.

0 a.. ........

b

1d rE. orE~P

cPrPO cP0 o

cPcP ~ 0 0 [jil CIIJ oCJJ o OJ c:ncP oc:P

0 ~ ~ ••o •• 0

10 • 00 ... 0

• .... 0 ·-·· 0 • 00

ocP 1 0

0

0

0.2 10

2 10

1 1 10 10

2

r I sec-1

Fig. 1. Shear rate dependence of shear stresses for 2.5 ( 0), 5.0 ( •), and 7.5 (0 )% silica suspensions in 2.0% aqueous 65SH-50 solution.

From dynamic measurements of the storage ( G') and loss ( G") moduli, we can reduce a viscoelastic character for the silica suspensions. Since the Lissajous figures of the oscillations of outer and inner cylinders gave an elliptical shape for all silic a suspensions studied, we did not make any correction for the values of G' and G" obtained from the Markovitz (1952) equation. Both G' and G" values increase with an increase in HPMC concentration for the respective suspension. Figures 2, 3, an<.< 4 show typical frequency dependence of G' and G" values for the 2.5, 5.0, and 7.5% sil i ca suspensions in 2.0% aqueous 65SH-400 solutions, respectively.

cP ........

<.!)

<.!)

0 a... ........

~

<.!) ~ ~

<.!)

10 0 00

G' ocP 0 ••

.......... ~0~·--· o oo ooc:x>

oa::P o

G'' 0.2

-2 10 1d 1 10

{,() /sec

Fig. 2. Frequency dependence of G' and G" for a 2.5% silica suspension in 2.0% aqueous 65SH-400 solution.

0

10 ,.

oOJ

.-~~ G' ...... ~ocP ". oe:Po:P 1 ··(S:P

00

G" 0.2

-2 10 10

1 1 10

w I sec-1

Fig. 3. Frequency dependence of G' and G" for a 5.0% silica suspension in 2.0% aqueous 65SH-400 solution .

57

58

As seen from these figures, for the 2.5 and 5.0% silica suspensions there is a frequency where the G" value exceeds the G' value in the respective figure and such a interception between the G' and G" values means that the structure of silica suspension will be changed from viscoelastic solid-like to viscoelastic liquid-like matter with increasing frequency. In particular, for the 2.5% silica suspension the G' value is almost independent of the frequency, in contrast with the

G' value the G" value above w = 1.0 s-1 tend to increase with an increase with frequency along a straight line with the same slope as the plot of a against y . The 5. 0% silica suspension shows a more marked frequency dependence of both G' and G" than that for the 2.5% silica suspension. The frequency where the interception between the G' and G" values for the 5. 0% silica suspension is higher than that for the 2.5% silica suspension. This difference is contributed to the higher elasticity of the 5.0% silica suspension.

0 a...

'

2 10

10

Fig. 4. Frequency dependence of G' and G" for a 7.5% silica suspension in 2.0% aqueous 65SH-400 solution.

On the other hand, for the 7.5% silica suspensions the G' value is larger than the G" value in the entire frequency range. This is indicative of a viscoelastic solid behavior with weak viscous properties. The same trend is observed for the 5.0% silica suspension in 1.0% aqueous 65SH-50000 solution.(not shown here)

Namely, such a behavior of the silica suspensions should substar; t.ially stem from the silica aggregated (flocculated)

59

structure and moreover, its structure is reinforced by adsorption of HPMC.

REFERENCES

Iler, R. (1978). The Chemistry of Silica; John Wiley & Sons : New York.

Kato, T, Tokuya, T. and Takahashi, A. (1982). Measurements of molecular weight and molecular weight distribution for water- soluble cellu~ose derivatives used in the film coating of tablets. Koubunshi Ronbunshu (in Japanese)., 39' 293-29.

Kawaguchi, M., Hayakawa, K. and Takahashi, A. ( 1980). Adsorption of polystyrene onto silica at the theta temperature. Polymer~., 11, 265-270.

Kawaguchi, M. (1990). Sequential polymer adsorption : competition and displacement process. Adv. Colloid Interface Sci., 32, 1-41.

Kawagu c hi, M., Ryo, T ., and Hada, T. (1991) Rheological properties of silica suspensions in aqueous cellulose derivatives solutions. 1. viscosity measurements.

Langmuir, in press. Markovitz, H. (1952). A Property of bessel functions and its

application to the theory of two rheometers. ,L_ ~ Phys., 23, 1070-1077.

60

RECENT DEVELOPMENTS IN THE UNDERSTANDING OF FOAM GENERATION AND STABILITY

P R GARRETT

To be presented at the European Federation of Chemical Engineers/International Association of Colloid and Interface Scientists Conference on "The Preparation of Dispersions", 14th October 1991, Veldhoven, The Netherlands.

ABSTRACT

Foams are prepared by incorporating gas into a liquid which may be single or multi-phase. Incorporation of gas may for example be achieved by injection through orifices (sparging), nucleation of dissolved gas or direct entrainment. It is these processes which essentially determine both the initial bubble sizes and the initial state of the gas-liquid surfaces in a foam.

Bubble sizes at orifices are determined by surface tension and buoyancy at low flow rates and inertia at high flow rates (Ruff (1972)). However foam generation by entrainment (an Oakes foam generator for example) usually involves turbulent conditions where bubble break up and coalescence can occur. Using arguments based on Kolmogoroff's treatment of turbulence expressions have been derived (Thomas (1981)) which yield rough estimates of the size of the largest bubbles stable against break-up and the smallest bubbles stable against coalescence as a function of surface tension and agitation conditions. Some comparison with experiments can be made.

During gas incorporation surfaces may be formed at rates which can exceed the rate at which any surface active species present can adsorb so that they may markedly differ in surface tension and composition from equilibrium. The extent to which those surfaces differ from equilibrium will in turn influence the initial stability of foam films formed as two such surfaces approach in a foam. Malysa et al (1991) argue that this factor is of importance in determining the foamability of dilute aqueous solutions of carboxylic acids. Here the foam films are unstable and rupture at thicknesses > 100 nm where disjoining effects are supposed unimportant. Foamability is, however, shown to correlate with estimates of the effective dialational modulus d0/dlnA of the non-equilibrium surfaces existing at the top of the foam column. Poor surface transport rates mean low levels of adsorption, low values of the effective dilational modulus and low foamability. However, by contrast rapid transport to air-water surfaces during foam generation is not always claimed to enhance foam stability. Thus for example Varadaraj et al (1990) and Abe and Matsumura (1983) compare dynamic surface tensions with foam stability to purportedly demonstrate that foam stability is diminished if transport to gas/fluid surface is rapid so that maintenance of stabilising surface tension gradients (see Gibbs (1876) and Lucassen (1981) is diminished.

61

62

Formation of a foam may be inhibited not only by intrinsically unstable freshly formed foam film but also by the presence of finely divided hydrophobic antifoam in those films. Comparatively few papers have appeared in the literature during the past decade or so concerning the mode of action of such materials. The role of contact angle and particle geometry on the antifoam effect of hydrophobic particles has been the subject of a number of papers (Garrett (1979), Dippenaer (1982), Aronson (1986), Fry and Berg (1989). New explanations for the antifoam synergy found with mixtures of oils and particles have also appeared (Fry and Berg (1989) for example) .

Once the gas phase volume ~c of - 0.72 in the case of polydisperse gas bubbles or 0.74 in the case of monodisperse gas bubbles then distortion of bubbles occurs so that planar films and plateau borders form. As ~ --> 1 then the foam consists of polyhedra. Only the so called Kelvin minimal tetrakaidecahedron will tessalate in the case of a monodisperse system to satisfy the Plateau conditions of foam geometry (Princen and Levenson (1987)). Real foams in practical situations are, however, usually polydisperse and Kelvin Tetrakaidecahedra are rarely if ever observed.

When ~ > ~c the pressure inside the foam is reduced so that there is an osmotic pressure driving continuous phase into the foam to push the bubbles apart and reduce the gas-liquid surface area . Under certain circumstances of foam generation the osmotic pressure is compensated by the hydrostatic head so that there is a progressive increase in ~with foam height. Princen (1990) has analysed which drainage occurs where the osmotic pressure is not sufficiently high to match the hydrostatic head. The analysis is interestingly extended to account for the shape of the confining vessel.

n general foam changes with time not only because of drainage but also because of bubble disproportionation and film rupture. various attempts have been made to model these processes in a foam. Examples include that of Barber and Hartland (1975) where film drainage due to Plateau border suction and gravity drainage down those borders in a monodisperse foam consisting of dodecahedral bubbles is modelled. Foam film collapse is assumed to occur when films reach a certain critical thickness. All films are supposed to have the same thickness at a given height in the foam. Since the film thickness monotonically declines with increasing height film rupture will only occur at the top of the foam column. Steiner et al (1977) in a more elaborate model relaxed this assumption by allowing film rupture to occur at different film thicknesses. However, neither of these approaches accounts for either bubble disporportionation due to gas diffusion or polydispersity.

By contrast Lemlich (1978) has developed a theory for prediction of the effect of gas diffusion upon bubble size distribution in a foam where the effects of drainage and film collapse are ignored. Here the concentration of dissolved gas in the continuous phase is supposed everywhere the same and is shown to be in equilibrium at all times with bubbles of number mean radius by second and first moments. Bubbles larger than that radius grow in size and those smaller shrink in size and eventually disappear. Cheng and Lemlich (1985) claim some agreement between experiment and this theory in model experiments where the effects of film collpase and drainage are minimised by use of a stabilising liquid feed into the top of the foam column. The importance of the initial bubble size distribution in determining the rate of foam surface area reduction due to bubble disproportionation by diffusion has also been emphasised by Monsalve and Schechter (1984). These authors show that if two foams have the same initial surface are and 0 but different initial bubble size distributions then different rates of surface area decay will result.

The approach of Lemlich ignores any contribution to the process of diffusional disproportionation from changes in the gas-liquid surface tension due to the effect of surface area changes upon the dilational properties of the surface. Prins (1990) demonstrates that this effect can be important in experiments which single bubbles in beer where surface dilational viscosities are high enough to cause significant surface tension changes during gas diffusion so that the process is inhibited.

An ambitious model of foam behaviour is presented by Narsimhan and Ruckenstein (1986) which accounts for Plateau border and film drainage, film collapse at a critical thickness, polydispersity and diffusion. Gas-fluid surfaces are assumed to be mobile so that film drainage may be faster than that predicted using the Reynolds equation. This model seeks to predict surfactant enrichment in the foam. Unfortunately however Narsimahan and Ruckenstein do not give comparisons with experiment.

A feature of many of these models of foam behaviour is the use of the Reynolds equation to describe film thinning in polyhedral foam. Modifications to allow for flow at the gas/fluid surface are sometimes considered. These approaches all predict that film drainage times are proportional to the square of the radius R of the film. Recent work with isolated cylindrical foam films by Manev et al (1984J has, however, revealed drainage times proportional to R0 • • Sharma and Ruckenstein (1987) advance a hypothesis to explain this behaviour. Clearly models of foam behaviour based upon drainage to a critical thickness at a rate given by the Reynolds equation may have to be reconsidered in the light of these findings.

All of the processes of decay in a foam conspire to produce a reduction of gas/fluid surface area. This in turn produces an

63

64

increase in the over-pressure P if the foam is in a closed vessel. This follows from the equation of state for a foam where •

P = nRT - 2/3 aA ( 1)

Here A is the total gas/fluid surface area, a the surface tension and n the total number of moles of gas. This equation has recently been validated theoretically for certain special cases by Morrison and Ross (1983). An attempt to use this equation to measure the rate of decay of foam surface areas by monitoring P has been described by Nishioka and Ross (1981). However Lachaise et al. (1990) suggest that measurement of P to obtain information about surface area decay using equation (1) may be misleading. These authors argue that measurement of the intensity of light reflected from the surface of a foam may give such information more conveniently and reliably.

On the whole most of the developments in understanding foam during the past decade have concerned phenomenological approaches. They have however unfortunately not produced unequivocal identification of the key phenomenological properties. Significant progress linking for example the molecular structure of surfactants and the foam behaviour of their solutions is therefore lacking.

THE INFLUENCE OF SOLID PARTICLES ON CTAB FILMS

P.J.M . Baets and H.N.Stein

Department of Chemical Engineering, Eindhoven University of Technology, Post box 513, Eindhoven, The Netherlands.

ABSTRACT

In this paper, marginal regeneration in films drawn from CTAB (=cetyl­trimethyl ammoniumbromide) solutions in a frame will be discussed. The film thickness was measured as a function of time and height , using interference colours which were evaluated by a computer program, and a film thinning relation was derived for this type of films. The program used for calculating film thicknesses is briefly discussed.

Film thickness measurements were performed on polystyrene (PS) dispersions in CTAB solutions up to 25 vol% PS. The thinning velocity of the film was related to the viscosity of the dispers ion .

PS particles in the film ~uld be observed through their light scattering . The particles were present in a film from the bottom up to a height whe re the film had a certain thickness . This thickness could be correlated with the particle diameter and the contact angle of the PS particles with the CTAB film .

KEYWORDS

Free liquid films, measurements of film thickness, polystyrene latex, marginal regeneration, contact angle, foam film stability, vi scosity .

INTRODUCTION

Three phase systems are often used in industrial processes . In the flotation process for example, particles are separated from the liquid by creating foam in which the particles disperse preferably . The present investigation deals with the influe nce of so lid particles on foam.

Some partic les lower the surfactant concentration and therefore ac t as a destabilizer (P . M.Kruglyakov 1972).

Most investigations showed that hydrophobic particles have a desta­bilizing effect on foam (P.R. Garret 1979), whereas hydrophilic particles in general have a stabilizing effect (Hudales 1990b) . Fang-Qiong Tang et al. ( 1989 ) however found that small hydrophobi c

65

66

particles could also have a stabilizing effect ascribed to the reduction of Ostwald ripening in foam.

which was

The destabilizing effect of hydrophobic particles has been theore­tically discussed by G.C. Frye and J.C. Berg (1989) and was found to be due to promoting of film rupture . M. P. Aronson (1986) showed that hydrophobic (solid) particles stimulate rupture better than hydro­phobic droplets because of higher surface roughness. He also found that particles can be swept out of a microscopic foam film into thicker regions of the film. Dippenaar (1982) used high-speed cine­matography to study the behavior of large glass and silica particles (>160 ~m) in small films. His measurements showed that particles moved in thin films in order to have the right contact angle with the liquid .

In this work we used monodisperse PS particles (1900 nm, 1070 nm and 300 nm) in 20mmx15mm films drawn from CTAB (~cetyltrimethylammonium­

bromide) solutions. The place of the particles in the film is cor­related with the film thickness measured with a Fizeau interferometer. The influence of higher volume fractions of PS on the drainage rate is studied.

THEORY

A film of thickness d reflects in normal direction an amount of light I given by (Mysels 1959):

I=I sin2

(2rrnd/A) 0

(1)

In this equation n is the refractive index of the liquid film (1 . 33), and A is the wavelength of the light (546 nm) . The absolute val ue of the film thickness can be ca l culated at the top of the film as soon as a black film becomes visible . Equation (1) can be used for a l iquid film which is free of solid particles only, because in films contai­ning solid particles the scattering of light makes observation of interference fringes difficult.

We observed a particle borderline (above which there are no partic les in the film) as the films were draining. We will first show that this effect is not directly caused by gravity (the particles did not fall down), but indirectly.

The effect of gravity on the particle velocity in an infinite amount of liquid or gas can be calculated with equation 2 (a balance between gravity and viscous forces on a single particle) :

2 v ~ t,pg • _i_. ( ~ ) (2)

l) 18 2 The ve locity in wa t er and air according to this equation :

Air :l)~1.8xl0- 5 Pas, 6p~1000 kg/m3, g~9 . 81 m/ s 2

, d~2x10- 6m Water:~1 . 0x10- 3

Pas, 6~70 kg/m3

, g~9.81 m/s2, d~2x10- 6m

The Reynolds number (Air): p vd/ l) ~ 1. 2( kg/ m3

) x 1.3e-5 ~ 1.6e-5 Calculated velocities:Vatr~0.12 mm/s;Vwater~0.15 ~m/s , the Reynolds number is small enough, equation 2 can be applied .

We can conc lude from the fact that the part i cles would fall slower in air than they do in the foam film (measurements: 13.4 mm in 24 sec ),

that gravity indeed does play a minor role, and that there must be another reason for the separation of the particles from the liquid. This is the contact angle phenomenon.

EXPERIMENTAL METHODS

The Apparatus

A film was drawn in a vertical brass frame (see fig 1), which was held at a fixed position. The four legs of the frame formed four identical films.

67

all angles 120 degrees

' ..!--- -- - -------------- .......

20 mm

Fig.l. The brass frame in which the films were drawn

A fifth film in the middle of the former four mentioned, was a film with completely free Plateau-zones . The frame was positioned in a thermostatted tank in order to avoid evaporation of the liquid. The film could be observed from both the front side as well as the bac k side through two windows in the tank. From the front side the film was illuminated by a SO W s uper pressure mercury lamp (Osram HBO SO W) (see fig 2 ) . Through the front window, the interference pattern between light reflected from the front and back surfaces of the film was observed; through the back window, light scattering information was obtained .

68

Hg lamp Lens

F ilter

I

sem1 ref lec t1ng M irror

fronts1de

Frame

~ backs1de w 1ndow

Thermosta t ted tanl<

Fig.2. The Fizeau interferometer

We placed a light filter (SFK21 Schott, 546 nm) in the beam in order to separate the (green) light from the other wavelengths .

Film thickness measurements

The film was observed with a Panasonic CCTV camera through the semi-ref l ecting mirror (fig . 2), and the pictures were analyzed on-line with a computer . The program whi ch calculated the film thickness from the interference pattern was as follows . First we determined the exact position of a film in the pic ture and the magnification (mmlbyte). After forming a new film in the frame pictures (384.288 byte, 256 grey levels) were taken with a variable interval (0.5 sec t o 10 sec) . We masked every picture so that only film information was visible . We added al l bytes in horizontal direction and put the result in a word (16 bit information). It appeared that the value (so ca l culated) never exceeded the maximum value of a word. Thi s array of words was stor ed in a file and processed afterwards. The film thi ckness was determined by using equation (1) . All films were measured unt il the black or silver-black film was visible.

Light-scatter i ng measurements

The presence of the PS partic les could be easily detected by thei r

light scattering causing a hazy aspect of the film (see fig . 3).

Fig.3. the particle borderline and marginal regenaration a 10 vol% dispersion of PS (s ample 1, 1900 nm)

Therefore we measured the decrease of the height concerned in time . For these measurements we again crunched the pictures into an array of words. This array was processed afterwards in order to calculate the height of the particle borderline .

The preparation of the PS particles

We used for our experiments three PS samples. The preparation of the first sample is described below. The s econd and the third sample s were kindly donated by H.Leendertse, and B.Krutzer respectively. The second and third samples were prepared surfactant-free .

We used a recipe similar to the one described by Almog et al., (1986) . We used PVP, ACPA and CTAB>99% (the recipe gives also good mono­disperse particles if SDS is used instead of CTAB) . The PVP (poly­vinylpyrrolidone, average MW 40000) was used for steric stabilization, and the ACPA (4,4'-Azo- bis (4- cyanopentanoic ac id), >98%) is the initiator for the emulsion polymerization. The styrene (99%) was stabilized with 10-15 ppm p-tert-butyl-cathochol.

We prepared the particles in a batch reaction at 70°C in 1000 ml. ethanol . The PVP (40 gram in 150 ml ethanol) was added with the CTAB (12 gram in 50 ml ethanol). We mixed 2.8 gram of ACPA in 100 ml. ethanol and after s tirring (the ACPA did not dissolve completely), 300 ml of styrene was added to the ACPA. This was s tirred for 5 seconds

69

70

and added to the reactor . The emulsion was slight ly turbid after 10 minutes . The reaction stopped after 24 hours . The PS was centrifuged 4 times with water.

The characterization of the PS particles

The particle diameter was determined both with the Coulter counter 2M and with the Coulter LS 130 (see table 1). The ~-potential of the particles was determined with the Malvern ~-sizer 3 (see table 1) in a 0.002 M CTAB solution .

Table 1 . The particle size and ~-potential of the particles

Sample 1 diameter(j..im) stand.dev(j..im) ~-pot. (mV)

Coulter LS130 1.895 0.281 +15

Coulter Counter 2M 2 . 032 0.187

Sample 2 ~-pot. (mV)

Coulter LS130 0. 270 +64

Electron microscopy 0.300

Sample 3 ~-pot. (mV)

Coulter LS130 0 . 980 0.050 +72

Coulter Counter ZM 1 . 034 0.125

RESULTS

The film is essentially free from particles above a certain height. This is what we can see in fig . 3, a picture taken through the back side window. We can also see that marginal regeneration causes thin film elements, nea r the Plateau-border, whi ch rise in the film .

We will first compare the he ight a t whi ch the particle borde rline is visible to the he ight at which the film has the thi ckness of the particles for all the PS samples (see fig.4,5) . The volume fraction of PS in the bulk was lower than 0.5%.

14

12

~ 10

1. 8 f-I 0 6 w I

4

2

0 0 5 10 15 20

TIME [S ]

0 PS 1900 nm 0 19 00 nm fi lm

Fig.4. Drai'nage of hydrophobic polystyrene (sample 1)

0 JOOnm 0

PS JOOnm film

o 1070nm + PS

25

1070nm film

Fig.S . Drainage of hydrophilic polystyrene (samples 2 and 3)

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72

Both the 300 run as the 1070 run particles have almost the same diameter as the thickness of the film . The 1900 nm particles can be incorporated in a significantly smaller film. This indicates that the hairy stabilizer present at the 1900 nm particles, decreases the amount of CTAB at the surface. This is confirmed by (-potential measurements. The lower absolute value of the (-potential for sample 1 compared with samples 2 and 3 (table 1) indicates that the former has surfaces which are only partially covered by CTAB, whereas samples 2 and 3 have surfaces which are covered by a micellar layer of CTAB. Our results suggest that the smaller amount of CTAB adsorbed at the PS surfaces in the presence of polyvinylpyrolidone (sample 1) r esult in a hydrophobicity, and that this sample has a finite contact angle.

We checked the existence of the particle borderline for glass parti­cles 1.61 ~. s.d.=0 . 44 ~m. The film was after a whil e free of particles as far as detection by light scattering is concerned . The glass particles were not as monodisperse as the PS particles, there­fore a sharp particle borderline was not observed. This is to be distinguished from the microscopic measurements by Hudales (1990b), in which he observed glass particles which became visible after a while, when the film was much thinner already. The explanation for this might be that he looked at reflected light, while our measurements are based on through-falling scatte red light.

If the logarithm of the film thickness is plotted against the loga­rithm of time at a fixed height than a straight line results in agreement with measurements by Hudales (1990a) (see fig.6). Equation (1) in his pape r Q=kdn, where Q is the volume flow out of or into the film per unit length (in height) can be rewritten to :

d=Axtb (3)

here d represents the film thickness , t time, and A and b are con­stants .

We made double logarithmic plots for the glass dispersion (VOL% glass<0 . 5%), and for a 0 . 002 M CTAB film at two temperatures . Traces of glass did not have any effect on the film drainage, and the temperature increment increased the thinning velocity slightly .

Secondly we investigated whether the particle concentration has any effect on the film thickness at the particle borderline. Therefore we calculated for all films (volume fractions <0.5%, 11.1%, 17.4% and 25 . 0%) the film thickness at the particle borderline for a ll pictures . The average value and standa rd devia tion is given in t a ble 2. From this we can see that the particles can be incorporated into the film at a rather well defined thickness (1310 nm).

Table 2. The Film thickness at the particle borderline

Vol % PS Thickness average [nm]

Thickness s . d. [nm]

<0.5 1371 79 11. 1 1500 156 17.4 1384 127 25.0 1109 75 25.0 1201 210

Number of points

37 17 32 49 46

The influence of the particles on film thinning can be seen in fig.6, if the amount of PS (sample 1, 1900 nm) increases, the film thinning process becomes slower.

14

12

~ 10

~ 8 I-I ~ 6 w " I 6

4

2 ~ ~ ~" 0

0 10 20 30 40 50

TIME [SJ

0 <0.5 + 11. 0 17 .4 t:;

VV% PS VV% PS VV% PS

Fig.6. The drainage of the particle borderline as a function of vol% PS (sample 1, 1900 nm)

60

25.0 VV%

70

PS

The lines in the figure can be extrapolated to zero-height, and the corresponding time can be used as a measure for the film thinning velocity. We measured the viscosity of the dispersions with an Ostwald viscosimeter. The data fitted reasonably well with the Mooney equa­tion, with ~max=70 . 0 vol%. Although this is not a realisti c value for the constant ~max, we will use it for interpolation since it fits the

73

74

measurements satisfactorily. Table 3 gives the film thinning velocity in relation with the viscosity of the dispersion .

Table 3. Film thinning veloc ity as a function of the bulk viscosity

Vol % PS Total film Extrapolated Velocity VxT)IT)0

CTAB

Height [mm) Time [s) V[mm/s) [mm/s) [moll!)

<0.5 13.4 24 0.56 0.56 2.0e-3 11. 1 13.5 30 0 . 45 0.63 5.1e-3 17.4 13.0 42 0.31 0.55 5. 1e-3 25.0 12.5 65 0. 19 0.50 6.7e-3

DISCUSSION

In fig . 3 we can see an interesting phenomenon. The process of marginal regeneration has been made visible by means of the PS particles. Marginal regeneration creates thin film parts which rise in the film. These parts again are essentially free of PS particles. This implies that gravity is not the reason for the fact that the particles used can not be present in a film which is much thinner than the particle diameter itself .

The place of the partic le borderline (above whi ch there are no particles in the film), can be explained by the contact angle of the PS particles and the CTAB film with the measurements performed by Dippenaar (1982) . The film i s expected to thin until it has reached a slightly smaller thickness than the particle diameter (see fig 7). The particles will create a contact angle and fall dry for a part . The film continues thinning until it has no radi us of curvature near the particle. The particle will be pushed downward in a thicker region . In our case it is no t clear whether the last drawing of fig 7 will be reached in the thinning process, since the film is very large compared to the particle. The film therefore has no significant rad ius of curvature in all direct ions.

Fig . 7. a particle in a film , the drainage process of the particle in the film.

The hydrophilic particles (both 300 nm and 1070 nm) were pushed out of the film when the film reaches there own thickness . Hydrophobic particles could be present in a film which was thinner than the particle diameter. This can be explained by the larger contact angle of the hydrophobi c particles. The small particles act the same as large particles (>160 f.im) with which Dippenaar (1982) performed his experiments. The contact angle causes drainage, and this phenomenon appears to be strong enough to suppress Brownian motion of the 300 nm spheres . We found a simila r behaviour for glass particles (1-2f,lm) which did not have a di s tinct effect on the film thinning process of films from CTAB solutions unless they lower the CTAB concentration by adsorption. This however could not happen at the volume fractions used ( <0. 5%) . The hydrophilic glass particles were not monodisperse, and the particle borderline therefore was not very sharp.

In table 3 we find within experimental accuracy a linear correlation between the thinning veloc ity and the viscosity of the liquid, were

(4)

The result of the present investigation ind i cates that marginal regeneration is inversely proportional to the viscosity of the solution, since marginal regeneration is the major mechanism of film drainage.

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76

CONCLUSIONS

The actual thickness of the film at the particle borderline is determined by the hydrophobicity of the particles , this is in agree­ment with other investigations (Dippenaar 1982) . The particles do not flow down because of gravity directly .

The thinning rate from foam films of PS dispersions in CTAB (up to 25 vol% PS) is more or less linearly correlated with the viscosity. This suggests that marginal regeneration is also linearly correlated with the viscosity, because marginal regeneration is the major mechanism of film thinning in this type of films .

REFERENCES

Y.Almog, S.Reich, M.Levy (1982).Monodisperse Polymeric Spheres in The Micron Size Range by a Single Step Process. Brit . Polym. J., 11. No.4, 131-136

J.B.M. Hudales, H.N.Stein (1990a). Marginal regeneration of a Mobile Vertical Free Liquid Film. J.Colloid Interface Sci. 138 . No.2, 354-364

J.B.M. Hudales, H.N.Stein (1990b). The Influence of Solid Particles on Foam and Film Drainage. J.Colloid Interface Sci.140, No.2, 307-313

J.B.M. Hudales, H.N .Stein (1990c) . Profile of the Plateau Border in a Vertical Free Liquid Film. J.Colloid Interface Sci. 512, No.2, 512-526

A.Dippenaar (1982). The destabilization of froth by s olids.l.The Mechanism of film rupture. Int.J.Hiner . Process. 2. 1-14

G.C.Frye, J .C. Berg (1989). Antifoam Action by Solid Particles. J.Colloid Interface Sci.127, No.1, 222-238

Fang-Qiong Tang, Zheng Xiao, Ji-An Tang, Long Jiang (1989) . The effect of Si02 particles upon Stabilization of Foam . J.Colloid Int erface Sci. 1]1, No.2, 498-502

P . R. Garrett (1979) . The effect of Polytetrafluore thylene Partic les on the Foamability of Aqueous Surfactant Solutions. J.Colloid Interface Sci.69, No.1, 107-121

M.P.Aronson (1986). Influence of Hydrophobic Particles on the Foaming of Aqueous Surfac tant Solutions . Langmuir ~. 653-659

P. M.Kruglyakov, P . R.Taube (1972) . Syneresis and Stability of Foa ms containing a so lid phase. Colloid Journal of the USSR, 34, 194-196

K. J.Mysels (1959). Soap films studies of their thinning and a Biblio­graphy. Pergamon Press , London

PRINCIPLES OF EMULSION FORMATION

Pieter Walstra

Department of Food Science, Wageningen Agricultural University, Wageningen, the Netherlands

ABSTRACT

The phenomena occurring during emulsion formation are briefly reviewed. Droplet break-up in laminar and in turbulent flow is discussed and quantitative relations given. The roles of the surfactant are considered, i.e. lowering the interfacial tension (and thereby facilitating break-up) and preventing recoalescence (via the Gibbs-Marangoni effect), in relation to the time scales of the various processes occurring.

INTRODUCTION

This article concerns the formation of classical emulsions, thus not micro-emulsions, multiple emulsions or high-internal phase emulsions (HIPEs). This subject was reviewed earlier in some detail by the author (Walstra, 1983), from which we will take most informati on, without referring to literature listed there. Since this review was written - in 1978 - new results and considerations have become available, and some of these will be given here, in addition to briefly reviewing again the most salient points.

To make an emulsion, we need oil and water (or more general an oily and an aqeous phase), a surfactant and energy. The essential characteristics of the resulting emulsion are:

The emulsion type: oil-in-water or water-in-oil. This is primarily determined by the type of surfactant (see further on).

The droplet size distribution, since smaller droplets are nearly always more stable to creaming, coalescence and often also flocculation . It is easy to make droplets (gentle shaking suffices), but it may be difficult to make the droplets small enough. This means that the essential process is not droplet formation but droplet break-up. Moreover, newly formed droplets may coalesce again during emulsification, and this should be avoided as much as possible.

ENERGY RELATIONS

Why is energy needed? In order to break up a droplet it must first be deformed and this is opposed by the Laplace pressure,

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which is the difference in pressure between the convex and the concave side of a curved interface and is given by

( 1)

where y is the interfacial tension and R1 and R2 are the principal radii of curvature. For a spherical drop of radius r we thus have pL = 2 y I r and taking, for example r = 0.2 ~m (which is often desired) and y 0.01 N m·1 (which is a reasonable value), we have a Laplace pressure of 105 Pa ( 1 bar) . In order to deform the drop, a larger external stress has to be applied; this implies a very large pressure gradient, since the stress difference has to occur over a distance of the order of r. The stress can be due to a velocity gradient and then is a shear stress, or it can be due to a pressure difference arising from inertial effects (chaotic motion of the liquid).

To achieve the very high shearing stress or the very intense velocity fluctuations needed to deform and break up small droplets, very much energy has to be dissipated in the liquid . Assume that oil droplets with a radius of 1 ~m have to be formed in water and that the volume fraction of oil 4> = 0.1 a nd y = 0.01 N m·1

, we obtain a specific surface area A of 3 x 105 m· 1 and the net surface free energy needed to create that surface Ay = 3 kJ m~. In practice, we need about 3 MJ m~ to make the emulsion, which means that by far the greatest amount of the energy supplied is dissipated into heat.

It is seen from eq. (1) that the stress - and consequently the amount of energy - needed to deform and thereby break up the droplets is less if the inte rfacia l tension i s lowe r , which can be achieved by adding a sufficient amount of a sui table surfactant. This is one role of the surfactant , but not the most e s sential one, which is to pr event the i mmediate recoalescence of the newly formed drops. This will be discussed further on. We will first consider the break-up of drops. This can ·be achieved in laminar flow due to shear stresses, or in turbulent flow, where inertial effects (pressure fluctuations) are pre dominant, although shea r stresses may be of importance in some cases. For inertial effects due to cavitation, for instance caused by ultrasonic wave s, we r efer to our earlier revie w; since , some new literature has appeared (e . g. Li and Fogler, 1978; Reddy and Fogler, 1980) .

DROPLET BREAK-UP IN LAMINAR FLOW

The stress exerted 6n a drop in a laminar flow field equals TJcG , where G is the ve locity g r adie nt and Tlc the viscosity of the continuous phase . This stress is counteracted by the Laplace pressure and the r a tio is called the Weber number:

We = 'llc G r I y ( 2 )

Weer 10 .---------------------~~

8

6

0.01 0.1

Fig. 1 The critical Weber number for disruption of droplets in simple shear flow (curve, results by Grace, 1982) and for the resulting average droplet size in a colloid mill (hatched area, results by Ambruster, 1990) as a function of the viscosity ratio disperse to continuous phase.

If We exceeds a critical value Weer (of the order of one), the drop bursts. Weer depends on the type of flow and on the ratio of the drop viscosity to that of the continuous phase fl 0 /flc . Break-up of single droplets in simple shear flow (velocity gradient in the direction normal to that of the flow and thus equal to the shear rate) has been well studied and some results are shown as the curve in Fig. 1. These results agree well with theory. Others have often somewhat different results, Weer showing the same trend but being at a slightly lower or at a higher level; the explanation probably is that break-up of the drop also depends on the rate at which G is attained and on the time during which G lasts ( Torza et al. , 1972).

Eq. ( 2) shows that for a low viscosity of the continuous phase, deformation of small drops requires extremely high velocity gradients. For example, if y = 0. 005 N m-1 and flc = 10-3 Pa s (water), it would need G 25 · 106 s-1 to obtain droplets of r = 0.2 ~m (Weer ~ 1). Such velocity gradients can usually not be produced except over very small distances. It is also seen that no break-up occurs for flolflc > 4. The explanation is roughly that the drop cannot deform as fast as the simple shear flow induces deformation. Deformation time of a drop is proportional to its viscosity over the stress applied, that is fl 0 /flcG, whereas the deformation time according to the flow would be 1/G. If thus fl ol'llc > > 1, the drop does deform to some extent, but the deformed drop starts rotating at a rate of G/2. (For a low viscosity drop, the liquid in it rotates while the drop keeps its orientation with respect to the direction of flow; consequently, it can deform to a greater extent. ) The viscosity ratio above which no break-up occurs how ever large We, turns out to be 4, both from theory and experiment.

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In elongational flow (no shear, velocity gradient in the direction of the flow) no rotation is induced, and even very viscous drops can be deformed and broken up, if the velocity gradient lasts long enough; the latter may be a problem since in most situations elongational flow is a transient phenomenon. For the range of viscosity ratios given in Fig. 1, and for plane hyperbolic flow, Weer is almost constant at about 0.3. Thus, elongational flow is more efficient in breaking up drops, especially at a high viscosity ratio.

Up till fairly recently, the theory for droplet disruption in simple shear had only been tested for the deformation and burst of single drops. In practice, however, drops will be disrupted many times untill they have reached a critical size and conditions, i.e . Weer• will vary within the apparatus and during the process. Anyway, a spread in droplet size will result. The theory has now been tested in a colloid mill, made in such a way as to cause true simple shear; conditions as to composition of both phases and type and concentration of surfactant were varied widely ( Ambruster, 1990; Schubert and Ambruster, 1989). The average droplet size r 32 (being the third over the second moment of the frequency distribution of r) was determined and used for calculating Weer• Results are indicated in Fig. 1 and it is seen that a reasonable agreement with prediction was obtained . Break-up was observed at somewhat higher values of the viscosity ratio than 4, up to ~ 0/~c ; 10. This may have been due to some elongational component in the flow in the apparatus, but another explanation may be the presence of a surfactant. This allows the development of an interfacial tension gradient on the surface of a sheared drop. The latter causes the tangential stress to be not any more continuous a cross the droplet boundary (which is a prerequisite in the theories applied to drop disruption in laminar flow) and this hinders the development of flow of the liquid in the drop. This may, in turn, make deformation and thereby break-up easier. It would be useful to study this aspect in more detail.

Up till now, we have tacitly assumed that both liquids are Newtonian. If they are visco-elastic, the situation becomes much more complicated. If the disperse phase is visco-elastic, droplet break-up is in general more difficult, especially if the relaxation time is considerable. If the continous phase is visco-elastic, it becomes difficult to realize high elongational velocity gradients. These aspects have fairly recently been studied in some detail (Han and Funatso, 1978; Chin and Han, 1979, 1980).

DROPLET BREAK-UP IN TURBULENT FLOW

It will be clear from the previous section that laminar flow is mostly not sui table for breaking up drops suspended in water or another low viscosity liquid. Flow conditions have to be (intensely) turbulent. In turbulent flow (see e.g. Davies, 1972), the local flow velocity u varies in a chaotic way and

the fluctuations often are characterized by u', i.e. the root­mean-square average difference between u and the overall flow velocity. If the turbulence is isotropic (which is more or less the case if the Reynolds number is high and the length scale considered small), the flow can be characterized in a simple way, according to the Kolmogorov theory. There is a spectrum of eddy sizes, and the smaller they are the higher their velocity gradient (u'/x), untill it becomes so high that the eddies dissipate their kinetic energy into heat; the size of the smallest eddies x0 is called the Kolmogorov scale and droplets smaller than this are usually not greatly deformed. Somewhat larger eddies are called energy-bearing eddies and they are mainly responsible for droplet break-up. For these eddies we have

(3)

where x is eddy size (or distance over which u' is con­sidered), p is mass density and C a constant of the order of unity. The power density E (often called the energy density), i.e. the average amount of energy dissipated per unit time and unit volume, is the main parameter characterizing the turbulence. The eddies cause pressure fluctuations of the order of p{u' ( x) }2 and if these are larger than the Laplace pressure 4y /x of a neigbouring droplet of diameter x, the droplet may be broken up. This results in a largest diameter of droplets that can remain in the turbulent field of

(4)

The turbulent field is mostly not quite homogeneous and the resulting droplets will thus show a spread in size. Since in many cases the resulting droplet size distribution has a fairly constant shape for variable E, eq. ( 4) mostly holds also for an average droplet size (e.g. d32 ), albeit with a different constant. It is a very useful equation that has been shown to hold remarkably well for a wide range of conditions, provided that recoalescence of droplets is limited; see the earlier review, where also some additional conditions are discussed.

Some results are given in Fig. 2. It is seen that the stirrer is much less effective than the high pressure homogenizer (although the stirrer would have produced smaller droplets for the same energy consumption in a flow-through arrangement, presumably by a factor of about 5). This is because the homogenizer dissipates the energy in a much shorter time, thus causing E to be higher. The stirrer dissipates much energy at a level where it cannot break-up small droplets. Note that the stirrer and the ultrasonic transducer (which also produces pressure fluctuations) show the expected slope of -0.4, predicted by eq. ( 4): here power density is proportional to energy consumption. In the homogenizer the net energy consumption is given by the homogenizing pressure p, but here the power density is proportional to p 312 , since the time during which the energy is dissipated is inversely

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proportional to the liquid velocity through the homogenizing valve, which is, in turn, proportional to p11 2 • Consequently, the slope of log droplet size versus log energy input is -0.6, an additional reason why high-pressure homogenizers are very effective in producing very small droplets.

5 10 20 50 100

lOg x43 (~m) 20

10

5

05

2

-04 0 Homogenizer

05

-0.6 -05-'-------,-------,------'>..-----1

1.5 2 - log P ( MJ m-3)

Fig. 2 Average droplet diameter x 43 as a function of net energy input P (varied by varying intensity, not duration of treatment) for dilute paraffin oil­in-water emulsions produced in various machines. From Walstra, 1983.

Eq. (4) predicts that changing ~c does not result in a change in droplet size. This is indeed often roughly the case, but there are some exceptions, in that a slight dependency is observed, average droplet size mostly somewhat decreasing with increasing viscosity. Presumably, pressure fluctuations may not in all cases be the only cause for droplet break-up. On a droplet caught between eddies with a size > > droplet size, shear stresses will act and these may be sufficient for break­up; presumably, the type of flow is similar to plane hyperbolic flow. If this is the mechanism, the resulting relation is

( 5)

If the situation is in between true inertial and true viscous forces, viscosity may thus have some effect. Increasing viscosity also means decreasing Reynolds number, hence less intense turbulence, hence on average larger eddies, hence more

shear. This would also imply that the spread in conditions, hence the spread in droplet size, becomes larger for increasing viscosity, and this has indeed been observed (Walstra, 1974). Nevertheless, the effect of viscosity of the continuous phase on the resulting droplet size distribution is mostly slight.

If a soluble polymer is added to the continuous phase, this causes some increase in 'lc, but it also has the effect of turbulence depression; especially the smaller eddies are removed from the spectrum. This results in a larger avera ge droplet size (up to a factor 2) and a narrower droplet size distributi on. If a liquid contains many particles , they also depress turbulence, but the effect on emulsion formation has -to the a uthor's knowledge - not been studied. It may well be , however, that turbulence depression is o ne of the reasons why a high internal phase volume fraction causes larger droplets to be formed; nevertheless, other factors are probably more important (see the next section).

05

0

.o.s ll\o~.s----,o----,.5----::,o::---' l()g 'lg

Fig. 3 Effect of viscosity of disperse phase ( t) 0 , in mPa s) on average droplet size ( d 4 3 , in pm) for various machines (turbomixer, circles; ultrasonic generator, crosses; homogenizers, other symbols). From Walstra, 1974.

Eq. (4) also predicts no effect of the viscosity of the disperse phase on the resulting droplet size , and this is clearly not in agreement with experiments . Fig. 3 shows some results and it is seen that for constant E, log average droplet size versus log 'lc gave straight lines with a slope of 0.35 to 0.39. The viscosity effect has been discussed by Davies (1985). He added in the derivation of eq. (4 ) a viscous stress term = t] 0u' /d to the Laplace pressure 4y /d, where d = droplet diameter. This leads to

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84

(4a)

This equation does not agree with the constant and virtually parallel slopes in Fig . 3. Davies assumed the flow velocity in the droplet to be equal to the external u' and this may not be true anymore for ~ 0 >> ~c and it is certainly not the case in the presence of surfactant, which makes that the droplet surface can withstand a certain shearing stress. In other words, the viscous stress term to be added should not contain u' but the internal velocity u 1n. Because u 1nld equals the external stress over ~o and because this stress is at the prevailing conditions of the order of the Laplace pressure, the additional term is of the same form as the Laplace pressure and the result is merely a different constant in eq. ( 4), independent of ~0 •

In this connection, it is useful to consider the time needed for deformation of the droplet "d•" which may be defined as ~ 0 over the stress. The latter equals the external stress minus the Laplace pressure. We thus obtain

l:def " ~D I ( C E213 d 213 P113 - 4 Y I d) ( 6)

The constant C is unknown, but in order to obtain reasonable values for the resulting droplet size, we have taken it to be 5; some results are depicted in Fig. 4. It should be noticed that eq. ( 6) is different from the one given before: l:def

~0dly ( Walstra, 1983); the latter relation is based on the spontaneous relaxation of the droplet shape after it has been deformed, but this is not realistic. The dependence of the deformation time on d is according to eq. ( 6) even reversed: now the smaller the droplet becomes, the longer the deformatiom time. This is because according to the Kolmogorov theory - the size of a droplet disrupting eddy is roughly the same as that of the drop, and the pressure difference caused by an eddy increases with size. All these relations only hold within certain bounds and are not quite exact, but they serve to illustrate trends.

The life time of an eddy can be derived from eq . ( 3), which yields

(7)

Results are shown in Fig. 4, which gives several characteristic times throughout the emulsification process (ever decreasing droplet size); the finally resulting drop size according to eq. ( 4) would be about 0. 3 11m. It is seen that for a relatively low ~0 , the deformation time is mostly shorter than the life time of the eddies of the size of the droplet, whic h would imply that the pressure fluctuations last long enough for the droplets to be disrupted by these eddies. For higher droplet viscosities, this is not any more the case. This implies that larger eddies are r e sponsible for drople t break-up. Hence, for a larger droplet viscosity the resulting drops are on average larger and because of the greater

spread in flow conditions for larger eddies - show more spread in size. This has indeed been observed (Walstra, 1974). It would be useful to develop a more quantitative theory along these lines and, of course, test it.

droplet diameter ( f.Lm) 30 10 3 0.3

10 5 10 6

specific surface area ( m·1)

Fig. 4 Calculated characteristic times for deformation of droplets, adsorption of surfactant, duration of eddies and rate of droplet encounters, during the emulsification process (decreasing droplet size). Calculated from isotropic turbulence theory forE= 1012 W m·3

, TJc = 1 mPa s, TJ 0 = 0.1 or 10 Pa s, me = the erne (corresponding r = 2.5 pmol m· 2

, and y 5 mN m·1 ) or initially 2 mol m·3 (broken lines), y without surfactant 35 mN m·1

•

Surfactant is sodium dodecyl sulphate.

THE ROLE OF THE SURFACTANT

During emulsification three main processes occur: 1. Droplets are deformed and possibly broken up. 2. Surfactant is transported to and adsorbed onto the

deformed and the newly formed droplets. 3. Droplets encounter each other and possibly coalesce.

It should be realized that these processes occur simultaneously and also that they each occur numerous times during emulsion formation, which implies that a steady state is not necessarily reached. In other words, if emulsification would be continued, smaller droplets may possibly result. Of course, conditions change during emulsification and a fairly

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obvious change is that - due to the increasing droplet surface area - the concentration of surfactant in solution decreases.

The surfactant has two roles to play: it lowers interfacial tension, thereby facilitating droplet break-up; and it prevents (to a varying degree) recoalescence. Moreover, if surfactant concentration is high and the resulting interfacial tension very low, it may under some conditions cause "spontaneous emulsification" due to the strong interfacial tension gradients induced. Such a droplet break-up without putting in much mechanical energy is only of importance in the earlier stages of emulsion formation and has little to do with the final droplet size obtained, unless emulsification is achieved by simple shaking or when we come into the realm of microemulsions. These aspects will not be considered here.

Different surfactants lower y to a different degree and this should affect the final droplet size according to eq. ( 2) or eq.(4). For a surfactant giving a lowery less energy is thus needed to obtain a certain droplet size. As seen in Fig. 5, the predicted relations are indeed roughly obtained in turbulent flow, provided that there is an excess of surfactant. Similar relations have been found in a colloid mill (Ambruster, 1990). But there are some exceptions (e.g. Ambruster, 1990) and the course of the curves in Fig. 5. is not readily explained. Naturally, for a lower total surfactant concentration, the surface excess r (loosely speaking the concentration of surfactant in the interface) during break-up will be lower and correspondingly the effective y higher, but that does not explain the different shapes of the curves.

droplet surface area /~m- 1

15 "non -1oni( "

10

0.5

5 10 [ surfactant I / kg m-J

4

d..,!~m

Fig. 5 Effect of total surfactant concentration on the resulting average droplet size, other conditions being equal; $ = 0.2. Interfacial tension at high concentration for the non-ionic 2, caseinate 10 and the PVA' s 20 mN. m·2 , approximately. Approximate results from various sources.

l

2.

3.

Fig. 6 Diagram of the Gibbs-Marangoni effect acting on two aproaching droplets during emulsification. Surfactant molecules indicated by Y. See text.

There must therefore be differences in the degree of recoalescence. That recoalescence can occur, also in the case of polymer surfactants, has been shown in experiments where after emulsification the surfactant concentration is lowered and the emulsion is then again subjected to the same emulsifying treatment: the average droplet size is indeed observed to increase. Prevention of coalescence of newly formed drops is presumably due to the Gibbs-Marangoni effect. This is illustrated in Fig. 6. If two drops move towards each other (which happens very frequently) and if they still are insufficiently covered by surfactant, they will acquire more surfactant at their surface during their approach, but the amount of surfactant available for adsorption will be lowest where the film between the droplets is thinnest. This leads to an interfacial tension gradient, y being highest where the film is thinnest. The gradient causes the surface to move in the direction of the highest y or, in other words, surfactant moves in the interface towards the site of lowest surface excess. This gradient causes streaming of the liquid along the surface (the Marangoni effect), which thus will drive the droplets away from each other. Hence, a self stabilizing mechanism. Note that the mechanism only works if the surfactant is in the continuous phase . This must be the explanation of Bancroft's rule: when making an emulsion of oil, water and surfactant, the phase in which the surfactant is (best) soluble becomes the continuous one; and, in turn, the fact that Bancroft's rule is never violated (unless ~ is extreme) is a strong indication that the Gibbs-Marangoni effect is responsible for preventing recoalescence. Note also

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that the mechanism only works in a non-equilibrium situation: after the available surfactant molecules are evenly distributed over the droplet surface (as in a "finished" emulsion) it does no act. Then, the colloidal interaction forces primarily determine the coalescence stability.

Whether the Gibbs-Marangoni effect is strong enough depends on the Gibbs elasticity E of the film between the approaching droplets. E is defined as twice the surface dilational modulus ( E = 2 d y I d ln A, where A is surface area) and is given by (Lucassen, 1981)

E = 2 d y 1 d ln r ( 8) 1 + (h I 2) d me 1 d r

where h is film thickness. If E is high, the stabilizing mechanism works because now a strong interfacial tension gradient can develop -, if it is low it may be insufficient. A sample calculation for E as a function of the molar surfactant concentration in the continuous phase me is given in Fig. 7. It follows that E is higher if h is less and, for most situations, if me is higher. For most polymers, E is much lower than for small molecule surfactants. This is because for the same mass concentration the molar concentration of a polymer is much lower, which also implies that r (expressed in moles per unit surface area) is mostly low during emulsification, which, in turn, causes -dyld lnr to be almost zero. In fact, the values of -dy ld lnr obtained from experimental results will be too high, because these have been obtained at

40 sos. 6 = 1 fJ.ffi

---// ........... , f

I I I

20 ! I

-, ............ , _:_mixture"

-----

Fig. 7 Effect of concentration of sodium dodecyl sulphate in the liquid on the Gibbs e lasticity o f a film of 1 pm thick (after Lucassen , 1981). The broken line roughly indicates the relation for a mixture of surfactants. From Walstra, 1989.

equilibrium conditions. According to de Feijter and Benjamins (1982) the equation of state for surfactants in an interface is given by

y 0 - y "' r RT 1 ( 1 - 8 ) 2 ( 9)

where y0 is y for r = 0, RT has its usual meaning and 8 is the surface fraction covered by surfactant, e.g. given by nnr2 ,

where n is the number of molecules per unit surface area and r their radius. If a polymer molecule, say a protein, is adsorbed it commonly changes its conformation, thereby increasing the effective r, thus decreasing 9, thus decreasing y; the effect may be considerable (de Feij ter and Benj am ins, 1982). Consequently, the magnitude of the Gibbs elasticity, and thereby the extent to which recoalescence is prevented, will depend on the time scale of the rearrangement of the polymer molecule in the interface. This dependence will undoubtedly vary among polymers, but at present no experimental results seem to be available. In the author's opinion, this effect and the molecular weight of the polymer may be the main variables causing differences among polymer surfactants in the resulting average droplet size, if the polymer is present in a relatively low concentration. If its concentration is high, the "equilibrium" value of y will be determinant, and differences among polymers in resulting droplet size are indeed far smaller; see Fig. 5.

It is also useful to consider the time needed for the surfactant to reach the droplet surface , •act•· This not determined by diffusion; at the prevailing conditions of very high velocity gradients or very intense turbulence, transport towards the droplet is almost entirely determine d by convection (Levich, 1962). This implies, i n the aut hor ' s opinion, that experiments in which the decrease in surface tension at a macroscopic surface above a solution of the surfactant is measured as a function of time, are irrelevant to emulsification. That correlations are sometimes found between the rate of lowering y and the effectivity of the surfactant in producing small droplets, is presumably due to the fact that high molecular weight surfactants diffuse more slowly to the interface in the tests per formed, while t hey also give rise to a r e latively low Gibbs ela sticity under the conditions of emulsification. The actual situation may be more complicated because of the association of many surfactants in solution, especially the formation of micelles. It may be that in some cases the rate of dissociation of individual molecules from a micelle is rate determinant; on the other hand, it cannot be ruled out that micelles as such collide wi th the drople t, considering the str ong inertial forces in tur bulent flow. We will here only consider free molecules be ing trans ported by convection and we the n obtain approximately in laminar flow

(lOa)

and in turbulent flow

89

90

(lOb)

Some results are given in Fig. 4. It is seen that in turbulent flow, cads is definitely longer than cdef' the more so as the droplets become smaller and for a lower surfactant concentration. Similar relations hold for emulsification in laminar flow. Consequently, during droplet break-up r will be lower and c higher than their "equilibrium" values. This points to the Gibbs-Marangoni effect being essential and also to a situation in which break-up and coalescence go along for some time until the smallest droplet size is attained; even then, break-up and coalescence presumably go on, balancing each other.

Fig. 4 also gives some results for the average time elapsing before a droplet encounters another one, assuming them to be randomly oriented throughout the available volume. The relation is in isotropic turbulence

(11)

It is seen that for high <I> and small droplets, c e n c becomes (much) shorter than c ads. This certainly points to coalescence then becoming important. Some authors hold that break-up would be a first order rate process and coalescence second order, and that the change in the number of globules N would be given by dN/dt = K1N - K2N2

, but such a relation is usually not in agreement with experimental results. In the authors opinion, most of the recoalescence occurs with newly formed drops, that probably originate from one parent drop, and are thus close to each other anyway. In other words, c enc as shown in Fig. 4 is too long for these drops.

0.6 1.4 log ( p / MPa)

Fig. 8 Effect of homogenizing pressure (p) on the resulting average droplet size (d •• ) when varying the volume fraction of oil (indicated on the curves) and leaving the continuous phase (a protein solution) the same. From Walstra, 1988.

Nevertheless, at high volume fraction, recoalescence is probably more important. Fig. 8 gives some results from the author's laboratory (Walstra, 1988). Qualitatively, the higher average droplet size at a higher ~' and the relatively larger effect of ~ for a higher power density, are probably due to - the smaller amount of surfactant available per unit surface area created; this causes a higher effective y and a lower Gibbs elasticity (more coalescence); - the higher encounter frequency of droplets, particularly of droplets onto which yet little surfactant has adsorbed; this causes more frequent colaescence; - turbulence depression, causing droplet break-up to be less efficient.

CONCLUSION

The break-up of drops in laminar and turbulent flow is reasonably well understood, although quantitative explanation of the effect of the viscosity of the disperse phase in the case of turbulence would need further study. It appears as if droplet disruption due to cavitation (in an ultrasonic generator) is much like that in turbulent flow. To achieve a high efficiency it is necessary to dissipate the available mechanical energy in the shortest time possible.

The role of the surfactant is qualitatively understood, but quantitative relations are hardly available, especially for polymer surfactants, like proteins. The development of simulation models for adsorption of surfactant and for the phenomena occurring during a close approach of droplets, would be very useful. The role of the Gibbs elasticity needs further study, especially its dependence on time scale (of the order of microseconds) for different surfactants.

REFERENCES

Ambruster, H. (1990). Untersuchungen zum kontinuierlichen EmulgierprozeB in Kolloidmtihlen unter Bertick­sichtigung spezifischer Emulgatoreigenschaften und der Stromungsverh~ltnisse im Dispergierspalt. Ph.D dissertation, University of Karlsruhe.

Chin, H.B. and C.D. Han (1979). Studies on droplet deformation and breakup. I. Droplet deformation in extensional flow. J. Rheol. 23, 557-590.

Chin, H.B. and C.D. Han (1980). Sudies on droplet deformation and break-up. II. Breakup of a droplet in nonuniform shear flow. J. Rheol. 24, 1-37.

Davies, J.T. (1972). Turbulent Phenomena. Academic Press, New York.

Davies, J.T (1985). Drop sizes of emulsions related to turbulent energy dissipation rates. Chem. Eng. Sci. 40, 839-842.

de Feijter, J.A. and J. Benjamins (1982). Soft particle model of compact molecules at interfaces. J. Colloid Interface Sci. 90, 289-292.

91

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Grace, H.P. (1982). Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Chern. Eng. Commun. 14, 225-227.

Han, C.D. and K. Funatsu (1978). An experimental study of droplet deformation and breakup in pressure-driven flows through converging and uniform channels. J. Rheol. 22, 113-133.

Levich, V.G. (1962). Physicochemical Hydrodynamics. Prentice­Hall, Englewood Cliffs.

Li, M.H and H.S Fogler (1978). Accoustic emulsification. Part 2. Breakup of the large primary oil droplets in a water emulsion. J. Fluid Mech. 88, 513-528.

Lucassen, J. (198l).Dynamic properties of free liquid films and foams. In: Physical Chemistry of Surfactant Action (E.H. Lucassen-Reynders, Ed.), Dekker, New York, pp. 217-266.

Reddy, S.R. and H.S. Fogler (1980). Emulsion stability of acoustically formed emulsions. J. Phys. Chern. 84, 1570-1575.

Schubert, H. and H. Ambruster (1989). Prinzipien der Herstellung und Stabilitat von Emulsionen. Chem.­Ing.-Tech. 61, 701-711.

Torza, S., R.G. Cox and S.G. Mason (1972). Particle motions in sheared suspensions. XXVII. Transient and steady deformation and burst of liquid drops. J. Colloid Interf. Sci. 38, 395-411.

Walstra, P. (1974). Influence of rheological properties of both phases on droplet size of 0/W emulsions obtained by homogenization and similar processes. Dechema Monogr. 77, 87-94.

Walstra, P. (1983). Formation of Emulsions. In: Encyclopedia of Emulsion Technology. Vol.l Basic Theory (P. Becher, Ed.), Dekker, New York, pp. 57-127.

Walstra, P. (1988). The role of proteins in the stabilisation of emulsions. In: Gums and Stabilisers for the Food Industry 4. (G.O. Phillips et al., Eds. ), IRL Press, OKford, pp. 323-336.

Walstra, P. (1989). Principles of foam formation and stability. In: Foams: Physics, Chemistry and Structure (A.J. Wilson, Ed.), Springer, London, pp. 1-15.

MODEL EXPERIMENTS AND NUMERICAL SIMULATIONS ON EMULSIFICATION UNDER TURBULENT CONDITIONS

W.J. Tjaberinga, A. Boon, A.K. Chesters1.

Unilever Research Laboratory, Vlaardingen, The Netherlands.

1 Eindhoven University of Technology, Laboratory of Fluid Dynamics and Heat Transfer, Faculty of Applied Physics, Eindhoven, The Netherlands.

ABSTRACT

93

Numerical predictions of two phase (liquid-liquid) flow, including dispersed phase droplet break-up and coalescence under turbulent conditions, have been compared with emulsification experiments in a turbulent pipe mixer device at low volume fractions. This paper will give a short outlin·e of the theory, a description of the experimental techniques, an overview of the applied numerical techniques and the results of the comparison.

KEYWORDS

Emulsification; multiphase flow; break-up; coalescence; pipe mixer; jet mixer; tubulent.

INTRODUCTION

Previous practice for many aspects of engineering design and scale-up of dispersed systems has been based on empirical correlations or other 'lumped parameter' methods and not on the details of the local processes taking place. The validity and the reliability of the current methods are limited and it is time consuming and expensive to develop confidence from them for new process development. With the ever increasing speed of computers and the improvements of numerical flow solvers with respect to efficiency and effectiveness, the possibility of the complete prediction of flow in combination with various local processes is now coming within reach of every day engineering practice.

This paper concerns a verification study done as part of a BRITE project (Basic Research in Industrial Technologies for Europe, contract RIIB.OOSS.UK (H)) which had the aim to develop 3D computer codes for the fundamental design of process equipment, involving (non) Newtonian multiphase turbulent flow, based on:

- the development and experimental testing of non-Newtonian 3D multiphase turbulent now codes

- the development and experimental testing of effect codes which draw on the output of the flow codes in order to predict phenomena such as emulsification, chemical reaction, etc.

94

This paper deals with emulsification processes for which a pipe mixer device was chosen as a testing vehicle because of its simple geometry. The break-up and coalescence models concer surfactant-free systems without mass transfer. A full description of these models will be published shortly, the present paper providing only a short outl ine. Thereafter, the experimental set-up is described and results presented, followed by a first comparison with numerical predictions. The considerations are confined to pure systems, without mass transfer.

A SHORT OUTLINE OF THE THEORY

During emulsification processes, droplet break-up and coalescence are the most important phenomena determining the droplet size (distribution). For turbulent flows, there are two distinct regimes of interest for which break-up and coalescence relations have to be developed : that where the droplets are smaller than the energy dissipating Kolmogorov eddies in the turbulent field and that where the droplets are larger. As the Reynolds number related to the droplet size in the former situation is smaller than I, this regime is further referred to as the regime where viscous processes dominate while the latter, following the same reasoning, is the regime where the inertia dominated processes occur.

The major assumptions for the models are:

- no surfactant influences are taken into account -the droplets are assumed to follow the flow, consequently the density ratio must be about one. - there is no effect of the dispersed phase on the flow and tubulence into account and consequently the models are restricted to the low volume fraction regime, preferably lower than 1%.

For both regimes, the rate of break-up is determined by a criterion for break-up and a time scale. For coalescence the rate is determined by the number of collisions of two droplets per unit time and the probability that a collision will lead to coalescence. Although the rate of the processes is similar for both regimes, the mechanisms differ considerably.

Based on the assumption that the flow in a Kolmogorov eddy is viscous, relations developed for break-up and coalescence in viscous flow will apply. The break-up criterion in this regime is given by the capillary number: the ratio of viscous (disruptive) forces acting on the droplet, and stabilising interfacing tension forces . The capillary number at which a droplet will break-up is given by:

with d·,.-. the critical droplet size 11 the interfacial tension p., the viscosity of the continuous phase

( I)

i' the shear rate, which for turbulent flow is determined by the turbulent energy dissipation (f) according to:

(2)

with v the kinematic viscosity of the continuous phase.

The coefficientj(a,A) in equation (I) depends both on the amount of elongational flow inside a turbulent eddy (a=O corresponds to pure laminar flow and a= I to pure elongational flow) and). denotes the ratio of the viscosities of the dispersed and continuous phase. The coefficientj(a,A) can best be obtained from e.g. droplet break-up experiments as have been performed by Bently and Leal (1986) (see figure 1).

1.Qe+Q1 r--------------16 IIIP"'e=0.2 -o aiP"'e=0.4

t IIIP"'e=0.6

1.0e-01

1.0e-02 c___.~~'--~~.c_~~"'---~~..c_~~-'---~~....J

1e-04 1e-03 1e-02 1e-01 1e+OO 1e+01 1e+02

--> A

Fig. I. The cnhcal capillary number as a functton of the VISCOSity ratio for various values of the parameter a:.

95

The time scale for the break-up process is given by:

(3)

with g(A) a coefficient depending on the viscosity ratio. Tjaberinga and Boon (1991) have developed an empirical relation for g(A):

g(J..)=6.8J.. 0.35

which is also in good ~greement with observations by Grace (1982).

The coalescence rate is determined by two main factors. One factor is the droplet coli is ions rate C per unit time and unit volume. Saffman and Turner (1956) derived a relation for C for fine-scale turbulence neglecting hydrodynamic interaction. For droplets of equal size:

C=Klnw(~r (4)

with C is the collision rate and n the number of droplets, which can be expressed in terms of the volume fraction <P via:

and K1 is a constant given by (81!"115)' 12•

The other factor determining the coalescence rate is the probability that a collision will lead to a coalescence. An expression proposed in the literature for the coalescence probability P (Tavlarides and Stamatoudis (1981)) is:

(5)

with 1 the average contact time and T the time required for film drainage. Chesters (1991) has proposed an expression for tiT for the regime where the film drainage time is controlled by the drop viscosity. This model is adopted because of its applicability to many industrial turbulent liquid-liquid systems with a significant coalescence probability. The resulting expression for the probability is given by:

(6)

with K2 a constant of order unity, R the drop radius and h< the critical film rupture thickness. An expression for h< proposed by Chesters (1991) is based on the idea that the moment of rupture is determined by the balance of the Vander Waals 'disjoining' pressure II and the Laplace pressure (2o/R), which leads to:

96

(7)

with A the Hamaker constant for the liquid combination in question.

The other main regime of interest is the regime where the inertial effects dominate , that is the regime where the droplets are larger than the Kolmogorov eddies. In this regime, both break-up and coalescence mechanisms have their origin in the fact that the droplets are brought into rapid oscillation by the velocity fluctuations in the turbulent field. Droplet break-up in this regime is based on the assumption that break-up occurs when the oscillations reach the droplets resonance frequency (Savik and Park (1973)) . The break-up criterion for this regime is given by the droplet Weber number We, (the ratio of disruptive inertial forces and interfacial tension forces):

pu 2d; Wec=f(K,A) ~a c,br (8)

with u4 the velocity fluctuation over a distance comparable to the droplet diameter d;'·"': These velocity fluctuations can be expressed as a function of the turbulent energy dissipation (see Hinze, 1955):

(9)

Although the factor ] is lcnown to be dependent on the viscosity ratio (A) and density ratio (K) , investigations by for example Tsao and Hsu (1978) and Sleicher (1962) show only a little effect and indicated that a value of I for the factor f' is acceptable over a wide range of A and K values. At present the best guess for the critical Weber number is I .

The time scale for the break-up process can best be derived from the lowest mode free oscillation period of the drop, given by Lamb (1945):

(10)

with K1 an adjustable factor of order unity .

Although a model has been developed for coalescence in this regime, it has not been implemented because of the I imited range of applicability in the pipe mixer device.

THE EXPERIMENTAL SET-UP.

For the validation studies a pipe mixer device has been built. This pipe mixer device consists of a segmented plexiglas tube of I em internal diameter. In order to facilitate a large variety of flow conditions, the pipe inlet could readily be modified to allow (swirling) coaxial flows providing for flows varying from simple pipe flows to highly confined jet flows with recirculation. In the present studies, swirl has not been applied. The dispersed phase was injected upstream of the central inlet (see figure 3). The dispersion can be sampled locally with the use of a sample tube. This is a stainless steel tube with an inner diameter of 1.8 mm. This diameter is large enough to collect a representative sample, neglecting the effects which the edge of the tube has on the dispersion. It is also large enough to avoid break-up in the tube at the applied sample velocities. This sampling tube can be traversed radially at a given axial position. In order to avoid re-coalescence at higher volume fractions (:?: l %) in the tubing and measuring equipment after the sample tube, a small amount of surfactant (glycerol mono olaete in paraffin oil) can be added directly after the sampling tube.

The pipe-mixer was fed by two centrifugal pumps with a maximum flow capacity of 1.5 m3/hr each. The flow rate was monitored by two flowmeters. For the investigation under consideration, a 30 mPas paraffine oil was used as the continuous phase. This high viscosity is necessary to enter the viscosity dominated regime. In order to use the oil more then once (2*200 ltr was required for one experiment, 10 sampling points for each axial position), the dispersed phase (and consequently the contamination) was separated with a disk separator. The level of contamination after each separation was monitored by measuring the interfacial tension by the Wilhelmy plate method. The dispersed phase was double distilled water . In order to observe the effect of various viscosity ratios, the water phase was thickened with corn syrup . The flow rate of the dispersed phase was monitored by a small flow meter.

A modified Fraunhofer technique (see figure 3) was used for the determination of the total surface area of the dispersion. This quantity, in combination with a measure of the local volume fraction is enough to determine the Sauter mean droplet diameter, d,, according to:

(II)

97

11 Dispersion Inlet

.tl NoZZle l Af'Y'IUIUS

t~rd · ··:

=:f. Surfactant

r c::.:·::~ l

SA~E ANAL YSI$

Fig. 2. A schemallc picture of the ptpe m1xer device used in tllcse investigations .

with <P the volumefraction of dispersed phase, 6 the optical path of the emulsion sample, and (///0) the ratio of the observed I ight intensity in presence of the dispersed phase and the reference I ight intensity in the absence of the dispersion. A number of papers have been dedicated to the modified Fraunhofer technique, e.g. Lothian and Chapel (1951), Trice and Roger (1956), McLaughlin and Rushton (1973) and Lockett and Safekourdi (1977) .

Flow cell t

Reference s1tuat1on.

Parallel beams.

Fig. 3. A sehcmalically layoul of lhc modified Fraunhofcr sel.up.

The method is based on the scattering of light due to the presence of emulsion droplets in a parallel beam of light. As the to droplets are located in the focus of the second lens of the Fraunhofer setup, the (radially) scattered light will leave the lens as a parallel bundle. The undisturbed light will be focussed . By positioning a diaphragm in the focus of the second lens, all scattered light will be blocked and only the undisturbed light will be detected. This method will only be successful if the relative amount of

98

scattered light does not exceed 30%, a value which can be controlled by the sample thickness. The method proved to be very accurate when tested against reference dispersions.

The volume fraction of the dispersed water phase was determined of line. Both the determination of the interfacial area and the determination of the volume fraction gave a total error of d31 less than 7 %.

EXPERIMENTAL RESULTS

Two different types of experiments were undertaken. The first type concerned a confined jet flow, with a flow velocity of 15 rnls through a 3.5 mm diameter central inlet (the nozzle) and flow velocity of 2.5 mls through the coaxial inlet (the annulus). For one series of experiments, the volume fraction was

300 ,----------.---1 ~: ::::: ~ :-s::~ = \ ,5%/0.03

2 40 ~ · -& · ,

Cooo-ogtent~-

· ·0 5 .3 ffl!CtiO"l ! 1.5%l ~ i 180

~ a 120

60

0 0 . 1 100

--> Axtal pos1tlon /em}

Fig. 4. The measured the mean droplet SIZC d,, on the aXJs of the p1pe muer for a confined jet now.

varied at a constant viscosity ratio (0.03). For the other series, the viscosity ratio was varied by adding corn syrup to the waterphase, at a constant volumefraction dispersed phase (1.5%, see fig 4).

In fig . 4. a variation in the initial droplet size can be seen for the various experiments, which is due to the way the droplets are dispersed in the flow. The determined values of the mean droplet size are the results of multiple experiments which showed little variation ( < 10%) in the observed droplet size.

Both sets of experiments appear to be consistent with the models for break-up and coalescence. From the first set

of data, where the volume fraction is varied at a constant viscosity ratio, there is no coalescence for the lowest volume fraction, as may be expected. The coalescence increases with increasing volumefractions. In the other set of experiments, where the viscosity ratio is varied at a constant volumefraction, coalescence decreased with an increasing viscosity ratio (according to the viscosity controlled coalescence model) . Although there is a slight variation in the minimum droplet size one should be careful about drawing the conclusion that this is due to the dependence of the critical droplet size on the viscosity ratio (fig. 1.) since the most dominant break-up mechanism in the inlet region of the pipe, is the inertia dominated mechanism. The position in the pipe where break-up stops is in agreement with the point where rurbulence levels start decreasing for these flow conditions .

Because the inlet droplet size was difficult to control in the first serup, another type of experiment was carried out. In this case an orifice of an internal diameter of 4.6 mm was positioned in the pipe 8 em distance from the nozzle. The orifice made it possible to vary the droplet size of the dispersion upstream (by variation of the flow rate of the nozzle and annulus) of the segment while keeping identical flow

N ,.,

300

0 120

Contrac110fl - 200 miO'OO

70 m.O'Qf'l

10 100

--> Axial position /em/

Fig. 5. The measured droplet Sizes bchmd a eontrachon for vanous initial droplet sizes.

99

conditions downstream. These results are depicted in figure 5. The reproducibility of these results is better than 7%. From these results it is clear that the initial droplet size has almost no effect on the development of the droplet size after the contraction.

NUMERICAL PREDICTIONS

For the numerical predictions of the droplet size two different simulation packages were used. l11e first package is a flow simulation package DUCTFLO, which is capable of predicting flow and turbulence in cylindrical ducts. Turbulence levels (k) and turbulent energy dissipation (f) were predicted with a standard k-f model. The other package, DUCTREACT, is capable of predicting local mixing, chemical reactions and droplet sizes, based on the output produced by DUCTFLO for the similar problem. The droplet size predictions are obtained using the break-up and coalescence models mentioned before. Both the packages have been developed by ICI, Chemicals and Polymers Ltd (UK) and have been extended further (in particular to incorporate droplet size predictions) within the BRITE project.

The predicted droplet size can be represented in a number of ways. The development of the droplet size is most clearly shown by fig. 6, where the droplet size development after the contraction is plotted for

4 ]. 8 6

8 6· 17.2 0 1) 2- ]4 6

0 ]4 6· 69 5

0 69 5· 1]9. 5

0 1 ]9 j. 280.0

Fig. 6. The development of the droplet siZes behmd a contracllon for an imt1al droplet SlZC of 280 pm. The scale IS m microns.

an initial droplet size of 280 JLm. This plot shows clearly the break-up of the droplets and the coalescence after a few pipe diameters. Although these plots give a clear picture of the droplet size development, they are qualitative. The development of the droplets sizes is better represented by fig. 7, where the predicted values of the droplet sizes for a confined jet flow for an initial droplet size of 200 JLm (viscosity ratio 0.03 and volume fraction dispersed phase 1.5%) is depicted and compared with the experimental results. Fig. 7. shows that the general development of the droplet size is predicted reasonably well, although there is a quantitative discrepancy noticeable. A better comparison (both qualitatively and quantitatively) is obtained with the simulation of the droplet size development behind the contraction (see fig. 8.). Simulations of the other initial droplet sizes gave the same development, which is in agreement with the experiments.

DISCUSSION

In order to optimize agreement of the predicted droplet size and the experimental values, the initial estimates of the model constants were adapted. The result of a sensitivity analysis can be seen in fig. 8. in which the prediction on the basis of initially proposed constants is also depicted. Although the modification in the predictions appears to be rather drastic, the constants are only slightly modified. The only constants to be modified were:

100

- the critical shear rate 0, for a viscosity ratio 0.03: I ... 2

the time constant for viscosity dominated break-up : 6 .8 ... 34 - the ratio of film thinning time and droplet contact time was taken 10 times larger.

The first and second modification can be understood from the fact that a droplet will not be broken up during the life-time of one eddy, but needs to sheared by more than one eddy, in order to reach its final, critical deformation. Consequently the break­up time will be longer and the effective critical shear will be higher. The third modification is not

0.20

0 . 16

I 0 .12 •

N-nM o'

\Y 0.08 • •

- Sm"Uiat •on

• • 0.04 • 1\Aeasurements

0.00 L--~~-~-'--~~-~--'--~-~-...J

0 .001 0.0 1 0 . 1

--> Axial oos•llon lm )

Fig. 7. A comparison of the numerical predictions and experimental results for a confmc:<l jet now, with an inlet droplet size of 200 pm.

surprising bearing in mind the first-<Jrder character of the various mode! ling steps leading to the coli is ion frequency.

This set of constants has also been used for the simulation of the droplet size development in the confined jet situation. Here the agreement is not so striking. This is probably due to an overprediction of the turbulent energy dissipation levels by the DUCTFLO program. Consequently break-up will be overpredicted and coalescence will be underpredicted. More evidence about turbulence levels in the

1.00 ,--·------------ - --,

0 .80

0.60

0.40

' 0 .20

0.001

' '

0.01

- NlOCI•I•ed coeff•c•ents

Oelault coeff•c•eAts

• lv\easvernents

/

•

0.1

Fig. 8 . The comparison of the numerical prc:<lictions and experimental

m1xmg layer between both flows is required. Another reason for the overprediction of break-up may be the presence of a relatively high volume fraction dispersed phase in the nozzle flow (3.5%). Volume fractions higher than 1% are known to suppress turbulence; in the present investigations this volume fraction is even higher there where turbulence develops in the mixing layer. The simulations does not take into account a dispersed phase-eddy interaction, and is consequently not able to predict the influence of the dispersed phase on the turbulence energy dissipation levels.

results for the now behind a contraction. Finally, it can be concluded that one of the first attempts ever, to predict multiphase

liquid-liquid flows, including local processes such as break-up and coalescence has been successful. In order to improve the predictions however, more experimental evidence for the values of the model constants is required, as well as on the quality of the flow prediction. One stage further, the incorporation of a dispersed phase-eddy interaction, will open the door to the prediction of flows with a higher volumefraction of dispersed phase, making the numerical predictions more relevant for industrial applications.

101

ACKNOWLEDGEMENT

A special acknowledgement is directed to HJ . Ziman of ICI, Chemicals and Polymers Ltd, Winnington Cheshire (UK), who participated in the project and carefully built the microscopic models into the DUCTREACT package.

REFERENCES

Bentley, B.J. and Leal, L.G. (1986). An experimental investigation of drop deformation and break-up in steady, two-dimensional linear flows. J. Fluid Mech., 167, 241-283.

Chesters, A.K. (1988). Drainage of partially mobile films between colliding drops : a first-{)rder model. Euromech 234, Toulouse.

Chesters, A.K. (1991). The modelling of coalescence processes in fluid-liquid dispersiOns: a review of current understanding. Chern. Eng. Res. Des. July, Special Issue.

Grace, H.P. (1982). Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Chern. Eng. Commun., H. 225-277 .

Hinze, J .0. (1955). Fundamentals of the hydrodynamic mechanism of slitting m dispersion processes . AJChE Journal, l. 289-295.

Lamb, H. (1945). Hydrodynamics. Dover Press, 6"' Edition, New York. Lockett, MJ. and Safekourdi, A.A. (1977). Light transmission through bubble swarms. AJChE

Journal, 23, no. 3, 395-398. Lothian, G.F. and Chapel , F .P. (1951). The transmission of light through suspensions. J. Appl. Chern.,

1. 475-482. McLaughlin, C .M. and Rushton, J.H . (1973). Interfacial areas of liquid-liquid dispersion from light

transmission measurements. AJCh£ Journal, 1.2. no. 4, 817-822 . Saffman, P .G. and Turner, J.S . (1956). On the collision of drops in turbulent clouds. J. Fluid Mech.

1.. 16-30. Savic, M. and Park, S.H. (1973). The splitting of drops and bubbles by turbulent liquid flow . J. Fluid

Eng., 53-{)1. Sleicher, C.C. (1962). Maximum stable drop size in turbulent flow . AJCh£ Journal, .8.. 471-477. Starnatoudis, M. and Tavlarides, L.L. (1981 ), The effect of impeller rotational speed on the drop size

distributions of viscous liquid-liquid dispersions in agitated vessels . Chern. Eng. J . ll.. no . I , 77-78. Tjaberinga, W J . and Boon, A. In preparation. Tsao, G .T . and Hsu, T.A. (1978). AJCh£ Symp. Series , 74, no. 172, Food, Pharma and Bioeng . Trice, V.G. Jr. and Roger, W.A. (1956). Light transmission as a measure of interfacial area in liquid

liquid dispersions. A!Ch£ Journal, ~. no. 2, 205-209.

102

TIPSTREAMING OF DROPS IN SIMPLE SHEAR FLOWS

R.A. DE BRUIJN

Unilever Research Laboratory, P.O. Box 114, 3130 AC Vlaardingen, The Netherlands

ABSTRACI'

103

The tipstreaming phenomenon, as observed in simple shear flows, has been analysed. Tipstreaming is a mode of break-up in which the droplet develops a sigmoidal shape and a stream of tiny droplets is rupture1 off the tips of the drop.

Suggested causes of the tipstreaming phenomenon have been tested experimentally.

It was found that tipstreaming can occur if interfacial tension gradients can develop, resulting in low interfacial tension at the tips and a high tension elsewhere. Tipstreaming will not occur at extremely low surface active material levels, when the interfacial tension can not even be lowered locally, nor at high levels where there is so much surface active material present that the interfacial tension will be low all over the droplet.

KEYWORDS

Emulsion, drop, break-up, tipstreaming, simple shear flow, surfactant, emulsifier.

INTRODUCI'ION

Although most of the behaviour of small Newtonian drops in simple shear flows is reasonably well established, the phenomenon of tipstreaming is still poorly understood (Rallison, 1984). Tipstreaming is an experimentally observed mode of drop break-up (Taylor, 1934 Bartok and Mason, 1959, Rumscheidt and Mason, 1961, Grace, 1982 and Smith and van de Ven, 1985), in which the droplet takes upon increasing the shear rate, a sigmoidal shape and a stream of very small droplets is ruptured off the tips of the drop (figure 1). This break-up behaviour is potentially very important since the shear rates required for this type of break-up can be orders of magnitudes lower than for the normal type of break-up, in which the droplet is broken in two or three almost equally sized droplets with a few tiny satellite drops in between (figure 1) and the resulting droplets can be much smaller. Another area of potential applicability is the emulsification of a droplet phase containing a third phase (either solid or liquid) since the tipstreaming phenomenon may be useful for separation processes (Srinivasan and Stroeve, 1986 and Smith and van de Ven, 1985). In this paper it is tried to unravel the causes of the tipstreaming phenomenon.

104

oo tipstreuing

00~ •

fcac.ture

Fig. 1. Modes of drop break-up observed in simple shear flows.

EXPERIMENTAL

Introduction

The experimental programme was aimed at unravelling the causes suggested in the literature for the tipstreaming phenomenon (Taylor, 1934, Rumscheidt and Mason, 1961, Torza, Cox and Mason, 1972 and Smith and van de Ven 1985), namely the viscosity ratio, the rate of increase of the shear rate and the presence of surfactants. Accordingly various sets of experiments were performed. In the first set the viscosity ratio was varied from 2· 10- 4 to 0.1 for four different pairs of fluid combinations in order to see the the effect of the viscosity ratio and the type of fluid combination on the occurrence of tipstreaming. In the second set the tipstreaming phenomenon itself was subject to a closer examination and the time dependency of the phenomenon was studied. In the third set the effect of the rate of increase of the rate of shear was studied. In the fourth set the effects of surfactants were studied systematically by adding various levels of a surface active material to a fluid combination that did originally not show any tipstreaming. The experiments were performed in a Couette device (de Bruijn, 1989)

Viscosity Ratio

To scan the effect of the viscosity ratio on the occurrence of tipstreaming, combinations of several types of fluids were used. The experiments were done in a quasi steady way.

The results show that tipstreaming was not observed for the corn syrup and ester droplets in silicone oil, even though the viscosity ratio was varied between 0.1 and 2"10- 4

• For ester droplets in corn syrup, however, tipstreaming was observed for each of these viscosity ratios. The silicone oil droplets in corn syrup showed generally no tipstreaming. Only for a 5 mPas silicone oil tipstreaming was observed when the standard batch Rhodorsil 47VS was used. When a 5 mPas silicone oil was made by mixing the standard batches of 1 mPas and 10 mPas silicone oil, tipstreaming did not occur. These results indicate that the type of the fluids is very crucial for tipstreaming to occur. The viscosity ratio is not very important provided it is much smaller than unity. The 5 mPas silicone oil drop phase

105

results indicate that minor components in the liquids can determine whether or not tipstreaming will occur.

Time Dependency

In this section the tipstreaming phenomenon itself is subject to a closer examination. Especially the time dependency and the history effects involved in tipstreaming will be studied.

When a droplet was inserted in the Couette device and the shear rate was slowly increased, the droplet at first assumed an ellipsoidal shape. At higher shear rates a sigmoidal shape was assumed and at capillary numbers of around 0.5 tipstreaming occurred. When this shear rate was maintained during a period of time it was observed that tipstreaming ended after a certain period, varying between 10 seconds and a few minutes. However when the shear rate was further increased tipstreaming often started again at a higher shear rate and the same process could be repeated until the shear rate became too high and the droplet assumed an ellipsoidal shape again. At higher she arrates a normal mode of droplet break-up was observed. Contrary to the statement by Rumscheidt and Mason (1961), who ascribed the ending of tipstreaming to a decrease in drop volume and a subsequent lower capillary number, the observed ending and restarting of tipstreaming was not merely due to a reduction of the capillary number. When ending of tipstreaming was observed, the drop volume was decreased very little, the decrease was usually hardly detectable, while the necessary capillary number to restart tipstreaming was substantially larger.

When a droplet was subjected to a slowly increasing shear rate and tipstreaming had started at a certain shear rate it generally ended again at a higher shear rate. When the shear rate was then reduced to zero and the experiment was repeated it was observed that tipstreaming would start at significantly higher shear rates than before, although the ending occurred at comparable shear rates. If a droplet was left at rest after tipstreaming for a period of 10- 30 minutes, tipstreaming would start again at the initial critical shear rate.

It was further observed that tipstreaming never occurred when the shear rate was slowly decreased from close to the critical shear rate for normal fracture type drop break-up.

These observations of the tipstreaming phenomena indicate that there appears to be some sort of depletion effect and the occurrence of tipstreaming depends on the history of the droplet.

Acceleration

To examine the effects of the rate of increase of the shear rate, experiments were performed with model liquids, that had shown tipstreaming in the previous experiments, and with model liquids that had not exhibited any tipstreaming in the previous quasi steady experiments.

These experiments were performed at various constant rates of increase of the shear rate. The results show that there is a strong tendency for the critical shear rate to increase at higher accelerations.

The systems that did not show tipstreaming in the steady state experiments did not show it in these acceleration experiments either.

106

Surfactants

To study the effects of surfactants on the tipstreaming phenomenon surfactants were added to the dispersed phase of a fluid combination that did not show any tipstreaming, namely a 5 Pas corn syrup/Water mixture as the continuous phase and low viscosity silicone oils (10 and 50 mPas) as dispersed phases. It was found that glycerol-1-mono-oleate was a good surface active material for these fluids. At saturation concentration the interfacial tension was reduced to 2-3 mN/m. For both fluid combinations a set of experiments was perfonned with a range of surfactant concentrations added to the droplet phase. Some of the results for the 50 mPas droplet phase are given in table 1.

For both the 10 mPas and the 50 mPas silicone oil drop phases the results show the same trend. When no or extremely low levels of glycerol-1-mono-oleate were added the systems do not show any tipstreaming. At a certain level, however, tipstreaming is observed, whereas at much higher levels of the surfactant no tipstreaming was observed anymore and the droplets could only be broken up via a normal fracture mode of break-up. For the 10 mPas silicone oil drop phase, tipstreaming was not observed at surfactant levels below 0.001%(wt). At 0.001%(wt) sometimes no tipstreaming could be observed at all and only droplet fracture was observed, whereas for other droplets tipstreaming did occur, although sometimes the tip droplets were not emitted continuously (tipstreaming) but more intermittently (tipdropping). For the surfactant levels between 0.005%(wt) and O.l%(wt) tipstreaming was observed in all experiments. At the highest level of surfactant, 0.5%(wt), a normal fracture mode of drop break-up was observed, without passing through a tipstreaming stage. Higher levels of surfactants were not tried because of supersaturation. the radius of the emitted tip droplets was found to vary between 8 pm and 25 pm. For the 50 mPas silicone oil drop phase a very similar trend was observed although some variations were observed. At surfactant level below 0.00l%(wt) no tipstreaming was ever observed. At higher levels tipstreaming was generally observed, although some droplets exhibited drop fracture without passing through a tipstreaming stage. At surfactant levels of 0.05%(wt) and higher tipstreaming was never observed anymore.

For several emitted tip droplets the interfacial tension was estimated from the deformation method. Even though the results are not very accurate because the tip droplets were very small and the droplet deformations could not be determined very accurately, these experiments gave some striking results. The interfacial tension of the tip droplets was invariably lower (usually much lower) than the interfacial tension of the mother droplet. The interfacial tension of the tip droplets was often close to the saturation value.

The results described above indicate that tipstreaming can occur if an interfacial tension gradient can be developed in the droplet surface at a certain surfactant concentration range with lower interfacial tension near the tips of the droplet.

107

Table 1. Effect of surfactants on tipstreaming

drop phase 50 mPas silicone oil with glycerol-1-mono-oleate continuous phase: 5 Pas corn syrup

No. surfactant a r y Q mode of r . a . [%] [mN/m] [mm] [1/ sl [-] break-up !tiD~ [~/Ktl

1 0 30 0.391 30.1 2.0 fracture 2 0.430 27.4 1.7 fracture 3 0.560 21.7 1.7 fracture

4 0.0001 30 0.361 >16.2 >1.0 no tipstr. 5 0. 554 19.9 1.6 fracture 6 0.357 22.2 1.3 fracture

7 0.0005 30 0.305 >14.5 >0.8 no tipstr. 8 0.374 >14.9 >1.0 no tipstr. 9a 0.586 5.7 0.59 tipstr. 10 9b 20.1 2.1 tip. ~ fr.

10 0.001 26 0.736 5.6 0.69 tipstr. 10 5 11 0.854 3.6 0.52 tipstr. 20 2 12a 0.594 6.9 0.80 tipstr . 12b 19.1 2 . 2 tip. ~ fr. 13 0.502 7. 1 0. 69 tipstr . 6 14 0.573 6.3 0.69 tipstr. 6 15a 0.585 6.0 0.68 tipstr. 15b 20 . 5 2.3 tip. ~ fr.

16 0.005 22 0.349 7.2 0.55 tipstr. 8 17 0.271 7.5 0.53 tipstr. 10 18 0.334 5.3 0.49 tipstr. 10 19 0.338 7.3 0. 53 tipstr. 5-10 20 0. 516 5.1 0.46 tipstr. 10 21 0. 620 3.4 0.51 tipstr. 20

22 0.01 11 0.472 3.3 0.70 tipstr. 23 0.449 3.0 0.62 tipstr. 18

24 0.05 4 0.359 1.3 0.59 fracture 25 0.319 1.5 0.60 fracture 26 0.237 1.9 0.57 fracture

27 0 . 1 3.6 0. 440 1.3 0. 59 fracture 28 0.281 2.0 0.59 fracture 29 0.152 4.3 0.67 fracture

30 0.5 2.8 0.324 1.2 0. 75 fracture 31 0.214 1. 6 0.66 fracture 32 0. 250 1.4 0.68 fracture

108

NUMERICAL

A numerical technique (de Bruijn, 1989) has been used to calculate the position of the material points on the midplane of the drop surface, when the droplet is subjected to a simple shear flow. The numerical calculations are based on a surface integral method, which rewrites the Stokes-equations in and around the droplet, via Fourier transforms, to a surface integral. Thus one only needs values of quantities at the drop surface to calculate the velocity of a point at the surface. This surface integral was solved after discretizing the surface of the droplet.

Calculations were performed for droplets characterised by viscosity ratios of 0.5, 1.0 and 2.0, that were subjected to a step profile simple shear flow with capillary numbers ranging from 0.1 to 0.4. The results are presented in figure 2 where the contours of the midplane of the droplets are given after various time intervals after the onset of the flow. The results show that once the droplets obtain an ellipsoidal shape, the concentration of the material points around the points of the ellipsoid increases, indicating a contraction of the drop surface, whereas along the long side of the disk the concentration decreases, indicating an expansion of the drop surface. This effect is more pronounced for lower viscosity ratios. Closer examination of the contours on figure 2 reveals that the surface is most contracted just over the points of the ellipse. This corresponds exactly with the position of the tips during tipstreaming. The results show that for a capillary number of 0.3 and a dimensionless time of 0.5 the contraction effects are about four times more pronounced for the viscosity ratio of 0.5 than for 2.0. These calculations were performed assuming a constant interfacial tension. This assumption is only valid for small times.

For larger deformations the numerical calculations are not anymore appropriate, since interfacial tension gradients may than become important and these effects are not accounted for in these calculations .

,\ - 0 .50 , 1ime - 1.00 A - 2.00. Time • 1.00

Fig. 2. Droplet contours in simple shear flow as a function of the viscosity ratio after dimensionless times of 0.5 and 1.0 and at a capillary number of 0.3.

109

DISCUSSION

The experimental and numerical results seem to indicate that tipstreaming is a result of the built up of interfacial tension gradients over a droplet resulting in low interfacial tensions close to the points of the ellipsoids. Such interfacial tension gradients make the drop surface less mobile allowing the shear stresses exerted by the continuous phase to pull out a stream of tip droplets. This explanation however can only hold when the shear stresses exerted by the continuous phase are large enough to maintain such an interfacial tension gradient and when the diffusion of the surface active material from the droplet to the surface is slow enough not to interfere with the build up of the interfacial tension gradients. The restarting of tipstreaming after a droplet was brought back to rest and a new experiment was begun, indicate that in about a minute the concentration of surface active material can be restored.

An order of magnitude calculation to see whether or not the shear stresses exerted by the continuous phase will be able to maintain an interfacial tension gradient on the droplet can be performed by comparing both stresses for actual experiments. The viscous stresses will be of the order of: ~- y, whereas the interfacial gradient stresses will be of the order of 6ajr , in which 6a is the difference in interfacial tensic~ between the mother droplet and the tip droplet. These two stresses are of comparable magnitude at the point of break-up.

Whether or not surfactant diffusion occurs on these time scales is somewhat more difficult to estimate, since it involves an estimation of the diffusion coefficient of glycerol-1-mono-oleate in silicone oils. Tipstreaming was found to occur typically at a concentration, w, of 0.005%(wt) in the droplet phase. The number of surfactant molecules in a droplet is thus given by

(1)

where pis the density of the drop phase (p=lOOO kgm- 3 ), N the Avogadro

number and M the moleculfr weight of glycerol-l-mono-oleatev (M=348), resulting in Nd = 4.5"10 2 for a 0.5 mm droplet.

The number of molecules needed to cover the undeformed drop surface completely is given by

(2)

where A is the afea of a glycerol-1-mono-ole~te molecule in the drop interface, A =38A, resulting inN = 8.3"101

• Thus approximately a fifth of the totalmnumber of surfactant fuolecules in the droplet suffices to cover the droplet surface completely. To estimate the time scales involved in surfactant diffusion in the droplet, one can use the standard solutions to transient diffusion in a sphere. These show that complete equilibrium is obtained when the Fourier number (Fo = Dt/r2

) is about 0.5. At a Fourier number of about 0.01 already a substantial amount of diffusion from a layer of thickness r/10 has taken place (such a layer contains already enough surfactants molecules to cover the drop surface completely). A reasonable guess of the diffusional coefficient, taking into account the high viscosity, seems to be 1"10- 9 m2 s- 1

• This would imply that complete equilibrium by diffusion from a thin layer near the drop surface can, for a droplet with r=0.5 mm, already occur after 10 minutes. The time scale for equilibrium corresponds reasonably well to experimental time scales showing that when the droplet has been brought to rest after a tipstreaming experiment and an experiment was started again after about a minute that tipstreaming would take place, but at higher capillary numbers and that

110

when a droplet was brought back to rest after a tipstreaming experiment and an experiment was started after 15 minutes, tipstreaming occurred again at the original capillary number.

If the hypothesis is correct, that tipstreaming can only occur if interfacial tension gradients are present, the Peclet number based on a layer from which diffusion must occur to equilibrate the interfacial tension, must be smaller than 1.

Pe = Ud/ D = yd2

/ D < 1. (3)

An estimation of the layer thickness d for low concentrations of surfactants can be obtained from the lower limit of the Langmuir adsorption isotherm, such that there are as many surfactant molecules present in this layer as there are needed for equilibrium adsorption:

( 4)

with r. the maximum surface concentration of the surfactant and r. ; cl the slope at low concentrations of the Langmuir adsorption isotherm. r. can be estimated from the size of the surfactant molecules:

(5)

witl_l N v the Avogadro.number_f!rd f'., the ar~a o~ the adsor~~ molecul~. A typ1cai value for A 1S 4 · 10 m , resul t1ng 1n r. = 4 · 10 moles/ m . A typical value for c; is given by 0.005 wt% - 0.1 mole/kg. This implies that Pe = 1 is reacned for a shear rate of

(6)

Since tipstreaming is only thought to be possible if Pe >> 1 and tipstreaming was observed for shear rates typically between 1 and 10, the above order of magnitude calculations confirm the hypothesis derived from the experimental and numerical results that tipstreaming in simple shear flows is due to interfacial tension gradients near the tip of the droplet.

REFERENCES

Bartok, W. and Mason, S.G. (1959). Particle motion in sheared suspensions VIII singlets and doublets of fluid spheres. J. Cell. Sci. 14, 13-26.

Bruijn, R.A. de (1989). Deformation and breakup of drops in simple shear flows PhD thesis, Eindhoven University of Technology,

Grace, H.P. (1982). Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Chern. En~. Commun. 14, 225-277.

Rallison, J.M. (1984). T e deformatiOn of small viscous drops and bubbles in shear flows. Ann Rev Fluid Mech 16, 45-66.

Rumscheidt, F.D. and Mason S.G. (1961)~ Particle motions in sheared suspensions XII deformation and burst of fluid drops in shear and hyperbolic flow. J. Cell . Int. Sci. 16, 238-261.

Smith, P.G. and Ven, T.G.M. van de (1985). Shear induced deformation and rupture of suspended solid/ liquid clusters. Coll. and Surf. 15, 191-210.

Srinivasan, M.P. and Stroeve, P. (1986). Subdrop eJeCtlon from-aouble emulsion drops in shear flow. J. of Membrane Sci . 26, 231-236.

Taylor, G.I. (1934). The formation of emulsions in definable fields of flow. Proc. Roy Soc . A 146, 501-523.

Torza, S., Cox, R.G. , and Mason, S.G. (1972). Particle motions in sheared suspensions XXVII transient and steady deformation and burst of liquid drops. J. Coll . Int. Sci. 38, 395-411.

TRANSIENT PHENOMENA IN DISPERSIVE MIXING

P.H.M. Elemans, H.L. Bos

DSM Research, P.O . Box 18, 6160 MD Gelee n, The Ne therlands

and

J. M.H. Janssen, H.E . H. Meij e r

Eindhoven Unive rsity of Technology, Department of Fundamental Mechanical Engineering, P . O. Box 513, 5600 MB Eindhoven, The Netherlands

ABSTRACT

111

The deformation and breakup processes of single droplets in well - defined fields of flow have bee n extensive ly studied in the lite rature . In spite of the fact that in real mixers the conditions are far from equilibrium, most studies are confined to (Newtonian) systems undergoing almost stationary deformation . The transient character of the dispersive mixing process is much less documented . In a Plexiglas -walled Couette-apparatus , the time-dependent deformation of Newtonian droplets into extended threads has been studied . When the shear rate is very slowly increased, allowing for almost equilibrium deformation , the results of the c ritical c apilla ry numbe r Cac rit as a function of viscosity ratio, a s reporte d in the literature, a re reproduc ed . However, in transient flows at capillary numbers Ca >> Cacrit • droplets are deformed into long slender bodies which continue to extend, until the shear has stoppe d . They then disintegrate into lines of droplets bec ause of interfacial tension-driven disturbances . The time scale for deforma tion a nd breakup is important for a be tte r unde rstanding of the dispersive mixing process, e.g. , during polymer blending in screw extruders.

KEYWORDS

droplet breakup; liquid-liquid mixing ; interfacial tension; dispersive mixing

INTRODUCTION

When a blend of two incompatible polyme rs is subjected to shearing forces , e . g . , in a corotating t win-screw extruder, droplets of the dispersed phase will deform into long, threadlike particles, whic h can break up into smaller droplets (Grace, 1982 ; Elmendorp, 1986; Elemans, 1989) . The ultimate morphology the r e lative distribution of the constituent s - depends on volume or weight fraction (Bohm et al . , 1977; Elemans et al., 1987), vi s cosity ratio of both polyme rs and the type of flow (Grace , 1982) . The word 'polymer', deliberately used in the former paragraph , in contrast with 'liquids' as mentioned in the title , suggests a similarity in the behaviour of systems use d i n emulsion rheology a s well a s in polymer rheology.

112

Therefore, we will review some of the literature on time-dependent deformation and breakup of (Newtonian) droplets. The emphasis will be on isolated particles in shear flow (coalescence of droplets will not be considered). An attempt will be made to transfer the results from model experiments to the processing conditions of a polymer blend in a screw extruder .

AFFINE DEFORMATION OF DROPLETS IN SIMPLE SHEAR FLOW

The deformation of droplets depends on the ratio of the shear stress r -

~c ·1 and the pressure due to the interfacial tension ojR . This ratio is usually referred to as the capillary number Ca. For large capillary numbers (Ca ~c1R/o), and for viscosity ratios p < 1, droplets will deform affinely with the matrix . Their deformation can be expressed in terms of the total shear ~ (~ 1 · t), imposed by the flow field (Starita, 1972). In simple shear flow, a spherical droplet having an initial diameter ' a' will deform into an ellipsoid with length L and width B:

L/a- )(1 + ~2;2 + (~/2) ·)(4 + ~2 )) (1)

Bja - (L/a)·O.S ( 2 )

hence, by defining the deformation D (L- B) / (L +B),

(L/a)l. 5 - 1 D - --------------

(Lja)l.S + 1 (3)

Figure 1 shows t hese prope rties L/ a, Bja and D as a function of ~ -

~ _J

~ CD

0

1\ I I I

2,----,--------------------------------------.

1.75 L/a

1.50

1.25

0.75

0.50

Fig. 1.

D

B/a

-------

5 10 15

--- > 1

Relative length Lj a, relative width Bja and deformation D of an a ffinely deformed droplet a s a function of ~- The dashed line shows the influence of periodical reorientation on B/ a.

113

Periodical reorientation of the already deformed droplet increases the efficiency of the mixing process drastically (Ng and Erwin, 1981). This is illustrated by the dashed line in Fig . 1, which shows the influence of reorientation on the decrease in width of a droplet in simple shear flow.

BREAKUP OF THREADS

Until now, the shear rate ~ and the time t have been interchangeable. Once the droplet has become highly extended, it will exhibit initially small sinusoidal (so-called Rayleigh) distortions, each possessing a wavelength A along the thread. Depending on the viscosity ratio p ~d/~c · one wavelength, Am, will turn out to be dominant and will cause breakup (Rayleigh, 1879; Tomotika , 1935; Elmendorp, 1986). For a Newtonian thread of infinite length in a flu id matrix which is at rest, the time for breakup, tb, can be calculated using the theory of Tomotika (1935).

where

Ro ao q

1/q in (}(2/3) R0;a0 )

the initial thread radius the initial dis tortion amplitude the growth rate of the distortion

(4)

q - q(Ro)

The factor (j(2j3) stems from t he condition that breakup occurs when the amplitude is equal to the average thread radius (Elmendorp, 1986).

Fig. 2 . Sinusoidal dis tortions on a polyamide-6 thread (diamete r 55 ~m) e mbedde d in a PS matrix at 230 •c (Elemans et al., 1990). The photographs were taken at: t = 0, 15, 30, 45, 60 s. Reprinted with permission of the Society of Rheology.

Predicting t he s tability of a thread in a ma trix which is deforming i s more difficult, since the wav elength A is changing with time. For instance, at low deformations in shear flows the distortions are swept away, whereas a t high deformations in e longational flows a potentially dominant wavelength will be extending so fast with the matrix (Tomotika, 1936; Kalb ~. 1981; Elme ndorp , 1986) t hat its e ffect will be dampe d out before having been able to cause breakup.

114

BREAKUP OF DROPLETS

Starting with the work of Taylor (1932, 1934), numerous studies have b een devoted to the deformation and breakup of small droplets in a matrix undergoing simple s hear flow or hyperbolic extensional flow . Good reviews of the relevant experimental and theoretical work reported in the literature can be found in the work of Rallison (1984) and Elmendorp (1986) . Recommended as well is the almost 'classical' work on droplet breakup by Grace (1982), who used a Couette-type apparatus and a four-roll mill to generate simple shear flow and hyperbolic extensional flow, respectively.

More recently, Bentley et al . (1986a, 1986b) deve loped a computer-controlled four-roll mill. The continuous adjustment of the speed of each individual roller enabled them to position a drople t almost anywhere in the apparatus and to keep it there for a considerable period of time . Moreover , they succeeded in (approximately) generating a wide range of flows, characterized by a single parameter a, which is correlated to the ratio of deformation rate to vorticity (Giesekus , 1962). The conclusions of their experiments on steady droplet deformation and breakup are in general agreement with those of earlier authors.

Continuing Bentley's work, Stone et al. (1986 ) study transient effects in droplet breakup . By slowly increasing the shear rate, droplets are brought to a certain elongation ratio Lja . The flow is then stopped. Under the influence of interfacial tension, the droplets may return to their original shape or alternatively break up into several fragments. For a broad range of viscosity ratios p (0.01 < p < 10), the breakup mechanism via Rayleigh dis tortions is only observed for v a lues of L/ a > 15. For lower L/ a values, (6 < L/ a < 15), the droplets exhibit 'end-pinching', as shown in Fig. 3 (see Stone ~. (1986) for experiments, and Stone and Leal (1988) for numerical calculations on this phenomenon) . The ends of the droplet become sherical while the overall length decreases. The ends pinch off, and the newly formed fluid thread relaxes further, disintegrating (in general) more slowly, because of the larger thread radius. The time scale for end-pinching is thus shorter than that for the growth of Rayleigh distortions. A beautiful demonstration of end-pinching in a mi xing apparatus i s given by Tjahjadi and Ottino (1989).

~

Fig. 3 .

t a 1

I I ( 0 0 0 !;

t) n 0 0_

Relaxation and breakup of a molten high density polyethylene thread (diameter 20 ~m) in a polystyrene matrix at T 200 •c. The photographs were taken at regular intervals and cover a range of 216 s. Reprinted with permission of the Soc iety of Rheology.

115

EXPERIMENTAL

Breakup experiments with Newtonian systems were performed in a Plexiglas-walled Couette-type apparatus. The purpose of the experiments was twofold: (i) to investigate . the behaviour of droplets during deformation and breakup under non-equilibrium conditions; (ii) to check the time-dependent deformation of droplets at low capillary numbers .

Although insight mixers , and the

limited in direct practical applicability, these experiments give into the time scales involved in the deformation of droplets in real e.g., in the strongly varying flow field between the kneading flight

barrel of a twin-screw extruder.

EXPERIMENTAL SETUP

A simple shear flow is generated in a Couette-type apparatus. It consists of two counterrotating concentric cylinders. The speed of both the inner and outer cylinder can be adjusted to keep a droplet at the same position in the gap while being deformed at a shear rate ~. which for a Newtonian flow is given by (Trevelyan and Mason, 1951):

(5)

where the radius of the inner, resp. outer cylinder the angular velocity of the inner, resp . outer cylinder

In the pre sent apparatus, R1 - 50 mrn, R2 - 63.2 mrn. The height of the gap is 120 mm, which is enough to avoid disturbance of the flow field due to the bottom. Shear rates up to 20 s- 1 can be obtained. The deformation of a droplet can be studied from above by a microscope plus a video system, connected to a high-resolution monitor.

MODEL FLUIDS

Table 1 lists the characteristic properties of the Newtonian fluids used in the experiments . As continuous phase, silicon oil (Rhodorsil, Rhone-Poulenc) was used. As disperse phase, solutions of Corn Syrup (Globe 01138) in water were used. Viscosities at 23 •c were determined on a Bohlin Vor dispersion rheometer . Newtonian behaviour was observed up to approximately ~ 10 s- 1 . The interfacial tensions between the Corn Syrup (C.S.) solutions and the silicon oil was measured using a Du Nouy-ring tensiometer.

RESULTS

Experiments with model fluids in simple shear flow will be discussed first, each representing a stage of the dispersion proc es s that occurs on a distinct time scale. Only the most important results will be presented here. Details can be found in reports by Bos (1988) and Janssen (1989).

116

continuous phase

disperse phase

Table 1. Viscosities of the Newtonian model fluids at 23 'C. In brackets is the interfacial tension between the Corn Syrup (C.S.) solutions and (any of) the silicon oils.

'~23'C

(Pa.s)

Rhod v 60000 63.3 Rhod v 30000 29.9 Rhod v 12500 12.5 Rhod v 5000 4.95 Rhod V 1000 1. 04

96/4 28 .0 (40.0) (wt.% C.S./wt .% H20) 95/5 16 . 25 (40.0)

90/10 4 . 06 ( 41.4) 85/15 1.13 ( 46. 7) 83/17 0.75 (47.0)

AFFINE DEFORMATION

A spherical droplet (typica l diameter about 1 mrn) is suddenly subjected to a supercritical simple shear flow, i.e. Ca > Cacrit' Cacrit is the capillary number for breakup under steady conditions. For 0.1 < p < 1, Cacrit 0.5 (Grace, 1982) . The length Lor, at deformation D > 0.8, the width B, is measured from the monitor. The deformation, D, can be determined and compared with the theoretical prediction as given by Eq 3. Affine deformation occurs at Ca/Cacrit ~ 2, see Fig. 4.

0.9

0 .8

0 .7

0 .6

0 0.5

!\ I 0.4 I I 0.3

0.2

0.1

0

•

0

•• • • • •

0

~

X

•

.----C X

• • p=O.l35

Co/Co cril = 7. 1

Co/Co crit = 3.2

Co/Co cril = 2.1

Affine deformation Ca/Ca cril = 1.2

0

Fig. 4 .

' 5 10 15

---> -y

Affine deformation at number. Viscosity ratio p represent the deformation

20

supercritical capillary 0 . 135. The drawn lines calculated from Eq 3.

117

BREAKUP OF THREADS IN SIMPLE SHEAR FLOW

A supercritical simple shear flow, with Ca >> Cacrit• is stepwise appl i ed to a spherical droplet, which will deform affinely into a thread. At a certain moment, the thread will exhibit sinusoidal distortions which will cause breakup. The time for breakup, tb• is defined as the elapsed time between the onset of of the flow and the moment at which a line of separate droplets has been formed in the central region of the thread . Figure 5 compares the results concerning the dimensionless time for breakup with data from similar experiments by Grace (1982 ). Upon exceeding Ca/Cacrit• the time for breakup does not decrease, as in Grace's experiments . Grace might have observed end-pinching, which indeed yields a much smaller value for tb. This may explain the large difference shown in Fig. 5.

N ~

1\ I I I

Fig. 5.

10

---> Ca/Ca cril 100

The effect of exc eeding Cacrit on dimensionless burst time t*- t · a/(~c ·R0) Symbols indicate the value of the viscosity ratio p. Open symbols represent data from Grace (1982), whereas closed symbols refer to data from Elemans (1989). The dashed line represents p- 1.

CONCLUSION

In the case of Newtonian drople ts in a Newtonian matrix, affine de forma t ion occurs in simple shear flow at Ca/Cacrit ~ 2. The time required for deformation can be calculated from Eq 1 (with ~ ~-t). Upon cessat ion of the flow, the time for breakup of highly extended droplets (Lja > 15) can be calculated using Tomotikas theory (Eq 4) , see also Elemans et ~ (1990). For moderately extended droplets (6 < Lj a < 15), the numerical calculations of Stone and Leal (1988) apply. If viscoelasticity is introduced, deformation and bre akup of droplets is more complicated. Some scouting experime nts with Boger fluids have been performed by Bos (1988). Re s ults of a more systematic study can b e found in the work by De Bruin (1989), g~v~ng a n increased Cacrit with increas ing e l astici t y for almost all values of the viscosity ratio p.

118

APPENDIX

The following calculation may serve as an illustration how to use the results from the above sections. The problem concerns the dispersion of an isolated droplet in a single screw extruder. The extruder geometry and the flow field are represented as simple as possible .

Consider an extruder, with dimensions:

diameter flight clearance tip width length channel depth pitch angle relative flight

and further: throughput screw speed density

D ~ 25 mm 5 - 0.25 mm b 2 mm L/D = 5 H 2 . 5 rom cp 20°

width e bj(1rDsincp)

Q = 50 gjmin N 200 rpm p - 800 kg/m3

0 . 075

It is assumed that the material makes one pass through the nip between screw flight (or barrier flight, as in Maddock-type of screw elements) and barrel wall. The material is then transported towards the die by the drag flow in the screw channel.

The shear rate over the flight is :

1 ~ Vjo = 1rDNj(60 o) ~ 1000 s-l (6)

Polystyrene (PS), which has a viscosity ~d 100 Pa.s at this shear rate, is dispersed in high-density polyethylene (HDPE) with corresponding viscosity ~c 150 Pa .s . Hence, ~~e viscosity ratio p 0 . 7 . The interfacial tension is about 5 mN.m , so for droplets having a radius Ro ~ 1 ~m the local capillary number Ca can be calculated:

Ca - (~c 1 R)/a = 30 (7)

This capillary (Cacrit 0.5,

number exceeds Cacrit• required for breakup, by a factor 60 (Grace, 1982)). However, the residence time in the clearance

is very short:

t = B/V ~ 0.015 s. (8)

This yields a dimensionless time t*:

* t ~ t · (al~c R0 ) ~ 0.5 (9)

which is too short for the droplet to break up (compare Fig . 5, where a dimensionless time t* ~ 9 is required (at p = 0.7) for droplet breakup at Ca/Cacrit 60). Because of the large capillary number , the droplet will deform affinely into an extended thread. Its dimensions follow from the total shear ovBr the flight: ~ i·t 15, hence the elongation ratio L/2R0 15 (with Eq 1).

After passing through the nip, the droplet will be subjected to much lower shear ytresses in the extruder channel. The shear rate becomes (Eq 6) 1 -100 s- , and the capillary number (with a matrix viscosity ~c - 700 Pa.s) 14, which is high enough to keep the droplet extended. In this case, the value Ca/Cacrit = 14/0 .5 = 28. The dimens ionless time t* for

119

breakup is about 100, see Fig . 5.

At a throughput Q 3 -1 m .s , the average residence time in the extruder amounts to

t - ~DLH/Q ~ 24 s, hence t* ~ 1 70 (10)

The time available i s of the same order of magnitude as the time required, allowing for interfacial tension-driven disturbances to cause breakup.

REFERENCES

Bohm, G.G.A., G. M. Avgeropoulos, C.J. Nelson and F.C. Weissert (1977). The Relationship Between Rheology, Morphology and Physical Properties in Heterogeneous Elastomer Blends . Rubber Che rn. Tech., 50, 423-426.

Bos, H.L. (1988). Tijdseffecte n in afschuifstroming. internal report DSM Research (in Dutch ) .

Bruin, de, R.A. (1989). Deformation and Breakup of Drops in Simple Shear Flows. Ph . D. thesis, Eindhoven University of Technology.

Elemans , P.H.M., J .G.M. van Gisbergen and H. E.H . Meijer (1988). Structured Blends I. In: Integration of Fundamental Polymer Science and Technology (P.J. Lemstra and L.A . Kleintjens, Eds.), Vol . 2, pp. 261-266 . Elseviers Applied Science Publishers, London and New York.

Elemans, P.H . M. (1989). Modelling of the Processing of Incompatible Polymer Blends, Ph.D . thesis, Eindhoven University of Technology.

Elemans, P.H.M . , J.M.H . Janssen and H.E.H . Meijer (1990). The Breaking Thread Method: The Measurement of Interfacial Tension in Polymer Systems. J . of Rheol., 34(8 ), 1311-1325.

Elmendorp, J.J. (1986). A Study on Polymer Blending Microrheology , Ph.D. thesis, Delft University of Technology.

Giesekus, H. (1962). Stromungen mit konstantem Geschwindigkeitsgradienten und die Bewegung von darin suspendierten Teilchen, Teil II: Ebene Stromungen und eine experimentel l e Anordnung zu i hrer Realisierung . Rheol . Acta, £, 112-122.

Grace, H. P. (1982). Dis persion phenomena in hi gh vi s cosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Chern. Eng. Comm., 14, 225-277.

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Rallison, J.M. (1984). The Deformation of Small Viscous Drops and Bubbles in Shear Flows . Ann . Rev. Fluid Mech , 16, 4 5 -66.

Rayleigh, Lord (1879) . On the Capillary Phenomena of Jets. Proc . Roy . Soc. (London), 29, 71 -97.

120

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Taylor, G.I . (1934). The Formation of Emulsions in De finable Fields of Flow. Proc . Roy. Soc . (London), A 146 , 501-523.

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On the Instability of a Cylindric al Thread of Viscous Another Viscous Fluid. Proc. Roy . Soc. (London), Al SO,

Breaki ng Up of a Drop of Vi s c ous Liquid Imme rsed in Which Is Extending at a Uniform Rate. Proc . Roy . Soc.

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AN OPPOSED JETS DEVICE FOR STUDYING THE BREAKUP OF VISCOELASTIC DROPS AND THREADS

J.M.H. JANSSEN, G.W.M. PETERS and H.E.H. MEIJER

Eindhoven University of Technology, Department of Fundamental Mechanical Engineering,

P .0. Box 513, 5600 MB, The Netherlands.

ABSTRACT

121

Many studies on the dispersive mixing of immiscible liquids concentrate on deformation and breakup of a single drop in a well defined flow. This paper describes the design of a device, which has not yet been used in this field. Concept is the stagnation flow of two opposed jets in a closed circuit. A numerical study results in channel geometries for plane hyperbolic flow, which is purely extensional, and for a flow type, which combines extension and vorticity. A device with dimensions of several centimeters suffices to study deformation of a 1 mm drop. Experiments show that the model for plane hyperbolic flow is obeyed in a large region around the stagnation point. A control system is developed to position the deforming drop steadily at the, principally unstable, stagnation point. A control cycle consists of determination of the drop position and calculation and realization of the required flow adjustment. In the present experimental setup the deformation of a drop in 2--dimensionai elongational flow can be studied via video recording. The setup chosen not only allows for model liquids but can be adjusted to allow for polymer melts as well.

KEYWORDS

Dispersive mixing; drop breakup; elongational flow; opposed jets.

INTRODUCTION

Dispersive Mixing

The dispersive mixing of immiscible liquids is an essential subject in many industrial processes involving muitiphase flow. For example, in the melt blending of incompatible polymers, the morphology of the blend is of major influence on its mechanical (and other) properties. Therefore, it is important to model the development of the morphologies during the mixing process; starting with large (mm) domains of a distinguished liquid phase (disperse phase) and ending with a distribution of small (ttm) domains of the disperse phase in a continuous matrix phase.

A cla.ssical way to model the dispersive mixing process is to study the deformation and breakup of a single clrop of the disperse phase in a well defined flow field of the continuous phase. The dimensionless results of such analyses may be converted to real processes involving many drops and complicated flow fields. Deformation of a drop, suspended in an immiscible liquid, is due to the flow induced stresses acting on it and is counteracted by the interfacial tension between the two phases, which tends to keep the drop spherical. In order to study the influences of various parameters such as stress, (ratio of) viscosities, viscoelasticity, interfacial tension, and time, it is tractable to use model liquids and model flows.

Model liquids can be handled at roomtemperature, in contrast to molten polymers. Moreover, they offer the opportunity to control the rheological properties, such as the viscous, shear thinning, or viscoelastic behavior. Some of the flow types used in experimental or numerical investigations are simple shear flow,

122

generated in a parallel band (Taylor, 1934) or a Couette device (Grace, 1971), plane hyperbolic or 2-D elongational flow, generated in a four roll mill (Grace, 1971; Bentley and Leal, 1986), and 3-D axisymmetric elongational flow, often used in numerical studies (Rallison1 1984). The present study concerns the design of a s()-{;alled 'opposed jets device', for the experimental stuoy of drop deformation in 2-D elongational flow. Generally, in real processes the flow is a complex combination of all these types of flow .

Linear 2-D Flows

Most of the flow types used experimentally are linear 2-D flows. In general, a linear 2-D flow can be described by the velocity vector

.... .... .... c .... .... u=(Vu) ·x=L·x, (1)

where V is the gradient vector operator, ; the position vector, and L the velocity gradient tensor (Giesekus, 1962; Fuller and Leal, 1981)

G [ 1+a 1-a OJ L = 2 -1+a -1-a 0 , with -1 ~ a~ 1 (2)

0 0 0

In a Cartesian coordinate system; (x,y,z) the components of~ (u,v,w) are

u = ~[(l+a)x + (1-a)y), v = ~[(-l+a)x + (-1-a)y), w = 0. (3)

The parameter G (s·I) is called the shear rate and characterizes the magnitude of the velocity. The value of a characterizes the type of flow, ranging from purely rotational (a= -l) via simple shear (a= 0) to plane hyperbolic flow (a= 1); see, e:g., Bentley (1985). Using the common definitions of the rate of elongation, the rate of shear, and the vorticity, Janssen (1991) elaborated some properties of linear 2-D flows in general. This paper is mainly restricted to plane hyperbolic flow (a= l), which is the strongest in terms of deformation. Substituting a= 1, the velocity field equals

u=Gx, v=-Gy, w=O. (4)

Although the velocity ii equals zero at ; = 0, a deforming drop tends to leave this stagnation point along the positive or negative x-axis. The stagnation point is principally unstable since the velocity gradient tensor L has an eigenvector with positive eigenvalue along the x-axis. The rates of elongation and of shear are (for a= 1) given by

£ = G cos(2<P) (5)

and 'r = G sin(2<P), (6)

where <Pis the angle with respect to the positive x-axis . So, in plane hyperbolic flow, maximum extension appears at the x-axis and maximum compression at the y-axis. The rate of shear has its extrema at the diagonals, where the rate of elongation equals zero. The entire flow field is free of vorticity, i.e. irrotational.

The conventional four roll mill is flexible in generating all types of linear 2-D flows (Bentley and Leal, 1986). However, a disadvantage is its complexity: the roller speeds not only determine G and a but are also used to keep the deforming drop positioned at the centre of the device. Moreover, a four roll mill does not allow for highly viscoelastic fluids because the shear stresses generated by the rotating rollers may be too weak to overcome the large extensional stresses that appear; so, the fluid may not enter the compartment in between the rollers (Metzner and Metzner, 1970). Finally, it will be difficult to use molten polymers (at 200 to 300°C) in a four roll mill with its large volume of fluid and four mobile parts. The high temperatures may cause degradation of the polymer while high viscosities (102 to 104 Nsfm2) ask for very powerful drives.

The Concept of the Opposed Jets Device

The aim of the present study is to design a device which can generate linear 2-D flows (in particular plane hyperbolic flow), but is smaller and easier to construct and to operate than the four roll mill and which has the potential to be suitable for experiments with (highly) viscoelastic fluids. It is not new to apply the stagnation flow of opposed jets in order to generate an elongational flow (Miiller et a/., 1988). However, this concept (as shown in Fig. 1) has never been used in drop deformation studies.

Fig. 1.

y

• nmit ion ~ z~x

v

• · ·~'~"'ty ~ wJr--::u

Principle of the opposed jets device for drop deformation in plane hyperbolic flow.

123

The liquid is pumped from two opposite directions into a cell with a specific shape; the two flows impinge and leave the cell via two opposite exits. The cell consists of four solid blocks (thickness h), between two parallel plates of Perspex or glass (for optical entrance). The entrances and exits have all rectangular cross-sections (bxh) and are connected to a pump and a tank respectively. The 2-D character of the flow may be achieved around the midplane (z = 0) for sufficiently large h/b. Differently shaped cells cause different types of flow.

In comparison with the four roll mill, the opposed jets device is thought to generate a similar flow field in the central region. The three functions G, a, and the position control of the drop, which are all related to the roller speeds in the four roll mill, are completely independent in the opposed jets device: the shear rate G is determined by the flow rate, the flow type parameter a is related to the shape of the cell, and the position control is governed by the ratio of the exit flow rates, as discussed later. Separation of these functions makes the device less complex than a computer controlled four roll mill. Furthermore, the opposed jets device is expected to allow for highly viscoelastic fluids, in contrast to the four roll mill. The fluid is forced directly into the cell instead of driven indirectly via the rollers. The closed and small volume in the fixed opposed jets cell is quite suitable for polymer melts as well. The main disadvantage of the opposed jets device, however, is the fact that a different shaped cell has to be installed in order to change the type of flow . For this purpose, the four roll mill is more flexible.

DESIGN OF THE GEOMETRY

Strategy

The first step is to select geometries which can generate different types of linear 2-D flows, at least in the central region and for Newtonian liquids. From a number of numerical flow simulations a set of geometries is selected of which the calculated streamlines compare qualitatively well with those derived from the flow model. After this qualitative design of the geometries, the dimensions have to be chosen quantitatively to get a device which fu lfills the demands from drop deformation experiments (Rumscheidt and Mason, 1962; Grace, 1971; de Bruin, 1989; van der Reijden-Stolk, 1989; Elemans,1989): a central region of constant (within 10 %) shear rate G. Given the typical diameter of a drop: 1 mm, which should be homogeneously elongated by at least a factor 10 without reaching a deviating flow type, this region of constant G should be l to 1.5 em square. Furthermore, the value of G should be of the order I s·l, to be able to sufficiently deform a drop. Moreover, the total volume should be as small as possible in order to make the device suitable for polymer melts.

The flow was simulated with Sepran (Segal, 1989), a finite element package. The program iteratively solves the 2-D Navier-Stokes and continuity equations for a stationary incompressible Newtonian flow, using the penalty function method. First, the solution is obtained in terms of the velocity field. Based on this solution the pressure, streamfunction, vorticity, and rates of elongation and of shear are derived. The mesh consists

124 of quadratic triangles. The values of G and a can be determined from comparison of the extrema of the rates of elongation and of shear and the vorticity to their profiles as derived from the model (Janssen 1991).

Numerical Results

The geometries consist of circular parts and have extended entrances and exits, representing the tube connections and allowing an entering plug flow (boundary condition) to develop into a steady velocity profile. A tube length of half its width b is enough !'or the flow to develop since the Reynoldsnumber is small (typically 0(1)). For the a = I geometry, the ratio r/b (Fig. I) is set 2 to make the circular parts reasonably fit to hyperboles (Bentley, 1985). In the first series of calculations the density is 103 kg/m3, the dynamic viscosity 5 Ns/m2, the velocity at both entrances is a plug flow of 1 mjs, and the channel width b = 4 em. To get a quick first impression of the flow field, the convective (non-linear) term of the Navier-Stokes equation is neglected, resulting in a set of linear equations solvable without iterations (Stokes flow). For low Reynolds flows, this simplification should be of minor influence. Still, the calculations for the quantitative dimensioning involve the complete Navier-Stokes equation.

Plane hyperbolic flow (a = I) is easily generated in a square setup of 4 quarters of circles. Figure 2.a presents the streamlines for this case. In the central region the streamlines appear to be hyperboles with perpendicular asymptotes. The rates of elongation and of shear have their extrema and symmetry as expected from theory while the centre is free of vorticity. In this case, the approximate value of G amounts to 17 s·l.

Another geometry was shaped for the particular flow type a = 0.6, thus containing a certain amount of vorticity. This was realized by 'forcing' the streamline asymptotes to intersect at 75.5°, as required by the flow model. Starting with a rhomb setup of circular parts, the small circles are reduced and shifted one channel width (b) inward, the large circles enlarged and shifted outward (Fig. 2.b). This results in a pattern of streamlines that obeys the desired asymptotes in a large area around the stagnation point. From the complete results of the rates of elongation and of shear and the vorticity, the values of G and a are ev3luated: G = 20 s·1 and a= 0.55. It is evident that the streamlines give a reliable impression of the flow type; a geometry may be classified unsuitable if the streamlines do not coincide with the desired ones. Now

. it has been shown to be possible to design a geometry for a= 0.6, it seems possible to design geometries for all linear 2-D flows in between plane hyperbolic and simple shear flow (0 < a< 1).

a.

I I l _____ _

Fig. 2.

r-----' \ r------1 I I I I I

b.

Streamlines in geometries suitable for a. a = I and b. a = 0.6.

I I I I I I

------1

I I I I I I I I

--- \ ----1

125 The designed shapes have to be dimensioned in accordance with the requirements stated before. An evaluation of the complete results from the calculations in Fig. 2 shows that for a plug flow of 1 m/s through entrances of width b = 4 em the region of constant (±10%) shear rate is about 6 em along the x­and y-axis while G ;:; 20 s-1. According to the requirements the length scale may now be diminished by a factor 4 and the velocity by a factor 80. The case of a plug flow of 1/80 m/s through channels with b = 1 em is expected to give a region of about 1.5 em where G = 1 s-1. The newly scaled geometries for a= 1 and a= 0.6 are subjected to an analysis with the complete Navier-Stokes equation. As expected, the non-linear term is of no influence on the Stokes solution for this low Reynolds flow (after scaling: Re = 0(0.1)).

For a = 1 the two planes of symmetry are used in order to limit the cpu time for the iterative solution process; only one quarter of the geometry is taken into account. This also allows for a mesh refinement towards the centre. Figure 3 presents the complete results. Within the drawn box the flow corresponds to the linear 2-D flow model. This means that the region of constant (± 10%) shear rate at the centre is a square of b x b (b = 1 em). From the results it is seen that this central region is completely irrotational (a = 1.0) and G = 1.0 s-1. Also the scaled a = 0.6 geometry gives satisfactory results: using a plug flow entrance velocity of 0.0125 mjs through channels of width b = 1 em, the value of a is determined to be 0.54 while G = 1.0 s- 1 in the central region of b x b.

step 0.1 s·t step 0.1 s·t

Fig. 3. Complete results for the scaled a= 1 geometry; plug flow entrance velocity 0.0125 mjs; channel width b = 1 em; drawn box 0.5 em x 0.5 em.

step 0.2 s·t

As long as the Reynolds number stays of the order 0(0.1), the viscosity is not expected to significantly affect the flow pattern. This is verified by solving the problem for a= 1 with viscosity 1 instead of 5 Nsjm2. The velocity solution and all derived parameters appear to stay identical. Only the pressure diminishes by a factor 5. Based on the above calculations, it is possible to relate the shear rate G in the central region of the opposed jets device to the total flow rate supplied by the pump. Analysis of the fully developed flow in the rectangular entrance channels (Berker, 1963; White, 1974) gives a correlation between the total flow rate Q and the quasi plug flow velocity in the midplane (z = 0) of the entrances; this 2-D entrance velocity determines the shear rate G in the midplane of the cell, as determined by the simulations. Dependent on the cell thickness h, the proportionalities read

126

and

G(s·t) = 0.266 ·106 Q(m3/s)

G(s·t) = 0.118 ·106 Q(m3/s)

for h = 2 em

for h = 4 em.

(7)

(8)

In fact, the 2-D numerical simulations cannot be fully valid in a real 3-D cell. Still, in the midplane (plane of symmetry) between the flat front and back plates the 2-D simulation seems a quite good approximation, certainly on the scale of a deforming drop (I mm) in comparison with a cell thickness of 2 or 4 em.

In addition to the above computations, also the flow in the four roll mill has been analysed for a= I (plane hyperbolic flow). Dimensions, fluid properties, and velocities are comparable to those in Fig. 3. Surprisingly, the results are in disagreement with the linear flow model. For instance, the rate of elongation strongly varies along the x-axis, having its extrema quite far from the centre; consequently, it is not possible to determine a single value for G.

Equipment

Two cells were built to generate plane hyperbolic flow, both constructed of 4 solid blocks between two parallel Perspex plates. The inner volume is enclosed by 4 quarters of circles and has dimensions: radius r = 2 em, channel width b = I em, and thickness h = 2 em (prototype cell with aluminum blocks) or h = 4 em (final design with Perspex blocks). The 4 entrance and exit channels have a rectangular cross-section (I em x 4 em) over a length of 8 em and then gradually change into circular tubes, ensuring full development of the flow. The cell is positioned with its exits (x-axis) vertically, to easily get rid of any air bubbles. In one of the Perspex blocks a hole is drilled to allow for a syringe for drop injection. This hole is positioned in the midplane (z = 0) and points into one of the entrance channels, quite far from the centre of the device. A gear pump supplies a flow that is equally divided over the two opposed entrances. Using a frequency regulator and a computer the flow rate can be controlled; the maximum flow rate corresponds to a shear rate of G ~ 40 s·t. The exit flows are combined in the special control valve (discussed later) and lead into a tank from which the pump recirculates the fluid. About 1.5 liter of a model fluid is sufficient to operate the system. If the device is made suitable for molten polymers, it may be operated without a fluid tank (closed system) and with shorter and smaller tubes. The required volume of polymer melt may then be reduced to about 0.5 liter.

The centre of the cell is illuminated indirectly using a light source with a flexible optic fiber (Dolan-Jenner, Fiber Lite-3100) and a retroreflective film. The effect of the retroreflector is a more uniform distribution of the light beam, necessary to get a video image with minimal shading and optimal contrast; the contrast is only caused by the difference in refractive indices of the two liquid phases. A stereozoom microscope (Olympus SZ 4045 TR) is positioned perpendicularly to the front and back plates of the cell and magnifies the image in the range of 10 to 100 x . The microscope has a working distance of either 10 or 20 em. A colour camera (Panasonic WV CD 1301G) is mounted to the microscope which has a CCD-chip (574 (H) x 58i(V) elements; interlaced at 50 Hz . The camera signal is split: one line is lead to a VHS videorecorder (Panasonic AG 6720 E) and t e other one to an image processor (Philips SBIP; programmed for this application by Beltech, Eindhoven, The Netherlands), used for the position control of the drop (discussed later) . The real-time image (original or processed) as well as an earlier recorded tape can be displayed on a colour monitor (Philips CM 8833).

EXPERIMENTAL VERIFICATION OF THE FLOW FJELD

Laser DoPpler Anemometrv

In the prototype cell for plane hyperbolic flow (h = 2 em) the velocity field was examined using Laser Doppler Anemometry (LDA). Using a reference beam technique (Drain, 1981) with the laser beam directed parallelly to the z-axis, the velocity components u and v can be measured at any position within the flow field. Castor oil (Newtonian, with viscosity 0.7 Nsfm2) was used as a model liquid; the flow rate Q was 5.88·10·6 m3fs.

In the midplane (z = 0), at 25 y-positions the velocity proflie u(x) was scanned and likewise at 25 x-positions the profile v(y). According to the flow model, a.ll these curves should be linear. The bars in Fig. 4 indicate the length over which each of these curves is indeed linear. The total area where the flow field behaves linear (the drawn r!wmb) is even larger than expected from the numerical simulations, viz. 3 em along the axes of extension (x) and compression (y) . Figure 5 shows the variation of the velocity component v over the thickness h between the flat front and back plates. The experimental data, at different positions (x, y), coincide quite well with the parabolic fits (broken lines). Only further from the origin (C and D) the measured profiles are a little fl atter. As required, the extrema of v are linear withy and independent of x.

Fig. 4.

"' --§ >

Fig. 5.

I >,

-5

-10

-15

25

15

5

-5

-15

-25 -25 -15 -5 5 15 25

x (mm)

Region of constant shear rate determined from the length of the linear parts of the u(x) and v(y) profiles.

-25L_~--~--~--~~--~--~--~--~~

-10 -8 --6 -4 -2 0 2 4 6 8 10

z(mm)

Velocity profiles v(z) at four positions (x,y in mm): A (0, 4), 8 (-5, 5), C (0, 9), D (0, 15); the broken lines are second order polynomal fits.

Calibration of the Shear Rate

127

l<nowing that the flow field fulfills the model, experiments were performed to calibrate the shear rate as a function of the Dow rate supplied by the pump. The velocity component u linearly varies with the x-wordinate (u = Gx). Upon inte~ration it is clear that the x-coordinate of a fluid element or a passing drop increases exponentially with t1me (x = xo·exp(Gt)). So, the shear rate Gin the midplane (z = 0) can be determined by plotting the x-coordinate of a small immiscible fluid drop, which passes through the central region, on a logari thmic scale versus the time. ln the final design cell (thickness h = 4 em) droplets were traced, using video recording, at different flow rates. Figure 6 shows the results, which are expressed by

G(s-1) = 0.135 · 106 Q(m3js). (9)

This is in reasonable agreement with the numerical prediction (broken line). Deviations are thought to occur due to 3-D effects that are not included in the numerical simulations. For future drop deformation experiments, Eq. 9 seems the most reliable because the experimental method by which it was obtained is quite representative.

128 B

7

6

~ 5 ;, ~ 4 0

3

2

Fig. 6.

"

" {>~

p~ .JY

5 10 15 20 25 30 35 40 45 50 55

Q (10·6 m3fs)

Shear rate determined by following the trajectory of a passing droplet as a function of the flow rate. The solid line is a linear fit through the experiments; the broken line gives the numerical prediction (Eq. 8).

POSITION CONTROL OF THE DROP

As mentioned before, the position of the drop at the stagnation point is unstable to disturbances; the drop tends to leave the device. For studying the deformation behavior of the drop, the flow has to be adjusted to keep the drop at the centre. The way to keep the drop close to the origin, is to frequently shift the stagnation point beyond the displaced drop, forcing it to return towards the origin. Originally, the four roll mi II was used only for plane hyperbolic flow; the drops were positioned by varying the speeds of the left pair of rollers relative to those of the right pair, thus shifting the stagnation point along the x-axis. This principle of position control can be applied to all strong linear 2-D flows.

In the opposed jets device a shift of the stagnation point is achieved by variation of the ratio of the exit flow rates. For plane hyperbolic flow this is illustrated in Fig. 7.a. The two entrance flows are kept equal to restrict the stagnation point to the x-axis. Along the x- axis the stagnation point shifts to the exit with the smallest flow rate. The more the ratio of the exit flows differs from unity the further the stagnation point is shifted from the origin. By regularly adjusting the ratio of the exit flows and thus transferring the stagnation point beyond the centre of mass of the drop, the drop can be kept close to the centre of the device. In practice, the ratio of the exit flows is varied using a special valve (Fig. 7.b) in which both exits are combined to one flow. Rotating this valve increases one of the two flows and automatically decreases the other one. Thus, the rotation ~tngle of the valve is the only variable for this 1-D control problem.

Fig. 7. a. Principle of the control system for the drop posi tion in the opposed jets device; the stagnation point is shifted due to variation of the ratio of exit flows. b. The control valve, combining the two exi t flows to one that perpendicularly leaves at the centre.

129 Many researchers (Taylor, 1934; Rumscheidt and Mason, 1962; Grace, 1971; van der Reijden-Stolk, 1989) report difficulties in keeping a drop at the centre of the four roll mill. Manual control only suffices for shear rates up to about 1 s·I; therefore, for the opposed jets device a coml?uter-based control system was developed of which the sensor part is similar to that of Bentley 's (1985) control system for the four roll mill. The first step of the control cycle is the detection of the drop. An image processor grabs an image from the video camera and thresholds it, yielding a binary image representing a black drop on a white background. A contour operation is performed and the position of the drop centre is calculated as the mean of the positions of the contour pixels. Once the position of the drop is known, and thus the displacement from the centre of the device, a computer calculates the newly required position of the stagnation point and the corresponding angular position of the control valve. In the algorithm the time delay of the control cycle itself should be taken into account. Finally, a Maxon DC motor realizes the rotation of the control valve via a gear wheel reduction. A sample rate of about 25 control cycles per second results in a stable position of the deforming drop at the stagnation point; up to G "' 5 s·I, the variation in the detected drop position is typically one pixel (the theoretical minimum), corresponding to, e.g., 0.03 mm.

CONCLUSIONS

Strong linear 2-D flows (0 < a ~ 1) can be generated using the stagnation flow of two opposed jets. However, it is not possible to continuously vary the type of flow in one device because each flow type requires a different shaped cell. An opposed jets cell of only several centimeters (r = 2 em and b = 1 em; Fig. 1) is already suitable to study the deformation of a drop of the order of 1 mm.

The flow pattern in a prototype cell for plane hyperbolic flow (with thickness h = 2 em) was investigated using laser Doppler anemometry. In the midplane (z = 0) between front and back plates the flow is linear in a central region of at least 1 em along the axes. Over the z-<:oordinate the velocities and the shear rate vary almost parabolically. Consequently, a thicker device is more favourable in view of deforming drops in a midplane of known shear rate; the final design cell was made 4 em thick. Experimental calibration of the shear rate in this final cell agrees fairly well with the prediction from the 2-D simulations.

Using a special valve that combines the two ex.it flows in any desired ratio, the deforming drop can be kept near the stagnation point of the now, which it tends to leave. At high shear r.a tes a computer controlled positioning system is indispensable. For this purpose an image processor is programmed for real-time (25 Hz) detection of the drop position. Optimal illumination is crucial to obtain sufficient contrast in the image. From the detected displacement of tl1e drop, the required control action is calculated. Carrying it out, the drop is stabily positioned near the origin.

With respect to the four roll mill, conventionally used for experiments of drop deformation, the opposed jets device has a flow pattern that is in better accordance with the desired flow pattern (plane hyperbolic flow). Moreover, the opposed jets device is more suitable for studying polymer melts and viscoelastic test fluids. However, the four roll mill is more flexible concerning the generation of different types of flow, ranging from purely rotational (a= -1) to plane hyperbolic flow (a= 1).

ACKNOWLEDGEMENT

T he authors want to thank DSM Research (Geleen, The Netherlands) who contributed to the costs of most of the equipment.

REFERENCES

Acrivos, A. (1983). The breakup of small drops and bubbles in shear flows . 4th Int. Conf on Physiochemical llyd1·odynamics, Ann. N.Y. A cad. Sci., 404, 1-11 .

Bentley, B.J. (1985). Drop deformation and burst in two---dimensional flows. Ph .D. thesis, California Institute of Technology, Pasadena, California.

Bentley, B.J . and L.G. Leal (1986). A computer-<:ontrolled four roll mill for investigations of particle and drop dynamics in two-<limensionallinear shear flows. J. Fluid Mech., 167, 219-240.

Berker, R. (1963). Integration des equations du mouvement d'un fluide visqueux incompressible. In: Encyclopedia of physics (S. Fliigge, ed. ), Vol. VIII/2 Fluid dynamics, pp. 70. Springer Verlag, Berlin.

de 13ruijn, R. (1989) . Deformation and breakup of drops in simple shear flows. Ph.D. thesis , Eindhoven University ot Technology, Eindhoven, The Netherlands.

Cuvelier, C., A. Segal and A.A. van Steenhoven (1986). Finite element methods and Navier-Stokes equations. Reidel Publishing comp. , Dordrecht; Boston, Lancaster, Tokyo.

Drain, L.E. (1981). The laser Doppler technique. John Wiley & Sons, New York.

130 E:lemans, P.H.M. (1989). Modelling of the processing of incompatible polymer blends. Ph.D. thesis,

Eindhoven University of Technology, Eindhoven, The Netherlands. Fuller, G.G. and L.G. Leal (1981). Flow birefringence of concentrated polymer solutions in two-dimensionai

flows. J. Polym. Set. Polym. Phys., 11!, 557-587. Giesekus, H. (1962). Stromungen mit konstantem Geschwindigkeitsgradienten und die Bewegung von darin

suspendierten Teilchen, Teil II: Ebene Stromungen und eine experimentelle Anordnung zu ihrer Realisierun_g. Rheologica Acta, Band 2, Heft 2, 112-122.

Grace, H.P. (1971) . Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Chem. Eng. Commun., 14, 225-277.

Janssen, J.M.H. (1991) . Design and development of an opposed jets device. Internal report WFW-91.008, Eindhoven University of Technology, Dept. of Fundam. Mech. Eng., ISBN 90-5282--Q96-l.

Metzner, A.B . and A.P. Metzner l1970) . Stress levels in rapid extensional flows of polymeric fluids. Rheologica Acta, Band 9, Heft 2, 174-181.

Meijer, H.E.H. and H.L. Bos (1989). Mischen und Kneten im Einschneckenextruder. Extruder im Ext1-usionsprozess, Tagung Bamberg, 11 , 12 Mai 1989, VDI-Verlag, DUsseldorf.

Mikami, T., R.G . Cox and S.G. Mason (1975). Breakup of extending liquid threads. Int. J. Multiphase flow, £, 113-138.

MUller, A.J . , J.A. Odell and A. Keller (1988). Elongational flow and rheology of monodisperse polymers in solution. J. Non-Newtonian Fluid Mech., lQ, 99-118.

Olbricht, W.L., J .M. Rallison and L.G . Leal (1982). Strong flow criteria based on microstructure deformation. J. Non-Newtonian Fluid Mech., 10, 291-318.

Ottino, J.M. (1989). The kinematics of mixing: stretching, chaos, and transport. Cambridge University Press, Cambridge.

Ottino, J .M. and R. Chella (1983). Laminar mixing of polymeric liquids; A brief review and recent theoretical developments. Polym. Eng. and Sci., 2]_-7, 357-379.

Rallison, J.M. (1984) . The deformation of small viscous drops and bubbles in shear flows. Ann. Rev. Fluid Mech. , .l.Q, 45--66.

van der Reijden-Stolk, C. (1989). A study on deformation and breakup of dispersed particles in elongational flow. Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.

Rumscheidt, F.O. and S.G. Mason (1962) . Breakup of stationary liquid threads. J. Coil. Sci., li, 260- 269.

Segal , A. (1989). Sepran finite element package. lngenieursburo Sepra, Leidschendam, The Netherlands.

Stone, H.A., B.J. Bentley and L.G. Leal (1986). An experimental study of transient effects in the breakup of viscous drops. J. Fluid Mech., ill, 131-158.

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Separation of Dispersions

S.A.K.Jeelani and S.Hartland Department of Chemical Engineering and Industrial Chemistry Swiss Federal Insti tute of Technology,8092 Zurich,Switzerland

Abstract

131

T he behaviour of horizontal and vertical steady-state dispersions is considered. Equations for the variation in dispersion height, drop diameter and velocity for horizontal flow in box settlers are presented. The analysis is extended to include the variation in hold-up, drop diameter and relative velocity in the sedimentation zone of a vertical settler.

Keywords

Binary coalescence, drag coefficient, drop diameter, gravity settlers, hold-up, interfacial coales­cence, liquid-liquid dispersions, Reynolds number, sedimentation.

Introduction

The separation of liquid-liquid dispersions is encountered in many industrial operations such as in the recovery of th e valuable solvent after an extraction process and in the removal of immisci­ble oils in wastewater treatment before recyling the water. Another important use of immiscible liquid-liquid systems is in long distance pumping of crude oil-water mixture to give a lower effective viscosity and hence minimum friction losses than a pipe filled only with crude oil. T he two phase mixture is then separated into crude oil and water in a gravity settler. Dispersions a re usually classified into two types: (i) primary dispersions in which the drops have a diameter of about lmm or larger and settle rapidly and (ii) secondary dispersions in which the drops have a diameter of about lJ.Lm or less and take prohibitively long times to settle. It is the primary dispersions which are encountered in many indust rial gravity settlers and so are discussed below.

Industrial gravity settlers are usually horizontal cylindrical or rectangular tanks in which the liqu id-liquid dispersion is continuously fed at one end and the separated phases are withdrawn at the other end. The feed dispersion can be prevented from forming a jet by lowering its kinetic energy and providing ~n impingement baffie at the inlet thereby minimizing the disturbance to the settjjng drops and so the volume of the turbulent entrance region in the settler. The flow of dispersion in such settlers is essentially horizontal . However, there are a number of variations in the arrangement so tha.t the shape of the settlers and their lay-out is not standardized. Vertical cyl indrical or rectangular gravity settlers in which the dispersion is continuously fed from the side and the separated phases are withdrawn from the top and bottom are some t imes used in pilot plant experiments. T hese settlers involve essentially vertical flow of dispersions. Varia­tion in the geometrical design and operating conditions such as the physical properties of the liquid-liquid system, and the drop size, kinetic energy, volume throughput and location of the

132

feed dispersion can result in complicated flow of the dispersion in the settler which is neither horizontal nor vertical. In this paper equations which describe the spatial variation in hold-u p, droplet diameter and velocity in horizontal and vertical settlers are presented.

Horizontal settlers

The analysis of box gravity settlers in which the dispersion flow is essentially horizontal is com­plicated due to the fact that the dispersion throughput and height, the rlroplet diameter and velocity all vary along the settler length. Epstein and Wilke (1963), and Sweeney and Wilke (1964) found experimentally that for an unbaffled feed increasing the inlet velocity strongly in­creases the dispersion volume in the box gravity settler. The droplet velocity in the dispersion is then much higher than those of the individual separated phases. In contrast Drown and Thom­son (1977) found the droplet velocity to be much less than those of the individual separated phases. Jeffreys et a.l. (1967 ,1970) presented stage-wise and differential models relating the variation in the drop diameter, dispersion thickness and the number of drops flowing along the length of a wedge shaped dispersion allowing for binary and interfacial coalescence and assuming constant droplet velocity. This was further pursued by Vijayan and Ponter (1976). However, in practice, the droplet velocity decreases along the settler length and the dispersion thickness , which has a finite value at the settler exit, varies non-linearly. These are allowed for in the analysis discussed below.

When a dispersion formed in a mixer is continuously fed into a box gravity settler (Figure 1), the volume of the dispersion increases with time until the constant steady-sl <ttC' \·alue is reached for a given dispersion t hroughput. The steady-state volume of the dispersion band increases with the specific dispersed phase throughput. At steady-state drops entering the dispersion band undergo binary coalescence while moving both vertically and horizontally due to sedimentation and bulk flow and finally coalesce with the bulk homophase at the coalescing int-erface. vVhen the volume rate of flow of the dispersed phase per unit settler width Qdo is small , a dispersion band of variable thickness in which the interface between the phases is only partly covered by the drops is obtained. As Qdo is increased the dispersion band extends over the entire area of the interface. Thus the height of the dispersion band decreases with the length of the settler becoming zero or finite at the exit of the settler. Further increase in Qdo leads to the formation of a deep-layer dispersion of uniform thickness.

Interfacial coalescence

In the differential element of length dl, the decrease in the volume flow rate of the dispersed phase per unit settler width dQd must equal the volume rate of coalescence at the coalescing interface per unit settler width 'if;;dl (Hartland and Vohra, 1978) so that

'if; dQd 2/iEitPi

i = -dt = 3r;cosB (1)

where 'if;; is the specific volumetric interfacial coalescence rate, r; is the time taken by drops of diameter ¢; = ¢to coalesce with the coalescing interface where E; is the dispersed phase hold-up frac tion and /i is a shape factor which allows for the non-sphericity of the drops.

The interfacial coalescence timer; in dense-packed dispersions can be written (Jeelani and Hart­land, 1985) as

¢ Ho r; = r;o( ¢;~)(H) (2)

where r;0 is the interfacial coalescence time for drops of diameter ¢a and dispersion heigh t Ho at the entrance of the settler. Equation (1) thus becomes

Contln~WUS ,,_ I>Up<n<d .....

------1. Sepanltd ('Onlinuous pbuc

Fig. 1. Schematic variation in dispersion height H along the length I of a box settler.

0 ::r::

' 0~~~-===~===-~~~~~~~ ::r::

0 ::r::

L .6 . 8 1.0

Fig. 2. Variation in (flo- H )/(Ho- HI) with fractional distance L from entrance of a box settler wil h P as parameter.

133

134

dQd H 1/J; = -dt = 1/J;0 sec8(H

0) (3)

where 1/J;o = 2!;€;1/>o/3r;o is the specific interfacial coalescence rate at the entrance of the settler.

Binary coalescence

In general the number of drops flowing per unit time per unit settler width N, the volume rate of flow of dispersed phase per unit settler width Qd, the specific interfacial coalescence rate 1/J;, the drop diameter q,, the height of the dispersion H and the angle of inclination of t he coalescing interface with the horizontal 8 vary with distance l along the length of the settler. A volume flow balance in terms of the number of drops flowing per unit time per unit settler width and the drop diameter in a differential element of length dl located at distance l from the inlet gives

~ dif> + _!_ dN + 4!;€; = O q, dl N dl 7r N T;lj>2 cos(}

Similarly a number balance on the drops in this differential element yields

dN

dl

( 4)

(5)

where € is the dispersed phase hold-up fraction in the dispersion and rb is the binary coalescence time for drops of diameter if>.

Combining the preceeding two equations gives the increase with distance l along the length of the settler in drop diameter 4> due to binary coalescence which is independent of the interfacial coalescence as

dq, - __.1!_ df - 61"/,V

(6)

which was previously derived by Jeelani and Hartland (1985) where v = Qd/€H is the drop velocity in the dispersion.

The binary coalescence time 10 for drops of diamter q, = if>; is shown (Jeelani and Hartland, 1985) to be given by

q, Tb = rbo 4>o (7)

where 100 is the binary coalescence time corresponding to the drops of diameter 4>0 at the en­trance of the settler.

Variation in dispersion height along the settler length

The turbule nce in the feed dispersion entering the settler will, however, cause the dispersion height to increase followed by a natural decrease in dispersion height due to the subsequent interfacial coalescence. The variation in dispersion height H with distance l from the inlet of the settler can thus, in general, be represented by the quadratic equation

H = Ho(1 + cxL + /3£"2 ) (8)

where ex or f3 is negative and L = lfl, for a dispersion band of length 1,. If H 1 is t he dispersion height at L = 1 and H m = Jd H dL = H0 ( 1 + 0.5cx + 0.33(3) is the mean dispersion height , then

135

a= 2(3Hm- 2Ho- HI)IHo (9)

f3 = (HI I Ho) - a- 1 = 3(Ho + H1 - 2H m)l Ho (10)

The equations (8), (9) and (10) for the variation in the dispersion height H with length L can be rewritten as

(Ho- H) = (1 + P)L2 - PL (Ho- HI)

involving only one parameter P = 2[1- 3(Ho- Hm)I(Ho- HI)].

(11)

Figure 2 shows the variation in ( Ho - H)I(Ho- HI) with distance L from settler entrance for different values of the parameter P obtained using equation (11). Positive or negative values of P correspond to whether (Ho - Hm) is smaller or greater than (Ho- H!)l3. It can be seen that for a given positive value of P , (Ho- H)I(Ho- HI) decreases with L from an initial value of zero until a minimum value of -P2 14(1 + P) is reached when L = Pl2(1 + P), increasing thereafter and atta.ining again a value of zero when L = Pl(1 + P). It then becomes positive and increases until it finally attains a value of unity at the exit of the dispersion band when L = 1. Decreasing the value of P decreases (Ho - H)I(Ho- H1) and the values of the length L at which the minimum and zero values of the ordinate occur, the latter two values occuring at the origin when P = 0 corresponding to Hm = (2H0 + H1 )13. In contrast for negative values P, it can be seen that (H0 - H)I(Ho- HI) increases with L from an initi~l value of zero until a maximum value of -P2 14(1 + P) is reached when L = Pl2(1 + P), decreasing thereafter and attaining directly the final value of unity when L = 1. Decreasing the value of P increases the value of (Ho- H)I(Ho- HI) and decreases the value of L at which the maximum value of the ordinate occurs.

For a partially covered interface, H 1 = 0 and equation (11) reduces to

HI Ho = 1 + P L- (1 + P)L2 (12)

Since HI Ho is positive, the minimum value of the parameter P = a = 2(3H ml Ho - 2) is -2. The maximum value of Pis usuaUy about 2 corresponding to a value of 1.33 for the ratio of the maximum to initial dispersion heigl1ts. Figure 3 shows the variation in HI H0 with L with Pas parameter obtained using equation (18) . For a given positive value of P = a, the ratio HI Ho increases from an initial value of unity until a maximum value of 1 + P2 14(1 + P) is reached at L = Pl2(1 + P), thereafter decreasing to a value of zero at L = 1. Increasing the value of P increases the ra.tio HI Ho and the settler length L at which the maximum dispersion height occurs. In contrast, for a given negative value of P = a, the dispersion height monotonically decreases with settler length L without undergoing any maxima.

Variation in throughput, droplet velocity and diameter

In order to obta.in the variation in throughput along the settler length, it is necessary to know the angular inclination and height of the coalescing interface. Since tan (J = - dH ldl = - lfo( a+ 2f3L )lis is small, sec (J is approximately given by (1 + 0.5 tan2 (}) so that

H2 sec(}= 1 + 0.5 12° (a 2 + 4af3L + 4/32 L2

) $

(13)

Equation (3) can then be integrated from L = 0 to L to give the variation in the volume rate of flow of dispersed phase per unit settler width Qd with distance L from the dispersion feed as

(14)

136

1. 4 .

L

Fig. 3. Variation in dimensionless dispersion height H / Ho with fractional distance L from ent rance of a box settler in which the interface is partiaUy covered with parameter P ( -2 to 2: increment 0.4).

L

Fig. 4. Variation in Y with fractional distance L from entrance of a box settler in which the interface is partially covered for the range of P shown in Fig. 3.

137

when (Ho/1,)2 is small. Since Qd = 0 at L = 1, 1/!;o = QdoHofi,Hm so that equation (14) becomes

Ho 2 Qd = Qdo[1 - H m L(1 + 0.5aL + 0.33,BL )) (15)

The variation in droplet velocity v = Qd/fH with distance Lis given by

vo Ho 2 v = (1 + aL + ,BL2)[1- Hm L(1 + 0.5aL + 0.33,BL )) (16)

where vo = Qdo/fHo is the droplet velocity at the entrance of the settler.

The variation in drop diameter ¢with distance L can now be obtained by integrating equation (6) using equations (7) and ( 16) as

</>oi, Hm [ Ho ( 2) ¢ = ¢o- (6

H )In 1--11

L 1 + 0.5aL +0.33,BL ) 7),QVQ 0 m

Expa.nding the logarithmic term and neglecting the higher order terms gives

I 1> = ¢o[l + (-'-)L(l + 0.5aL + 0.33,BL2

)) 67bovo

( 17)

(18)

For a partia.lly covered interface, equations (15), (16) and (18) for the dispersed phase flow rate, droplet velocity a.nd diameter can be represented by the single equa.tion

Y = L + [0.5P- 0.33(1 + P)LW

in which the values of Y are given respectively by

Y = (1 - ~)(Hm) Qdo Ho

Y = (1 _vH)(Hm) voHo Ho

y = (1.. _ 1)(6TbQVQ)

¢o I,

(19)

(20)

(21)

(22)

The variation in the modified dispersed phase flow rate, droplet velocity and diameter Y with L is shown in Figure 4 for a partially covered interface corresponding to the variation in dispersion height shown in Figure 3. For a given value of P =a, Y increases from an initial value of zero to a final value of (P+4)/6 at L = 1. For positive values of P, the slope dY fdL = 1 +P L - (P+ l)L2

increases from an initial value of unity at L = 0 to a valueofl+P2 /4(P+ 1) at L = P/2(P+1), thereafter decreasing to a value of zero at L = 1. For negative values of P, the slope monotoni­cally decreases with L without any inflection point.

The droplet velocity v given by equation (19) becomes indeterminate but according to L'Hospitals' rule the velocity v falls to zero at the end of the dispersion when L = 1.

Effect of entrance region

As explained earlier, there is usually a turbulent entrance region adjoining the dispersion inlet port, the length le of which depends on the velocity of the inlet dispersion, the diameter of the inlet pipe, the physical properties of the liquid-liquid system and the presence or absence of baffles at the feed dispersion . The length of this region can be minimized by employing efficient baffles. Drown a.nd Tl10mson (1977) empirically related the length of the entrance region le (which is the distance from the entrance port where circulatory flow caused by the dispersion

138

X

Fig. 5. Variation in dimensionless dispersion height H / H c with fractional distance X measured from the exit of the tu rbulent entrance region in a box settler with parameter p (0.1 to 1: increment 0.1).

X

Fig. 6. Variation in Z with distance X measured from the exit of the turbulent entrance region in a box se ttler for the range of p shown in Fig. 5.

139

feed jet ceased to exist) to the dispersion feed velocity u; and pipe diameter d; in an unbaffied settler by

{ifiiJ;;: 1. = 1.7u;d; V----;;- (23)

where a is the interfacial tension and Pm is the mean density of the dispersion.

It has been observed experimentally (Jeffreys et al., 1970) that the droplets in the entrance region usually underwent no coalescence but rearranged themselves to form a stable packing. The dispersion height in the entrance region usually increases with distance until a maximum is reached and decreases once the dense-packed region is formed. When the maximum disper­sion height He occurs at the end of the entrance region, differentiating equation (6) and setting dHidL = 0 at L = Le gives

L- -~ e - 2{3 (24)

The equation (8) for the variation in dispersion height with length X = (L- L.)l(1- L.) then becomes

H 2 - = 1-pX He

(25)

where p = -{JH0(1- Le)2 I He is the only parameter. The constants Ct and {3 can be shown to be given by

_ 2(He- Ho)[ He - Jf1 ]

et- Ho 1 + He - llo (26)

{3 = l + (H1- 2He) _ (He - Ho) JHe- H1

Ho Ho He - Ho (27)

The equation given below can be derived following the analysis presented in the beginning of this section:

Z = X(l - 0.33pX2) (28)

in which the dispersed phase flow rate, droplet velocity and diameter are given respectively by

(29)

(30)

(31)

Figure 5 shows the decrease in the fractional dispersion height HI He with fractional distance X with parameter p obtained from equation (25). For a given value of p, HI H. decreases from an initial value of unity to" va lue of Hd He= (1- p) at the exit of the dispersion. The dispersion height at the exit of the dispersion band strongly decreases as p increases, becoming zero when p = 1. Since HI He is positive, the maximum value of pis unity. The variation with X in Z representing the modified dispersed phase flow rate, and droplet velocity and diameter is shown in Figure 6 for the same range of values of the parameter p as given in Figure 5. For a given value of p, the ordinate Z can be seen to increase with the fract iona.J distance X attaining a value of (1 - pl3) at the exit of the dispersion band.

140

Table 1: Parameters for disEersions in box settlers. Run Qdo fF Ho L. Ct (J Vo Bo 81

cm2/s em em em/s Present data : Agitation s12eed: 5s- 1

1 0.61 0.49 2.6 35.6 0.412 -1.412 0.235 -1.7 10.0 2 0.72 0.50 3.1 42.5 0.096 -1.096 0.232 -0.4 8.7 3 0.92 0.50 4.2 49.7 0.133 -1.133 0.219 -0.7 10.3 4 0.42 0.50 1.9 22.3 1.859 -2.859 0.223 -8.9 18.0 5 0.56 0.50 2.5 27.6 1.269 -2.269 0.220 -6.7 16.7 6 0.83 0.50 2.9 31.0 1.505 -2.505 0.290 -8.0 18.0 7 1.11 0.50 3.3 38.4 1.692 -2.692 0.336 -8.3 17.7 8 1.39 0.50 5.5 34.4 0.277 -0 .934 0.253 -2.5 14 .3 9 2.08 0.50 6.9 34.4 0.581 -1.024 0.302 -6.7 16.4 10 2.78 0.50 8.4 34.4 0.355 -0.587 0.332 -4.9 11.3 11 3.61 0.50 13.0 34.4 0.758 -0.707 0.277 -16.0 14.0 12 0.42 0.33 2.2 23.0 1.093 -2.093 0.191 -5.9 16.4 13 0.56 0.33 2.9 28.5 0.389 -1.389 0.194 -2.3 13.6 14 0.69 0.33 2.7 31.7 1.700 -2.700 0.258 -8.2 17.5 15 0.83 0.33 3.3 35.5 1.204 -2 .204 0.251 -6.4 16.7 16 0.28 0.25 1.8 22.9 1.720 -2.720 0.157 -7.6 16.1 17 0.42 0.25 2.3 27.6 1.468 -2.468 0.182 -7.0 16.1 18 0.56 0.25 2.9 32.2 1.134 -2.134 0.193 -5.8 15.7 19 0.69 0.25 3.3 34.3 1.027 -2.027 0.209 -5.7 16.3

Agitation s12eed: 5.83s- 1

20 0.56 0.50 2.1 25.4 0.817 -1.817 0.262 -3 .9 13.2 21 0.83 0.50 2.4 29.0 1.328 -2.328 0.343 -6.4 15.6 22 0.56 0.33 2.1 26.1 0.586 -1.586 0.262 -2.7 11.9 23 0.69 0.33 2.6 29 .8 0.779 -1.779 0.271 -3.8 13.4 24 0.83 0.33 3.0 33.7 0.919 -1.919 0.282 -4 .6 14.4 25 0.42 0.25 1.7 26.0 1.215 -2.215 0.241 -4.6 12.1 26 0.56 0.25 2.3 29.8 0.609 -1.609 0.245 -2.7 11.3 27 0.69 0.25 2.9 33.6 0.496 -1.496 0.236 -2.5 12.3

Vijayan and Ponter (1976): Agitation speed: 3.33s- 1

1 1.03 0.50 1.6 18.1 1.006 -2 .006 0.652 -5.0 14.8 2 1.33 0.50 1.9 23.0 0.346 -1.346 0.698 -1.7 11.0 3 1.67 0.50 2.0 28.6 0.256 -1.256 0.819 -1.1 9.1

Agitation s,eeed : 4.16s- 1

1 1.03 0.50 1.8 31.5 -0.371 -0.629 0.583 1.2 5.2 2 1.33 0.50 2.2 34.1 -0.295 -0.705 0.622 1.1 6.1 3 1.67 0.50 2.2 34.7 0.134 -1.134 0.763 -0.5 7.7

Epstein and Wilke (1963): 2990* 2.27 0.20 3.8 79.5 -1.693 0.693 0.598 4.6 0.8 3620* 2.27 0.20 4.5 91.2 -1.448 0.448 0.509 4.0 1.6 4470* 2.27 0.20 5.2 121.9 -1.557 0.614 0.438 3.8 0.8

* Reynolds number of dispersion through inlet pipe.

141

Figure 7 shows the experimental (symbols) variation in dispersion height H with distance l from the settler entrance at constant feed hold-up fF = 0.5 and impeller speed of 5 s-1 at different throughputs for the present data compared with that predicted (line) by equation (8) using the best fit values of o and fJ listed in Table l. It can be seen that when the dispersed phase throughput Qdo is less than 1.11 cm2 js, the dispersion height increases along the settler length until a maximum is reached and then decreases to zero at the end of the dispersion band. Present and published experimental data referred to in Table 1 on dispersion bands with zero thickness at the settler exit indicate that o is positive when a maximum exists in the variation in dispersion height while it is negative when no maximum exits as predicted by the theory. The box settler, liquid-liquid system, experimental set-up and the procedure in the present work are identical to those used earlier by Jeelani and Hartland (1988).

The agreement between the experimental (symbols) variation in the ratio of the droplet velocity vfvo and drop diameter <1>/<l>o with L and that predicted (lines) by the model equations (19), (21) and (22) using the values of o and fJ listed in Table 1 and the best fit values of TbQ (7.6, 56.8 and 40 s) for the runs 1, 2 and 3 shown in Figure 8 is good inspite of the simplicity of the model.

Vertical settlers

As explained in the Introduction, vertical flow of the dispersion is encountered in the disen­gaging sections of extraction columns and continuous settlers used in pilot plant experiments. These settlers usually contain sedimentation and dense-packed zones. The ,-,~riation in the drop diameter and hold-up with vertical distance in the sedimentation zone is complicated by the cir­culation of the phases. This is because drops simultaneously undergo sedimentation and binary coalescence in this zone unlike the dense-packed dispersion considered previously (Jeelani and Hartland, 1986) in which no sedimentation o•ccurs but only binary coalescence takes place. This is further complicated by the kinetic energy, geometry and location of the feed dispersion port. However, it is possible to predict theoretically the variation in drop diameter and hold-up with vertical distance in the sedimentation zone under plug flow conditions when no circulation of the phases occurs.

Consider a vertical steady-state dispersion of height H shown in Figure 9 in which the dis­persed ph.ase volumetric flow rate per unit area is Qd· Let Hs and Hp be the heights of the sedimentation and dense-packed zones. The vertical distance measured from the plane at which the dispersion enters is x, so that at x = 0 the drop diameter is </>o and the dispersed phase hold-up fraction is <o. The drops are assumed to move in plug flow through the dispersion so tha t the drop size is constant at any cross-section . At a distance x the volumetric flow rate of the dispersed phase per unit area qd can be written in terms of the flow rate of the number of drops per unit area N and the drop diameter </> so that Qd = 1r N </>3 /6. Since Qd is constant throughout the dispersion, differentiation of this equation and separation of the variables leads to

1 fJN 1 8</> - 3NBx = ~ax (32)

This equation can also be derived from a volumetric flow balance over the differential element dx shown in Figure 9.

In the differential element dz shown in Figure 9, the rate of decrease in the number of drops by binary coalescence is 3<dx/7r</>3r,, which must be equal to (-8Nj8x)dx, so that

(33)

where the binary coalescence timer, is in general a function of the drop diameter and hold-up.

142

E 0

1 lj l I I

10

Fig. 7. Experimental (symbols) variation in dispersion he.ight H with distance I from the entrance of a box settler for runs 4 to lllisted in Table 1 (triangles represent run 4) compared with those predicted (full lines).

7

_,/4< o: .0 ____ ,-

,<!:>---

3. 5:

3. 0:

2. s:

L

Fig. 8 . Experimenta.l (symbols) variation in dimensionless velocity vfv0 and drop diameter <I>/ <Po with fractional distance Lin a box settler for the runs 1 to 3 (Table l ) in box settler in which the inte rface is partially covered compared with those predicted (full and broken lines) by t he model.

143

Substitution of this in equation {32), when expressed in terms of tj> and Qd, yields

1 8¢ 4> ax 6Qd10

(34)

which was derived by Vohra and Hartland (1979) who integrated this equation, assuming Tb and f to be constant. The last equation corresponds to equation (6) for horizontal !low in which Qd = w = Qd/ H varies with dispersion length. The a bove equations are general and can be applied for both sedimentation and dense-packed zones which have different hydrodynamic con­ditions and hence different variations in </>, f and Tb.

Equation {34) can in principle numerically be solved to obtain the variation in the drop diameter and hold-up with vertical distance x for the sedimentation zone knowing the variation in the binary coalescence time ry, and using the sedimentation equation (Kumar and Hartland , 1985)

24 cd = o.53+­

Re (35)

where Re = PcVstP/J.Lc is the Reynolds number and cd 4l:.pgtj>(1- f)/3Pc(1 + 4.56fn)v; is the drag coefficient. However, an analytical solution can be obtained when the flow regime is laminar as is usually the case in practice since the sedimenting drops are small. The velocity v. of drops relative to the continuous phase flowing cou ntercurrently when no circulation of the phases occurs is given by

V _ ~ + _Q_c __ ..!.:qd'-"-[1_+~(R_-_1_,_)_,_f] s - f (1 - f) - f(1 - f)

(36)

where R is the ratio of the volume rate of flow of the continuous phase per unit a rea. qc to that of the dispersed phase qd. Since for laminar flow regime equation (35) reduces to Cd = 24/ Re, the drop diameter tj> can be written as a function of the hold-up f as

q,2 = 18J.Lcqd [1 + (R + 3.56)f + 4.56(R- 1)f2]

l:.pg €( 1 - f ) 2 (37)

The actual value of n. in equation (35) is 0.73 but is assumed to be equal to unity since this has been shown to have negligible effect on the rate of sedimentation by Jeelani et a! . (1990). Differentiati ng equation (37) with respect to x, combining with equations (34), {36) and (37), and integrating with the bounda.ry condition that E = fo when x = 0 gives

._ 3 1 [(f)R+s.s6(1-fo)2(1+4.56fo)4.56(1+(R-1)Eo)R-l] 3 (1 1) X - qdrb n - -- - qdrb - - -

Eo 1 - f 1 + 4 .56€ 1 + ( R - 1 )E fo f (38)

when the binary coalescence time Tb is constant. Since usually fo is equal to the feed hold-up fF = 1/(R+ 1), the variation in hold-up f with the vertical distance x in the sedimentation zone can be predicted from the above equation for given values of qd, Rand Tb· Alternatively, knowing the binary coalescence time Tb, the height of the sedimentation zone H, can be predicted from the above equation when applied a.t x = H.:

H s = 3qdrb In[( .:.~f+S 56( 1 - fo )2( 1 + 4.56 Eo )4.56( 1 + ( R- 1)Eo )R-1 J - 3qdrb( 2_ - 2_) (39) Eo 1 - f, 1 +4.56f3 1+(R-1)E3 fo f,

where E, is the dispersed phase hold-up at the boundary between the sedimentation and dense­packed zones which is usually equal to 0.74 corresponding to the close-packed spheres. Dividing these two equations eliminates the unknown binary coalescence time Tb a.nd gives f/fs implicitly as a function of xjH,. Figure 10 shows the variation in normalised hold-up fjf, with fractional vertical distance xj H, predicted by equations (38) and (39) with R as parameter using fs = 0.75 and fo = 1/(R + 1). The hold-up increases almost linearly with the vertical distance even when the flow ratio R is as high a.s 5 and can be approximately represented by the explicit equation :

Coalesced disp<rsed phaso

i [I

N+ ClNdx <ll+ oclldx C!x ' C!x

E + 2fdx j ax

N <!l T E

No 4>o Eo

l

H

1

Fig. 9. Notation for a steady-state vertical

dispersion with the l.ighter phase dispersed.

10

0. -~,I I I I I I I I I I! I I' 0 ' 2 . 4 . 6

X/H s

Fig. 10. Variation in normalised hold-up €/€9 with fractional vertical distance xfHs in sedimentation zone of a steady-state vertical settler with R as parameter predicted by equations (38) and (39) when €9 = 0.75.

Fig. 11. Variation in fractional drop diameter <!>/</>, with fractional vertical distance x /H. in sedimentation zone of a steady-state vertical settler with R as parameter predicted by equation (37) for the variation in hold- up shown in Fig. 10.

145

1 X

3(R + 1) [4 + (3R- 1) H,] (40)

The variation in fractional diameter of drops¢;/¢;, with fractional vertical distance xf H, in the sedimentation zone obtained from equation (37) with R as parameter is shown in Figure 11 cor­responding to the va riation in hold-up shown in Figure 10. For values of R upto 5, the hold-up profiles may be predicted using the linear variation in E/ Es with x fH, given by equation (40). The value of the drop diameter <Ps at the boundary between the sedimentation and dense-packed zones is also obtained from equation (37) when E = E, = 0.75. The variation in drop size and hold-up in the dense-packed zone was obtained by Jeelani and Hartland (1987).

References

Drown, D.C. and W.J. Thomson (1977). Fluid mechanic considerations in liquid-liquid settlers. lnd.Eng.Chem.Process Des.Dev., l.fi, 197-206.

Epstein, A.D. and C.R. Wilke (1963). Mechanism of liquid-liquid settling. University of Cali­fornia Radiation Laborat0171 Report No . UCRL-10625.

Hartland,S . and D.K. Vohra (1978). Koaleszenz in Vertikalen Dicht-Gepackten Dispersionen. em Chem.Ing.Tech., .5_0, 673-682.

Jeelani, S.A.K. and S. Ha rtland (1985). Prediction of steady-state dispersion height from batch settling data. A!ChE J., .ll, 711 -720.

Jeelani, S.A.K . and S. Hartland (1986). Variation in drop size a nd hold-up in a dense- packed dispersion . Chem.Eng.Process., 2.(), 271-276.

Jeelani, S.A.K. and S. Hartland (1988) . Design of horizontal liquid-liquid gravity settlers. Proc.lnt.Sol.Extr.Conf., !SEC 88, Moscow, 1,.

Jeelani, S.A.K. , A. Pandit and S. Hartland (1990). Factors affecting the decay of batch liquid­liquid dispersions. Can.J.Chem.Eng., 68, 924-931.

Jeffreys, G.V., D.V. Smith and K. Pitt (1967). The analysis of coalescence in a laboratory mixer-settler extractor. lnst.Chem.Engr.Symp.Series No. 26, 93-98.

Jeffreys, G.V., G.A. Davies and I<. Pitt (1970). Part I-Rate of coalescence of the dispersed phase in a laboratory mixer settler unit; Part II-The analysis of coalescence in a continuous mixer-settler system by a differential model. AIChE J., 1.2, 823-831.

Kumar, A. and S. Har tland (1985). Gravity settling in liquid-liquid dispersions. Can.J.Chem.Eng., QJ, 368-376.

Sweeney, W.F. and C.R. Wilke (1964). University of Cailfornia Radiation laboratory Report No. UCRL-11182.

Vijaya n, S. and A.B. Ponter (1976). Drop-drop and drop-interface coalescence rates for a liquid­liquid dispersion in a gravity settler. Tenside Detergents, 1.3., 193-200.

Vohra, D.K. and S. Hartland (1979). Coalescence in vertical close-packed liquid-liquid disper­sions. Indian Chem.Eng., 21, 27-34.

146

147

THE DYNAMIC STABILITY OF W/0 EMULSIONS PREPARED FROM VEGETABLE OIL.

F. GROENEWEG, F. van VOORST VADER and W.G.M. AGTEROF

Unilever Research Laboratorium, P.O.Box 114, 3130 AC Vlaardingen, The Netherlands.

ABSTRACT

The dynamic stability of 50% W /0 emulsions prepared from vegetable oil was measured as a function of the concentration of the emulsifier monolinoleylglycerol. Four concentration regimes were detected . Homogeneous emulsions could not be made at very low concentrations, while homogeneous emulsions with a relatively slow rate of coalescence were obtained at about 0.2% emulsifier. Coalescence became faster when the concentration was increased above about 0.5 %. Finally the emulsion became stable above about 2% (the CMC). These results can be explained by a model for the 'coalescence rate that accounts for: the hydrodynamics of the rate of approach of the droplets, the van der Waals force, an additional attractive force and hindered film drainage because of the adsorbed emulsifier molecules.

KEYWORDS

Emulsion stability, coalescence, monoacylglycerol, emulsification, drainage, film stability, emulsifier, destabilization.

INTRODUCTION

Margarine and halvarine are emulsions of water droplets in vegetable (triacylglycerol) oil. Their stabilization must allow processing and storage, while these emulsions should destabilize quickly in the mouth. To satisfy these requirements a combination of fat crystals and soluble emulsifiers is commonly used. Evaluation of their respective contributions to the stabilization is difficult however: during production the crystallization and emulsification processes occur simultaneously and influence each other, while in addition the temperature and the agitation changes.

To unravel the emulsification process, model experiments were performed in which the oil phase was crystallized first, while the water was emulsified subsequently at constant temperature. The droplet diameter was monitored continuously by light reflection. This allowed the determination of the rate of coalescence during emulsification as a function of the concentration of the emulsifier. Trends in the results will be explained by an approximate model.

EXPERIMENTAL

Materials

Tristearoylglycerol (the fat crystals) and monolinoleylglycerol (the emulsifier) were synthesized. Doubly distilled water was used. The dye methylene blue was ex Baker Chemicals. Sunflower seed oil was used as triacylglycerol oil. It was treated with silicagel 60, ex Merck, to remove surface active impurities.

148

Preparation of emulsions

Emulsification was performed in a thermostatted vessel with an inner diameter of 6.8 em, provided with a wire stirrer, which is very effective for emulsification.

The 50% W/0 emulsions without or with I% tristearoylglycerol crystals contained various concentrations monolinoleylglycerol in the purified sunflower seed oil (concentrations of the emulsifier or fat crystals are expressed in wt % on the oil). The water phase was coloured by the addition of methylene blue (50 mg/1), resulting in blue emulsions . The tristearoylglycerol was crystallized in the absence of the emulsifier. When the crystallization was complete the emulsifier was added and after a short equilibration time the aqueous phase was emulsified at 23 °C. The rate of coalescence was obtained by monitoring the average droplet diameter as a function of time after a decrease of the rotational speed of the stirrer from 1200 to 600 rev./min.

Characterisation of emulsions

Average droplet diameters were derived from reflectance measurements, on the basis of the principle, that a coarse emulsion with a blue water phase will be rather intense blue, while a fine emulsion will be less blue or even nearly white. When red light is reflected by the emulsion, a coarse emulsion will reflect less light than a fine emulsion. This technique was previously applied on emulsion batches in a spectrophotometer cell (Lloyd, 1959; Lucassen-Reynders 1962). In the present investigation this technique was adapted for use during emulsification: the intensity of a beam of red light reflected by the stirred emulsion through a plane window of glass in the vessel was monitored. Average droplet diameters were derived from the reflectance values by calibration against various stabilized emulsions . The average droplet diameters of these reference emulsions were determined microscopically.

RESULTS

Four emulsification regimes could be distinguished pertaining to certain monolinoleylglycerol concentration ranges. Homogeneous 50% W/0 emulsions could not be made in the low concentration range of about 0 - 0. 1% monolinoleylglycerol, as large volumes of water were swirled through the emulsion. The upper limit of this concentration range was not very sharp: when the emulsifier concentration was further increased, the emulsions became gradually less inhomogeneous .

The second concentration range, in which homogeneous emulsions were obtained during stirring, extends from 0.2 to 0.4% monolinoleylglycerol. This concentration range was below the CMC, the films between the droplets were not stable and emulsions without fat crystals slowly destabilized when stirring was stopped . However, for emulsions containing fat crystals it was observed that when the homogeneous emulsions were made, the fat crystals were able to stabilize the emulsion when stirring was ceased. These emulsions were stable for weeks .

The third concentration range, in which the rate of coalescence strongly increased , starts at concentrations above about 0.5% monolinoleylglycerol. Fig . I shows two characterist ic examples of the increase in average droplet diameter when the rotational speed of the stirrer was decreased from 1200 to 600 rev./min. At 0.32% monolinoleylglycerol the average droplet diameter increased very slowly, while this increase was much faster at 0.7%.

From the graphs in Fig . I half-value periods for the coalescence process were determined. Fig. 2 shows that coalescence -becomes faster above about 0.5% monolinoleylglycerol and that a similar effect occurs in the absence of fat crystals. The difference between these two lines indicates that the fat crystals contribute to the stabilization because they increase the half-value period for coalescence. This concentration range with increased rate of coalescence is characteristic for emulsions containing vegetable oils and is absent when paraffin oil is used as oil phase.

149

diameter (I'm) half-value period (min)

4.-=-------~-------,--~~--,

0:0 0 G)

20 3

2

1 o/o crystals

. \. ~ ..

no crystals '-... j 0 --·--.. 0.1 10

5o~--------5L-------~1L0--------~15.

time (min)

Fig. I . Rate of coalescence for emulsions containing I% fat crystals and 0.32% or 0 .7% monolinoleylglycerol.

concentration (% w/w)

Fig. 2. Half-value periods for coalescence at various concentrations of monolinoleylglycerol.

The fourth range involves concentrations above the CMC (~ 2%): these emulsions were intrinsically stable and half-value periods for coalescence could not be measured because the half­value periods became extremely long.

The destabilization phenomenon in the third regime was rather remarkable and was therefore investigated further. The results of this investigation can be summarized as follows:

- Emulsions with about I% monolinoleylglycerol but without fat crystals showed a fast destabilization into an oil phase and an aqueous phase when stirring was stopped. Fat crystals were, however, able to stop this destabilization shortly after ceasing stirring;

- Emulsions containing fat crystals had a different appearance when the monolinoleylglycerol concentration was above about I%. Such emulsions had a strongly increased viscosity and they were strongly flocculated , as was observed visually when pouring the emulsion. The emulsion appeared to be no longer homogeneous but it contained small clusters. The strong flocculation was also observed microscopically;

- The interaction between droplets of stable emulsions without fat crystals can be determined microscopically at concentrations above 2% monolinoleylglycerol. To this end, a very coarse 1% W/0 emulsion was observed microscopically. Two drops in contact with each other will be nearly spherical when only the van der Waals attraction is present. This was actually observed with e.g. decane as oil phase. However, with sunflower seed oil the droplets were strongly deformed. The contact angle between the film and the spherical part of the droplet was about 50°, showing that the attractive forces between the droplets were about 34 times as large as the van der Waals force. A contact angle of even 70° has been observed with Span 80 (monooleylsorbitan) in triacylglycerol oil (J .Lucassen, private communication). Large contact angles were also observed by Van Voorst Vader and Bak (1990) and by Princen (1984). The origin of this additional attractive force will be discussed below.

The above observations suggest that there is a strong attractive force between the droplets when the monolinoleylglycerol concentration is above about I%, resulting in a strong flocculation.

150

Below the CMC this leads to a fast coalescence as the films are not stable, while above the CMC, where the film are intrinsically stable, the flocculation will not lead to coalescence. As mentioned before, this effect is specific for vegetable oil: the additional attractive force is considerably less for paraffin oil. In that case regime 3 is not observed and there is a continuous transition from regime 2 to 4.

To understand the origin of the four regimes, a coalescence model will now be presented.

THE COALESCENCE MODEL

Qualitative discussion of the model

The coalescence frequency is defined as the number of coalescences per droplet per second. It is determined by the product of the collision frequency (CF) and the coalescence probability (P). The collision frequency describes the number of times that a droplet meets another one during one second:

CF = 2.5 * ¢ * ,Y (1)

where¢ is the volume fraction and .Y is the shear-rate. The probability P is defined as the chance that coalescence occurs when two droplets meet. The most important contribution to P is the rate of drainage of the film in between the colliding droplets in the period that the droplets are in their vicinity. Mason and coworkers have studied collisions of spheres in shear flow for many years (for a review see Arp and Mason, 1976). These authors discussed the following process: two spheres collide and form a transitory doublet (a "dumbbell"), which rotates in the flow until the mirror situation is obtained. Subsequently the spheres are separated again (see Fig. 3). During a fraction of this period of rotation the spheres are pushed together by the flow so that drainage of the film in between the spheres can occur. If this period is sufficiently long the drainage can be complete so that coalescence may happen. In their first, simplified model the flow lines were assumed to be straight until the collision occurred. This led to simple equations describing the rotation of the dumbbell and the drainage of the film during the contact time. It was surprising that this simplified model was in reasonable agreement with experiments. When the complete, much more complicated model was derived, it was possible to give arguments for this agreement (Arp and Mason, 1976).

~ / ~ ' f ,____ ' f

' ' .__..,. ' f I f

r-"1 'f .. ~ ,,

,"! ' ·' 1+-1

I I

'·

Fig. 3. Velocity profile and flow of two droplets during a collision.

In the present paper we base our reasoning on the simplified model, as additional effects contributing to the coalescence can easily be accounted for. It has to be emphasized, however, that the model in this paper is approximate in nature.

Equations describing the drainage during a collision.

The time available for film drainage is determined by the rotational speed of the dumbbell. According to Allan and Mason (1962):

da .Y * (0.8 * cos2 a + 0.2 * sin2 a)

dt (2) .

The initial film thickness hin'" at which drainage starts, equals (derived from Arp and Mason, 1976):

h;.;, = 0.19 *0 (3)

where 0 = droplet diameter.

The rate of film drainage depends on the boundary conditions for the flow and the geometry. When the interface of the film is rigid due to the presence of an emulsifier, the drainage is described by Poiseuille flow between rigid walls. This gives (Allan and Mason, 1962):

dh I dt = - 8 * h * F I ( 3 * 1r * 17, * 02 ) (4)

where F is the driving force for the film drainage and 17, is the viscosity of the continuous phase. Eq. (4) is valid when the droplets are perfect spheres. It shows that the drainage becomes faster when the force exerted on the film increases.

When the drops are pressed too hard against each other, the film will flatten and drainage is described by (Mackay and Mason, 1963):

dh I dt = - 32 * 1r * rl * h3 I (3 * 11, * 0 2 * F) (5).

Eq. (5) shows that an increased force slows down the drainage due to an increased area of the flat film .

The film thickness at which flattening becomes predominant, can be approximated by the film thickness at which Eqs (4) and (5) predict the same rate of drainage. This gives:

hn = F I (2 * 1r * u) (6)

where hn is the film thickness at which flattening starts (A .K.Chesters, private communication).

So, there is a gradual transition for the rate of drainage for the non-flattened and the flattened droplets: both predict the same rate of drainage at hn. However, for a flattened film the rate of drainage will decrease rapidly because it is proportional to "h3

" , while it is proportional to "h" for a non-flattened film.

The rate of drainage depends on the hydrodynamic force Fhyd exerted by the continuous phase along the principal axis of an ellipsoid with axis ratio 2. Allan and Mason (1962) derived:

F•Y• = I. 085 * 1r * 17, * 0 2 * .Y * sin 2a (7).

Eqs. (2) and (7) are somewhat different and much more simple than the equations of the exact theory but give a good approximative description.

When the spheres are at a small separation of each other, the attractive van der Waals force F,,w is operative, which enhances film drainage. This force is given by:

151

152

F vdw = A * D I (24 * h'} (8)

where A = the Hamaker constant (the retardation effect being neglected). In Eqs (4)-(6) the force F equals thus Fbyd + F.dw·

The equations above were solved numerically.

A typical example of the film drainage during a collision

A typical example of the drainage is shown in Fig. 4, in which the following can be observed:

- A symmetrical curve (dashed line), is obtained when it is assumed that there is no flattening and that the van der Waals force can be neglected. The film thickness decreases gradually, reaches a minimal value at an angle of zero degrees, where the hydrodynamic force has decreased to zero and then the film thickness increases again, as the gradually increasing hydrodynamic force is pulling the droplets apart. This curve is independent of the shear-rate, as the collision time decreases with increasing shear-rate, where the drainage rate increases. Both contributions balance;

- When the full model is applied, flattening of the film is found at a relatively large shear-rate where the hydrodynamic force will be relatively large;

- At a relatively small shear-rate an effect of the van der Waals force is obtained: at a certain film thickness the van der Waals force becomes comparable with the hydrodynamic force. This results in an acceleration of the drainage. Due to the additional force the film thickness decreases, this leads to a still larger van der Waals force, etc. Gradually the drainage becomes completely determined by the van der Waals force.

Fig. 4 shows that a shear-rate of 20.7 s·' is the critical value at these conditions: a very thin film can just be formed, but at a slightly larger shear-rate the hydrodynamic force will separate the droplets .

Rupture of the film is also indicated in Fig. 4, as a very thin, unstabilized film can exist only for a short period. This depends on the film thickness and on the period during which such a small thickness is maintained. According to Vrij (1966) rupture of thin films will occur due to growing waves. The characteristic growth time for the fastest growing wave equals (for rigid interfaces):

(9).

Vrij (1966) calculates that the time required for rupture equals a few times t ... OWih: for a film of 10 nm 4.5 * t.,.Wih is required, while this is 6.9 * t,rowtb for a film of 100 nm. The present investigation concerns films of e.g. 2-5 nm, therefore an average: t.u., = 3 * t,.....,. was used to estimate the film thickness at which rupture will occur.

The coalescence probability

All collisions occurring at an angle of at least 75• will lead to coalescence if the shear-rate is less than 20.7 s·' (Fig. 4). These collisions represent a certain fraction of the total number of collisions, which is thus the coalescence probability. Calculation of this fraction leads to Fig. 5: at smal.l shear-rate a relatively large fraction of the collisions will lead to coalescence and this fraction decreases with-increasing shear-rate. There is also an upper limit for the shear-rate: above this shear-rate flattening occurs leading to such a slow drainage that no coalescence will occur.

153

coalescence probability film thickness (nm) 10000~------------.--------------, 0.40 r-----------------------------,

1000

100

10

10 +-rupture

0.1~---L--~-----L--~----~---" -90 -60 -30 0 30 60 90

angle a

Fig. 4. Film drainage at various shear-rates when the collision starts at 75° (see Fig. 3). Viscosity of the continuous phase 0 .05 Pa.s; droplet diameter 10 lim; interfacial tension 30 mN/m; Hamaker constant 4.88* IQ-21 J.

The coalescence frequency

Fig. 5. Coalescence probability as a function of the shear-rate.

The coalescence frequency is obtained by multiplying the coalescence probability with the collision frequency (Eq. (1)) . Fig. 6 shows a maximum, which can be understood as follows. At small shear-rates the coalescence probability is relatively large, but there is only a very small number of collisions, leading to a low coalescence frequency. At large shear-rate there are many collisions, but they rarely lead to coalescence. At intermediate values of the shear-rate there is a reasonable number of collisions and a reasonable fraction leads to coalescence which explains the maximum.

Fig. 6 also shows the large effect of the droplet diameter on the coalescence frequency. This is due to the fact that smaller droplets show less flattening, leading to a faster film drainage, and for smaller droplets the van der Waals force can still become comparable with the hydrodynamic force at a relatively large shear-rate.

The coalescence frequency can also be given as a function of the rotational speed of a stirrer. Such calculations were performed for a baffled vessel with inner diameter 15 em stirred with a turbine impeller of diameter 5 em. These dimensions were chosen because measurements on coalescence in such a vessel are in progress. From the rate of the energy dissipation of the impeller, the following, approximate relation was derived, which relates this rotational speed and the shear-rate in the quiet part of the vessel, where coalescence will occur:

)- = 0. 135 * Nu * D ..,P * 11""·5 (10).

Using D..,. (diameter of the impeller) = 0.05 m and 11 = 50 * 10"" m2/s allows the calculation of Fig. 7, having a similar shape as Fig. 6, but now with the rotational speed of the stirrer on the horiwntal axis.

154

coalescence frequency 1

/ /

0.1 ,/'

0.01

0.001

,/'

/ /

/

.··· ···

, collision / frequency

40,m rigid

0.0001 .'----"'"-'~ ........ __.--'--'U..U""'=--'--'-'-'-'-':''!-=-~C..U.~ 0.1 10 100 1000

shear-rate

Fig. 6. Collision frequency and coalescence frequency as a function of the shear-rate at various droplet sizes. Volume fraction 0.01.

Incorporation of emulsifier effects into the model

coalescence frequency 1.---------------------------~

0.1

0.01

0.001

/ /

,/

/

,/collision / frequency

,, - _,1

I I

lO, m rigid --- ...... .... '

20,m rigid

0"0001 ;-1 ------'--~"'"--'~"'"'-'::1';;:0--~--~~~ .... 1:';!00

rotational speed (1/s)

Fig. 7. Collision frequency and coalescence frequency in a stirred tank as a funct ion of the rotational speed at various droplet sizes. Volume fraction 0.01.

The calculations above were performed for rigid interfaces and other emulsifier effects were not yet considered. Subsequently sets of conditions will now be formulated, which are supposed to be valid in certain concentration ranges of the emulsifier. In this way the coalescence frequency will be calculated for various concentration regimes, but it remains unknown whether there is a rather steep or a more gradual transition between these concentration ranges.

In the first concentration range there is no emulsifier present or only a very small amount. The interface is then mobile as there are no interfacial tension gradients opposing the flow . It is obvious that drainage will be faster for mobile interfaces than for rigid interfaces. A description of the film drainage contains several steps, e.g. development of a boundary layer in the droplet, reaching a steady state flow in the droplet, flattening of the film, etc. As the combination of all these steps is not yet solved, it is not yet possible to calculate the drainage. But there is an "upper limit" : the coli is ion frequency. Figs 6 and 7 show that with rigid interfaces the coalescence probability was already relatively large for small droplets or for a small shear-rate; mobile interfaces can then only give a small increase. However, in situations where the coalescence probability with rigid interfaces is small (large droplets or large shear-rate) mobile interfaces can give a large increase. Preliminary results with a vessel stirred with the turbine impeller showed indeed the latter effect. In conclusion, the first regime in Fig. 2 is probably the consequence of rapid drainage when the interfaces of the droplets are mobile.

On increasing emulsifier concentration the interface will become rigid, as mentioned before. Depending on the droplet size, this might retard the coalescence rate by an order of magnitude.

On increasing the concentration of the emulsifier further, the adsorption increases and gradually the film will consist of two layers of emulsifier with a liquid layer in between. The hydrocarbon tail of the emulsifier will then cause steric hindrance: the flow resistance is relatively large (as determined by the thin liquid layer), while the van der Waals force is relatively small (as this is determined by the total film thickness). This situation starts at about 0.2% monolinoleylglycerol, where saturation adsorption is gradually approached. The interfacial tension is about 20 mN/m at this concentration.

The steric hindrance is easily incorporated into the model. If "h" is the total film thickness and h:><m the combined th ickness of the two emulsifter layers, in the equations for the rate of drainage "h" is to be replaced by "h-h:><m", as the flow resistance is determined by the thickness of the liquid layer. For h:><m a value of 2 .5 nm was used, as obtained by Waldbillig and Szabo (1979). These effects cause a further reduction of the coalescence frequency, as shown by regime 2 in Figs 2 and 8.

The enhanced coalescence in Fig. 2 (regime 3) can be attributed to an additional attractive force which occurs at monolinoleylglycerol concentrations of about I%. The details on this force are not yet known. Contact angle measurements indicate that the additional attractive force can amount to 34 times the van der Waals attraction. The force becomes noticeable when the film thickness becomes rather small and it seems to be related to the fact that the oil molecules no

longer fit in the film. With decane as oil phase, the film thickness is 5 nm and decreases when oil molecules of increasing size are used, as these molecules are immiscible with the film. It is thus reasonable to assume that the additional attractive force will start to occur at a film thickness of somewhat more than 5 nm. Tn the present calculations a value of 7 .5 nm was taken.

coalescence frequency

0.76 .__mobile

0 0 0 0.20

increased rigid anraction

a=30 a=6 • 0.10

to~m 101-'m r"' o.oo b'-:e~o----'---

o.oo 0.50 1.00 1.50 2.50 concentration (%)

Fig. 8. Coalescence frequency at I 0 rot/s as a function of the concentration of monolinoleylglycerol. Volume fraction 0.01.

Results of the calculations on the coalescence frequency are given in Fig. 8, where the following can be seen:

155

- The coalescence frequency is very high for mobile interfaces, where the collision frequency is a reasonable approximation for the coalescence frequency . This explains why 50% W/0 emulsions could not be made at very small emulsifier concentrations (Regime I in Figs 2 and 8);

- The coalescence frequency is strongly decreased when the interfaces are rigid . This decrease is further continued when steric hindrance is involved. This explains why 50% emulsions could be made at this concentration and why the half value periods for coalescence were relatively long. (Regime 2 in Figs 2 and 8);

156

- The coalescence frequency can be increased considerably by the increased attraction, but this depends also on the droplet diameter. This increase in the coalescence frequency is thus in agreement with the observed decrease in the half-value period for coalescence (Regime 3 in Figs 2 and 8). This effect was not observed when paraffin oil was used as oil phase. In this case, large contact angles were not observed and therefore the additional attractive force must be considerably smaller; no concentration range with increased rate of coalescence was observed;

- At 2% the films are stable and the coalescence frequency thus becomes zero .

There is thus a promising agreement between the measured and calculated trends. However, many approximations and assumptions were involved in the model. The theoretical considerations were based on emulsions of low volume fraction, while the phenomena observed were obtained for concentrated emulsions . Although the phenomena can be explained qualitatively, a quantitative agreement can only be expected if the consequences of the volume fraction on various aspects has been unravelled at hydrodynamically well defined conditions . Work in this direction is in progress.

REFERENCES

Allan, R.S and Mason, S.G. (1962) . Particle motions in sheared suspensions 14. Coalescence of liquid drops in electric and shear fields. 1. Colloid. Sci., 11. 383-408.

Arp, P.A. and Mason, S.G. (1976). Orthokinetic collisions of hard spheres in simple shear flow. Can. 1. Chern . ,~. 3769-3774.

Lloyd, N.E. (1959). Determination of surface-averaged particle diameter of coloured emulsions by reflectance, and application to emulsion stability studies . 1. Colloid. Sci., 1.1, 441-451.

Lucassen-Reynders, E. H. (1962). Stabilization of water in oil emulsions by solid particles. Thesis University of Utrecht, The Netherlands.

Mackay, G.D.M. and Mason, S.G. (1963) . The gravity approach and coalescence of fluid drops at liquid interfaces . Con. 1. Chern. Eng. !L 203-212

Princen, H.M. (1984) Geometry of clusters of strongly coagulated fluid drops and the occurrence of collapsed Plateau borders . Colloids Surfaces, 2, 47-66.

van Voorst Vader, F. and Bak, M. (1990) . The influence of the film contact angle of emulsion droplets on the dispersibility of their sediments. 1. Disp. Sci. Techno/. , .U, 555-579

Vrij, A. (I 966) Possible mechanism for the spontaneous rupture of thin , free liquid films. Discuss. Faraday. Soc., 42, 23-33 .

Waldbillig, R.C. and Szabo, G. (1979) . Planar bilayer membranes from pure lipids. Biochirn. Biophys. Acta, ill. 295-305.

MEASUREMENT OF DROP SIZE DISTRIBUTION IN

LIQUID/LIQUID DISPERSIONS BY ENCAPSULATION

W.Q. Zhao, B.Y. Pu and S. Hartland

Swiss Federal Institute of Technology Department of Industrial and Engineering Chemistry

Univer.sitiitstr. 6, CH-8092 Zurich, Switzerland

ABSTRACT

157

Direct photography is often used to measure drop size distribution on liquid-liquid dispersions, but when the holdup is high or drop size is small , the resolution is poor. Madden and McCoy ( Ma.dden eta!., 1964 ) proposed encapsulating the drop using a rapid polycondensation reaction to form a thin film of Nylon 6-10 a.t the drop surface. However, it was reported that the drop size was influenced by the chemical treatment employed.

T his is overcome in the presents work using acetalization reaction and a specially designed en­capsulator. Small amounts( < 0.1% by the volume of dispersed phase) of isobutylaldehyde and butylaldeyde were dissolved in t he toluene dispersed in the vessel. Samples were sucked out into the encapsula tor where the polyvinylalchol ( a water soluble polymer surfactant ) reac ted with the mixed aldehydes at the surface of toluene drops and to produce a third phase which immediately encapsulated each drop. Since the film prevented drops from coalescing, the stabiUzed drop size distribution can be directly obtained from photographs taken through an optical glass dish.

Comparison of mean drop diameter obtained by this technique and direct photography shows good agreement. The mixed aldehydes do not influence the mean drop diameter and the drop size dis­tribution. The results indicate that the technique can be used to accurately measure the drop size distribut ions in liquid-liquid dispersions.

KEYWORDS

Drop Size Distribution; Measurement; Liquid-Liquid Dispersion ; Encapsulation.

INTRODUCTION

In petrochemical , hydrometallurgical, food, pharmaceutical and polymer industries, drop size dis­tribution data are essential to carry out operations involving mass transfer with or without reaction in liquid-liquid dispersions . Drop sizes have been determined by a number of techniques includ­ing direc t photography, light transmission, tight scatte.ring, laser droplet velocimetry, electrical method, chemical reaction, drop stabilization, capillary sampling probe, acoustic wave and scintil­la.tion. However, direct photography is still the most common method since it is simple, easy and accurate, but it is difficult to use when the holdup is high and the dispersion is optically dark ( Da.e ami Tavlarides, 1989).

158

Shinnar ( R.Shlnnar, 1961) studied a stirred dispersion of molten wax in hot water, stabilized by a protective colloid . The sampling procedure is restricted to rather stable dispersions which do not tend to coalesce in the sampling process (Church and Shinnar, 1961 ). Madden and McCoy (Mad· den and McCoy, 1964, 1969) proposed drop stabilization method via encapsulation technique to determine drop size distribution in liquid-liquid dispersion systems. The dispersed tetrachlorethy­lene contained !%(volume) sebacyl chloride. At the moment at which droplet encapsulation was desired , a small volume of aqueous hexamethylene diamine (plus NaOH) was quickly added to the continuous water phase . An extremely rapid interfacial polycondensation reaction occurred at the surface of each drop resulting in the formation of a thin encapsulating film of Nylon 6-10. The encapsulated droplets were then sampled and size measurements made by a microscopic tech­nique. Such a procedure requires rapid formation of the encapsulating film which made drops stable enough to be measured. Their technique, in addition , does not permit the study of local drop diameter variation and only the gross situation throughout the vessel can be analyzed . Mlynek and Resnick (Mlynek and Resnick, 1972 ) developed a local drop size measurement by using a special designed trapping technique which permits reliable sampling at any desired location in the vessel. The monomer pair used was piperazine, which is soluble in water, and terephthalic ac.id chloride, which is soluble in the organic phase ( mixture of ca.rbon tetrachlorid and isooctane). A small amount of the continuous phase plus the monomer soluble in it was added to the trap, the other monomer being dissolved in the dispersed phase in the vessel. The trap could be placed in any desired sampling position , interfacial polymerization taking place instantly where the trigger was released. After trapping , a sample of the encapsulated drops was transferred to a flat glass dish and photographed . In a recent review ( Bae and Tavlarides, 1989) , Bae and Tavlarides point out that chemical treatments (Madden and McCoy, 1964, 1969, Mlynek and Resnick, 1972 ) influence the drop size.

This is overcome in the present work using a specially designed glass encapsulator and acetalization reactions. Small amounts ( <0.1% by volume of dispersed phase ) of isobutylaldehyde and buty­laldehyde were dissolved in the toluene dispersed in the vessel. Samples were sucked out into the glass encapsulator where the polyvinylalcohol ( a water soluble polymer surfactant ) in the aqueous phase reacted with the mixed aldehydes at the surface of the toluene drops to produce a third phase which immediately encapsulated each drop . Since the film prevented drop from coalescing, the stabilized drop size distribution can be directly obtained from photographs taken through an optical glass dish. Comparison of mean drop diameter obtained by this technique and direct pho­tography shows that the measured values are in good agreement.

EXPERIMENT

l.Apparatus and Reagents

Chemical Reagents Isobutylaldehyde ( Fluka ), Butylaldehyde ( Fluka ), Toluene ( MERCK ), Polyvinylalcohol ( Fluka ), Hydrochloric Acid ( MERCK ).

Apparatus Fig.l shows the schematic drawing of the experimental apparatus, which includes a stirred vessel and a optical window for direct photography. The mix.ing vessel was a 2 liter glass beaker filled with continuous phase which was 1.5 liter distilled water pre-saturated with toluene. The amounts of dispersed toluene was changed for each run. The vessel was equipped with a 98W variable-speed motor (Janke & Kunkel ), which drove a 6-bladed impeller at different speeds monitored by a speedometer (Ies & Braun ). Samples at any desired location in the vessel were taken out by using specially designed glass encapsulator which included a reactor and an optical dish. The reactor consisted of a sampling pipe through which toluene drops were sucked out. A

159

bigger pipe for polyvinylalcohol solution fluid was mounted on the outside of the sampling pipe. As soon as the toluene drops, in which mixed aldehydes dissolved, oozed out from the top of the sampling pipe and fell into the polyvinylalchohol solution, the acetallization reaction instantly took place. Toluene drops were sucked out into the polymer surfactant one after another, encapsulated, collected and photographed . Coalescence was prevented during transport and in the dish.

flflllh

I J A

If ~ Ui~h

'1'''

8 Gn11 11·rn

Fig.l Schematic Drawing of Glass Encapsulator for Trapping Drop

Photographic Apparatus A l\'ikon Fl camera was used in the performance. The Nikon SB-15 flash was mounted at a distance of 45 em from the vessel at angle of 45° for direct photography. In addition , the flash was mounted at a distance of 60 em from the dish at an angle of 180° for dish photography. A minimum of 2 photographs were taken on each condition, using Kodak Tech Pan 2423 black and white film. A stainless steel rod was attached the vessel window as a reference and colored particles in dish as standards (Duke Scientific Corp . ).

2.Measurement Procedure

Experimental Method The liquid-liquid system was prepared with toluene as the dispersed phase and distilled water as the continuous phase. 0.05%(by the volume of toluene ) isobutylalde­hyde and 0.05%(by the volume of toluene ) butylalhyde were added into the dispersed phase and the system was agitated for 30 to 40 min before sampling was begun. polyvinylalcohol solution (1.5wt.% acidifi ed by HCl before using ) was introduced into the glass reactor by gravitation. Samples were gently sucked out by vacuum, as soon as the polymer surfactant reached the dish . Photographs were taken through the optical dish. Fig.2 shows typical stabilized toluene drops in the polymer surfactant.

The Direct Photography Direct photography were taken through an optical window fixed on the beaker wall and filled with water to minimize optical distortion. When the agitation speed and holdup were low, the photographs obtained were sharp and could be easily analyzed (Fig.3) . The photography negatives were analyzed on an optical digitalizer , which connected to a PC (olivetti M240 ). A minimum of three hundred drops were counted for each operation condition. The programma calculated the mean diameter according to Eq.l

160

L;:, 1 n;dJ

L;:,1 n;df

Fig.2 Toluene Drops Dispersed in PYA in Dish

Fig.3 Toluene Drop Dispersed in Vessel

(1)

161

RESULT AND DISCUSSION l.Inftuence of the mixed aldehydes on the mean drop diameter and the drop size distribution

In order to know the influence of the reagents to the dispersion system, direct photography was employed. Fig.4 and Fig.5 show the addition of the mixed aldehydes slightly influences to mean diameter and drop size distribution data.

........ E E .... Ql

Ql

E 0 Ci a. ~

Cl

c 0 ., :::. .... Ql

:J 0 til

~

~ >-" c: .. :J <T

~ .._

2.0

1.5

1.0 .. .. ~---------- .----A----.A.--.6..------------------------. ..

0.5

0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

30

20

10

Concentrat ion of Aldehyde in Dispersed Phase ( Vol%

Fig.4 Influence of Mixed Aldehydes an Sauter Mean Diameter

HJH Without Aldehydes

[llil 0 . 1% Mixed Aldehydes (v/v)

0.1 0.3 0.5 0.7

Drop Diameter (mm)

Fig.5 Influence of Mixed Aldehydes on Drop Size Distribution

Ba.jpai and Prokop (Bajpai and Prokop, 1974 ) reported that hydrolysis of sebacyl chloride occurs to a considerable extent, results in its flocculation from the dispersed phase and thus interferes ""ith polymerization. T he encapsulation method ( Madden and McCoy, 1964 ; 1969 ) has the dis­ad vantages of changing physio-chemical properties of dispersed phase.

162

In the proposed method, the chemical properties of isobutylaldehyde and butylaldehyde are stable in the condition employed, the acetalization reaction used in the encapsulation method are mild, no flocculation phenomenon was observed.

E E

.... .. a; E 0

Ci c 0 Q)

::::E

.... Q)

"S 0

V1

t-1

>-0 c .. :J 0" e "-

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

25

20

15

10

5

N - 460 rev/min.

HOLDUP - 6.25%

• • •

10 100

Time ( s )

Fig6. Sauter Meah Diameter Measured in Different Time

E£E3 H DISH

[[!I1 H VESSEL

...

o~~~~~~~~~~~~~~~~~cu~~~~-­

o~o~oPo~o~o~o~o~o~o~o~o~o~o~o~o~o~

Drop Diameter ( mm )

Fig. 7 Comparison of Drop Size Distribution Data

2.Stability of the encapsulated toluene drops

The mean diameter data obtained from the photographs taken through the optical dish at different time indicate the encapsulated toluene drops are stable in 5 min at least( Fig.6 ). Owing to the acetalization taken place at the interface forming a polymer film, the encapsulated and stabilized

163

toluene drops provided high quality photographs (Fig.2).

3.Accuracy of the proposed method

Comparison of mean drop diameter obtained by the proposed method with the direct photography technique in the same agitated vessel indicates the data are in good agreement. Holdup and im­peller speed are changed during the measurement. On the other hand, at high holdup and/or high impeller speeds the quality of the direct photograph picture was not adequate . Good results could be obtained only when the direct photographs are sharp and easy be analyzed. Table 1 shows d32

data. and the deviation of the tow methods. Fig. 7 gives the drop size distribution data obtained from direct photography and the proposed method.

Table 1. Comparison of Drop Diameter Obtained by The Two Methods

Holdup N rev/min d32(vessel) mm da2(dish ) mm Deviation from Mean

6.25% 460 0.631 0.547 +7.1% 6.25% 409 0.665 0.603 +4.9% 3.2% 425 0.439 0.464 -2.9% 3.2% 375 0.582 0.522 +5.4%

The static photography technique was carried out using an optical digitalizer. since the choice of the area for counting caused the error for randomness , at least 300 drops were digitalized and counted from each negative picture. Error were elircinated by using the glass encapsulator in which the stabilized and separated sample drops could be photographed through the optical dish without any tra.nsfer.

4. Acetalization of polyvinylalcohol and encapsulation mechanism

In previous encapsulation method ( Mlynek and Resnick, 1972 ), a small amount of polyvinylalco­hol "'as used for the purpose to prevent adhesion of encapsulated drops. Tanaka ( Tanaka, 1985 ) reported the encapsulated drops were transferred to flat glass dish containing 1.0 wt% polyvinylal­cohol aqueous solution to prevent the drops from adhering. Now the a.cetalization reaction make the procedures simple and elimina.te the error of Nylon 6-10 film thickness which is estimated to be as much as 10%.( Tanaka, 1985 ). Water-soluble polymer, polyvinylalcohol, rea.cts with small aldehyde molecules. Finch (Finch, 1983) explained the stereochemistry involved in typical exam­ples . Polyvinylalcohol is easily soluble in water to from a gel consisting of a three-dimensional fiber network ( Lissa.nt, 1974 ), in which the OH- radicals are acetilized by aldehyde molecules and form a product neither soluble in water nor in toluene.

R-CHO -CH2-CH-CH2-CH-CH2- ----> -CHz-CH-CH2-CH-CHz-

l I I I I OH OH 0 H 0

I c I R

164

-CH2-CH-CH2-CH-CH2- -GH2- CH-CH2-CH-CH2-

I I I I OH OH 0 OH

R-CHO I

OH OH

I I -CH2-CH-CH2-CH-CH2-

R-C-H

I 0 OH

I I -GH2- CH-CH2-CH-CH2-

Five kinds of polyvinyl alcohol and mixed aldehydes were used in the encapsulation test. Polyviny­lalcohol 100000 (Fiuka No.81386 ) and mixed aldehydes of isobutylaldehyde and butylaldehyde ( volume/volume = 1/1 ) are suitable for the encapsulating purpose. The solubilities of isobuty­laldeyde and butylaldehyde in water are 11 and 7.1 respectively. In addition, the aldehydes are miscible with toluene and mainly concentrated in toluene drops dispersed in water. The acetal­ization reaction at the toluene drop interface played an important role in encapsulation which prevented drops from coalescing and made drops stable enough to be photographed. Furthermore, polyvinylalcohol aqueous solution kept the encapsulated drops from sticking to each other and made drops separated and easy to be distinguished.

CONCLUSION

A new encapsulation method for determination of drop size distribution in toluene-water dispersion is proposed, in which acetalization reaction of polyvinylalcohol and a glass encapsulator are em­ployed. Small amounts of mixed aldehydes were added into the agitated system, which no obvious influence was observed on mean drop diameter and drop size distribution in liquid-liquid dispersion. The proposed method has the advantages of local drop sampling and easy photographing in situ. The measured data show a reliable agreement. Application of the new technique where holdups and impeller speeds are high is being investigated.

REFERENCE

A.J.Ma.dden and B.J.McCoy (1964). On the problem of determining drop size distribution in stirred liquid-liquid systems. Chern. Eng. Sci.l.fl,50G-507.

B . .J.llfcCoy and A..J.Ma.dden (1969). Drop Size in Stirred Liquid-Liquid System via. Encapsulation. Chern. Eng. Sci., 24,416-419.

C.A.Finch (1983) . Chemistry and Technology of Water-soluble Polymers. New York; London; Plenum Press.

J .H.Ba.e and L.L.Tavlarides (1989). Laser Capillary Spectrophotometry for Drop-Size Concentra­tion Measurement. AIChE J., 35 1073-1084 .

.J.M.Church and R.Shinna.r (1961). Stabilizing Liquid-Liquid Dispersions by Agition Indust. Eng. Chern., :23_, 479.

I< . .J .Lissant (1974). Surfactant Science Series, Emulsion and Emulsion Technology. Volume 6, Marcel Dekker Inc. New York.

165

M.Tanaka (1985). Local Droplet Diameter Variation in a stirred Tank. Can J. of Chern. Eng., 63,723-727.

R.K.Bajpai and A.Prokop (1974). a New Method for Measuring Drop-Size Distribution Biotech­nology and Bioengineering, l.Q, 1557-1546.

R.Shinnar (1961). On the bevaviour of liquid dispersions in mixing vessels J. Fluid Mech. , .ill, 259.

Y.Mlynek and W .Resnick (1972). Drop Size in a Agitated Liquid-Liquid System . A/ChE J., 1.8, 122-127.

166

STABLE OIL DISPERSIONS OF GRAFITE: PREPARATION, TESTING, AND APPLICATION

F.I.Liaschenko, A.M.Romaniukha, N.N.Zaiets, E.V.Radzievski, M.A.Al'tshuler

Zavalie Graphite Factory, Zavalie VNIIPKneftekhim, Kiev

167

Production process of finely dispersed colloid preparations using natural graphite is developed and used in Zavalie Graphite Factory.

The cristalls of natural graphite passing stages of chemical concentration and dispersing in jet (up to 2 - 5 mcm) and vibration mills. After that the product is further dispersed in liquid phase up to over 50 % fraction with particle size less than I mcm. During vibration milliry of graphite in the process of oil dispersion preparation mineral oils are used as dispersing media.

Addition of surfac tants at the stages of grinding and dispersion preparation enhances dispersing power, aggregation and sedimentaton stability. Succinimides, Mannich bases and certain synergistic compositions containing the latter show the greatest stabilizing power.

Obtained dispersions show good antifriction properties and long-time storage stability and may be used as additives to mineral oil for various applications.

Adre ss: ing. A.M.Romaniukha Zavalie Graphite Fac tory 317614 Zavalie Kirovograde obl. Ukraine. USSR

Prof. Dr. M.A. Al' tshuler, Inst. "VNIIPKNeftekim", prosp. Palladine, 46, 252180, Kiev, Ukraine, USSR

168

The Creation of Dispersions by the Electro-Hydraulic Effect.

Victor A. Pryamitsyn, Valery P. Glinin and Gennady V. Kotov.

Leningrad Branch of Institute of Machine Sciences Academy of Sciences of the USSR

61 Bolshoj pr., V.O., Leningrad, 199178 USSR

ABSTRACT

169

The electro-hydraulic (EH) effect is an underliquid explosion produced by the high-voltage electric spark in the bulk of liquid. This effect can be applied for crushing and dispersing of different substances. The emulsification of liquids in liquid, the dispersion of some superhard materials as diamonds, silicon carbide, silicone nitride, titanium carbide and boron nitride and also asbestos and mica are discussed.

KEY\IORDS

electro-hydraulic effect, underliquid spark, shock wave, dispersion, dispersing, milling, crushing, emulsion.

Introduction

The strong impulse electric field in a liquid is known to be able to cause the electric breakdown of the liquid. The mechanism of the breakdown depends on the voltage and the steepness of the electric impulse and the electric properties of the liquid. If the power of the electric spark in the liquid is large enough the electric explosion in the liquid takes place.

The nature of the electro- hydraulic effect (EH) is that the power spark in the bulk of liquid can cause an electric explosion that produces a shock wave which is capable of performing the mechanical action. This method for creating high pressures in liquid was suggested by Yutkin (1950).

The direct measurement of the pressure and temperature of the shock wave generated by EH is quite impossible because all available sensors can only generate electric signals dumped by power electric pulse of EH. Therefore parameters of EH are usually appreciated by indirect measurement, the theory of shock wave being applied.

Up to the moment one of the best works in this field is the paper of Komel'kov and Skvortsov (1959). In this work the velocity of the shock wave caused by a spark in water was measured by optical methods. The other parameters of the shock wave were determined using the theory suggested by the authors. Based on this theory they established that the pressure in the spark can reach 6 GPa, the pressure in the shock front can reach 2 GPa, the local heating in the spark being about 2000 K and the density of the water in the front of shock wave increasing by 30-50%. The discharge dumped, the steam cavity appears. The cavitation "clapping" of this cavity causes the wave of unloading. The

170

interacting waves of loading and unloading produce the main crushing action in EH process.

EH causes powerful electric and magnetic fields. The dispersed particles in a liquid can electrically charge extensively and discharge. The parameters of the EH action can be changed by changing the parameters of the electric pulse.

Fig. 1 presents the electric scheme of the simplest EH installation. A pot like spark tube is used as a mill. The tube is the negative electrode, the positive electrode is an isolated metal rod with bare tip. This geometry provides the spark arising only on the positive electrode. The parameters of the electric pulse are regulated by the selection of the voltage, the capacity, and the air and liquid gaps. At present many kinds of different EH installations are created. They can also be designed as equipment with continuous dispersion for the promotion of productivity. The important advantage of EH intallations is the absence of any moving parts in the disperser.

C.. I-t A. r(, c; Ill(;. RESI~ToR,

HIG-H VO'-TP.GE:.

G ENE.'i\~101\.

A\R. GrAP

CAPACITOR..

Fig. 1 The electric scheme of the simplest EH installation

The typical EH installation consists of a high voltage generator, a control desk and a set of different spark tubes. We designed a series of experimental and commercial EH installations for the dispersion and the activation of different substances.

The EH crushing mechanisms

Let us consider the possible mechanisms of failure of particles caused by the shock waves. Two mechanisms are discussed in the work of Carley-Macauly (1968).

The first one is the spoil of the surface of a solid body in reflecting the shock wave. In this case the thickness of chopped layer is approximately equal to the distance between the fronts of loading and unloading of the shock wave. This distance is seldom less than one millimeter.

The second mechanism is associated with the concentration and the focusing of

171

the shock stresses due to multiple reflection of the shock waves from the boundaries inside the solid particle. The lower limit of crushing by this as well as by the first mechanism is above one millimeter.

Hence, the crushing mechanisms dealing with propagation and interaction of the shock wave in the solid bodies cannot explain the dispersive action actually reached in EH crushing (often as small as one micron) .

The nonuniform shock loading of a polycrystal hard particle results in great internal stresses due to the nonuniformity and the anisotropy of the material properties of the polycrystals . The cracking of the polycrystal particles occurs first along the cleavage fractures and the clefts. Stronger loading can lead to fracture in the defec tive zones in monocrystal particles. In general the sufficient shock compression is able to crack hard particles down to small monocrystals without any defects . This mechanism seems to occur in EH dispersing of superhard crystal materials. The lower limit of crushing by this mechanism is a fraction of one micron.

In tangential moving shock waves along the EH tube solid surface, strong gradients of the liquid velocity resulting in high shear stress in the liquid appear. These shear stresses can break the dispersing substance. The flow of the liquid that appeared mixes and homogenizes the dispersion. For intensifying the influence of these processes special bars and sieves can be installed in the EH tube . These processes are essential to emulsification and dispersion of soft substances such as asbestos and mica .

The interference shock wave of loading and unloading appearing during EH can result in cavitation. The power streams of liquid mentioned above are another cause of cavitation. The clapping of the cavitation bubbles with the surface of a dispersed substance results in cavitation, erosion and fracture of the substance.

Influence of EH processing on liquids

While using EH the choice of operating liquids is limited . The liquid must be very stable both thermally and chemically and has to possess the required electric properties for EH. The specific electric resistance should as high as possible. If the specific electric resistance of the liquid is less than 10m the electric breakdown in the liquid usually does not arise. On the other hand, if the electric strength is too large, the liquid electric gap has to be very small, but the intensity of the EH action is in fact proportional to the length of the liquid electric gap .

Usually water is applied for EH. Distilled water has the best qualities, but polluted technical or natural water and poor electrolyte may be applied . In EH processing the pH and specific electric resistance are decreased . In absence of dispersing substances these phenomena in most cases are due to scattering of the electrode substance and to the oxidation of nitrogen from air that has been dissolved in water in the spark zone . By applying the hermetic tube and high-melting electrodes these effects may be reduced. However, this is not essential in dispersion processes, as the complicated physical and chemical effects of the interaction between water and disperse particles are of the main importance .

Besides water other liquids may be applied . We used ethanol, methanol, ethylene glycol, toluene and diesel fuel. In EH processing a pure liquid, the conductivity of the liquid usually increases, the colour and viscosity change, the sediments appearance being possible. In dispersing, these processes are intensified and complicated. In dispersing in organic liquids some substances such as asbestos and mica, which form very large surface in dispersing, "cold"

172

liquid dissociation and gas secretion occur and sometimes an explosion takes place. For these reasons the use of organic liquids has been very restricted so far. Usually these are applied only when water application is impossible. For example, ethanol was used for dispersing titanium carbide due to oxidizing titanium carbide in dispersing was inadmissible.

Very interesting results were obtained in mixing incompatible liquids . We succeeded in creating stable emulsions of high viscosity of hydrophobic liquids in water without using any surfactants, which is difficult by usual methods. We have carried out investigations of the creation of water fuel emulsions for the improvement of economizing and ecological properties of the engines . By EH processing water emulsions in the diesel fuel with a water concentration up to 30% were produced without any special dopes . The average size of microglobules of water was approximately 1~. The stability of the emulsion was provided by possitive electric charge of the microglobules of water. These emulsions remained stable for a few weeks.

In EH processing of incompatible liquids, emulsification as well as demulsification can occur depending on the set-up of the EH installation.

It should be noted, that the EH processing results in protrac ted sterilization of the treated substance. For example, treated milk does not become sour for more than a year, the biological wastes are completely disinfected. The application of EH for extracting biologically active substances from vegetables and drug manufacturing is very prospective.

The dispersion of the superhard materials

The important field of application of EH is the dispersion of superhard materials such as diamonds, silicon carbide, silicone nitride, titanium carbide and boron nitride. In combining EH dispersion and elutions the dispersed particles with an average size less than 0.2~ were obtained .

Evidence from electron microscopic and X-rays investigations indicate that the received received parti c les have few defects and structural breaks . The micro particles have dinstinct crystal facets; the amorphisation and the strain hardening are absent. We suppose that in this case the cracking of the particles occurs first along the cleavage fractures, the clefts and defective zones .

In dispersing synthetic diamond powder from the fraction of average size 100~. above 75% particles transform to fractions less 0.5~ in size. The typical electron microscopic photography of the diamond particles after EH processing is presented in Fig. 2. The average size of the diamond dispersion measured by sedimentation was 0 . 3~ .

The dispersion of silicon carbide and boron nitride was similar to that of diamond. In all cases the high level of the product dispersed was combined with high purity . The absence of pollution is the main advantage of the EH in comparison with routine mechanical method for milling of superhard substances .

The special purity and the absence of oxidation is necessary in dispersing the titanium carbide. To provide these conditions a special teflon tube was designed, ethanol as operating liquid and titanium electrodes are used. We reach the average size of dispersion 0.3~ . The amount of pollution was less than 0.1%. The samples of highly dispersed titanium carbide had high chemical activity and technological properties.

173

The asbestos and mica dispersion

Extremely interesting results were obtained in dispersing asbestos in water medium . It is known that the preparation of the stable water dispersion of asbestos by usual mechanical methods takes several hours . Using EH we prepared one during a few minutes without any surfactant. The dispersion goes up to the monofibers of asbestos with a diameter less than 300A, but the length of monofibers ca n be kept up to millimeters in some conditions .

By the EH the complete homogenization of the mixture of submicron fractions of Cr

20

5and asbestos was achieved within a few minutes, the usual methods taking

some hours. The electron microscopic photography of the blend of asbestos fiber with Cr

20

5 particles after EH processing is presented in Fig . 3 .

The dispersion of asbestos is accompanied by an extremely intensive process of the formation of the fresh surface . This leads to the intensive interactions between the asbestos fibers and the medium. The occurring processes are very interesting. For example, the attempt to disperse asbestos in toluene l e ads to intensive dissociations of the toluene and the evolution of gases and soot. Note tha t toluene is stable above 700K. The dispersion of asbestos in water polymer latices allows us to create new composite materials. The EH processing results in the increasing of homogeneity and adhesion between fibers and polymers.

100 11m'

Fig. 2 The electron microphotography of the diamond partic les .

174

Fig. 3 The electron microphotography of the blend of asbestos fiber with Cr2

05 particles after EH processing.

We dispersed mica in water and in ethylene glycol. In dispersing of mica in water, we created a stable, non-settling dispersion of sheet-shaped particles of mica. As in the case of asbestos, we created new composite materials by the dispersion of the mica in water polymer latex.

Dispersion of drilling mud, cement mortar and slip technology.

We investigated possibilities of using EH for creating water dispersions of loamy minerals and kaolin . These dispersions are used for drilling mud and slip technology . Usually the initial material is disperse enough. They should be disaggregated, mixed, homogenized and stabilized in the dispersion, the special chemical dopes being added to this dispersion. The EH processing allows us to change purposely pH of the dispersion, the yield of water and wetting ability. The EH installations prove to be more reliable, economical and easy in operating. The EH installations provide the high quality of obtained product in using cheap materials . By the order of the geological

enterprises of Tumen the mobil EH installation "MEHDA" and "EHDAM" were created (Glinin et al (1986-1990).

175

For the processing of the cement mortar the same installations are used. The EH processing can promote or retard the setting and reinforce of the concrete, what makes possible to r educe the consumption of the cement or to use the cheaper one for the concrete production .

The EH application for creating slip dispersions is greatly encouraged. The high homogeneity and reactivity provide the high quality in the ceramics production. It should be mentioned that the use of the spark tube and the electrodes of the aluminium allows us to avoid polution of the porcelain clay by ferroxide. We consider the slip technology is the most prospective field of EH application.

Dispersion stabilizing in EH processing

The routine method of the stabilization by surfactants was usually applied. Under specific conditions EH processing allows us to prepare stable dispersions without any surfactants . It can be reached by the electric charge of the disperse particles obtained in EH. Another way of stabilization is the stabilization by the polymer. If a small amount of a soluble polymer is added to operating liquid before the EH execution of dispersion, the polymer will be adsorbed onto the fresh clefts and will form the l ayers preventing the aggregation of the disperse par ticles . Sometimes the gela tinization accompanies the EH processing of polymer solutions. In such cases a little amount of polymer is able to stiffen a great volume of suspension.

Conclusion

The EH processing is a very prospective method of dispersing different substances. Somet imes it provides unique possibilities which a re inaccess ible by the use of other methods , though the further inves tigation of processes occurred in EH execution are required. It should be noted that the commercial prospects depend strongly on availability of electrical components.

References

Carley-Macauly K. W. (1968) . The Electrohydraulic Crushing . Chemical and Process Engineering, 49, No. 9, 87-96. Glinin V.P., et al (1986) . The Disperser . The USSR Au thor Certifi ca t e No125140105, (1 989 ) The Disperser-Ac tiva tor Ibid No1513671, (1 990) . The Method of Process ing of Hard Materials Ibid No1 560324. Komel'kov V.S. and Skvortsov Iu.V. (1959) Widening of a powerful spark in a liquid. Proceedings of the Academy of Sciences of the USSR (DN) 129, No6, 1273-1277 . Yutkin L. A. and Goltsova S.V. (1950) The method for creating high and superhigh pressure in a liquid The USSR Author Cer tifi cate No105111.

176

RECENT ADVANCES IN THE PREPARATION OF LATEXES

J. w. Vanderhoff

Emulsion Polymers Institute and Department of Chemistry Lehigh University, Bethlehem, PA 18015, U.S.A.

ABSTRACT

177

The industrial production of latexes has grown from the first po­ly(butadiene-co-styrene) produced in the U.S. for synthetic rub­ber and the first poly(vinyl acetate) produced in Germany for ad­hesives to many different polymer families produced for a wide variety of applications. Both conventional (oil-in-water> and in­verse (water-in-oil) emulsion polymerization comprise the emulsi­fication of an immiscible monomer in a continuous medium, follow­ed by polymerization with a free radical initiator, to give a colloidal sol of submicroscopic polymer particles smaller by an order of magnitude than the original emulsion droplets. Both pro­cesses give "emulsion polymerization kinetics," i.e., a propor­tionality of both polymerization rate and number-average degree of polymerization to the number of particles, instead of the in­verse relationship between these two parameters observed for mass, solution, and suspension polymerization. The emulsion po­lymerization process can be divided into particle nucleation and particle growth stages, and it can be carried out using batch, semi-continuous, or continuous processes. Seeded emulsion polym­erization can be used to obviate the particle nucleation stage in all three processes. The mechanisms proposed for initiation of emulsion polymerization can be divided into four categories, ac­cording to the locus of particle initiation: 1) monomer-swollen emulsifier micelles; 2) adsorbed emulsifier layer; 3) aqueous phase~ 4) monomer emulsion droplets. Three generations of latex development are defined, according to the emulsifiers used: 1) conventional emulsifiers~ 2) functional monomers~ 3) polymeric emulsifiers. The formation of coagulum (polymer recovered from the latex in a form other than stable latex) during emulsion po­lymerization is attributed to two causes: 1) a failure of the colloidal stability of the latex~ 2) polymerization by a differ­ent mechanism, e.g., mass (monomer layer), surface (walls, roof, agitator shaft), vapor (atmosphere). The failure of the colloidal stability is attributed to diffusion-controlled, agitation-induc­ed, or surface flocculation of the particles, according to the agitation rate (low Reynolds numbers) and the power consumption (high Reynolds numbers).

KEYWORDS

Preparation of latexes; mechanism and kinetics of emulsion polym­erization~ particle nucleation and growth; stability of latexes.

178

INDUSTRIAL PREPARATION OF LATEXES

Many different latex families are produced in industry, each with its own applications.

ll poly{butadiene-co-styrenel and poly{butadienel for synthetic rubber.

2) poly{vinyl acetate) and vinyl acetate copolymers for adhesives and coatings.

3) poly{styrene-co-butadienel for paints, paper coatings, carpet backing, and nonwoven fabrics.

4> acrylate ester copolymers for exterior paints and nonwoven fa­brics.

5) poly{vinyl chloride) and vinyl chloride copolymers for plasti­sols and coatings.

6) vinylidene chloride copolymers for barrier coatings. 7) poly{ethylenel and ethylene copolymers for adhesives and coat­

ings. 8) poly<tetrafluoroethylenel and other fluorinated polymers. 9) poly<acrylamide), acrylamide copolymers, and derivatives for

flocculants and water absorbers.

The preparation of a latex is both a science and an art. It is a science in that the kinetic principles of free radical-initiated vinyl addi.tion polymerization are superimposed on the heterogene­ous polymer latex. It is an art in that the operator uses a re­cipe which comprises monomer, water, emulsifier, initiator, and other ingredients, and the quality of the latex obtained often depends upon his skill. Conventional emulsion polymerization com­prises emulsification of a water-immiscible monomer in a contin­uous water medium using an oil-in-water emulsifier and polymeri­zation using a water-soluble or oil-soluble initiator, to give a colloidal dispersion of polymer particles in water. The average particle size of conventional latexes is usually 100-300 nm, in contrast to the emulsion droplet size of 1,000-10,000 nm. Thus, any mechanism proposed for this process must explain the order­of-magnitude reduction in particle size observed in converting the monomer to polymer.

Inverse emulsion polymerization comprises emulsification of a wa­ter-miscible monomer, usually in aqueous solution, in a continu­ous oil medium using a water-in-oil emulsifier and polymerization using an oil-soluble or water-soluble initiator, to give a col­loidal dispersion of water-swollen polymer particles in oil. The average particle size of inverse latexes is usually 50-300 nm, as compared to the original droplet size of 50-1,000 nm. Similar systems include the preparation of nonaqueous dispersions, in which a water-immiscible monomer in organic solvent solution is polymerized using an oil-soluble initiator, so that the polymer precipitates as it is formed; in the presence of a suitable oil­in-oil emulsifier, spherical particles of 100-10,000 nm diameter are formed from the precipitating polymer. Thus, these polymeri­zations begin as precipitation polymerizations, but become emul­sion polymerizations upon stabilization of the polymer particles.

NUCLEATION AND GROWTH STAGES

The emulsion polymerization reaction can be divided into particle nucleation and particle growth stages. The particles are nuclea­ted by some appropriate mechanism and then grow until the supply

179

of monomer or free radicals is exhausted. The particle nucleation and growth stages occur concurrently or at least overlap, i.e., the particle growth stage begins with the nucleation of the first particle. For convenience, however, the two stages are considered separately, and the end of the particle nucleation stage is often taken as the beginning of the particle growth stage. In the par­ticle nucleation stage, the number of particles N depends upon the type and concentration of emulsifier, the type and concentra­tion of electrolyte, the rate of radical generation, the type and intensity of agitation, and the temperature, as well as several other parameters which are not well-understood. Thus, the parti­cle nucleation stage is often difficult to reproduce in consecu­tive experiments. In contrast, the growth stage is tractable and reproducible. As a first approximation, the rate of polymeriza­tion (or propagation) Rp is proportional to the number of_par­ticles N, and the number-average degree of polymerization Xn is proportional to the number of particles relative to the rate of radical generation Ri·

RATE OF POLYMERIZATION AND POLYMER MOLECULAR WEIGHT

As a first approximation, the rate of polymerization and the num­ber-average degree of polymerization are given by (Harkins, 1947; Smith and Ewart, 1948; Smith, 1948, 1949):

Rp = kp[MHiN

Xn = kp[MlnN/Ri

(1)

(2)

where kp is the rate constant for propagation, [M] the monomer concentration in the particles, n the average number of radicals per particle, ~nd Ri the rate of radical generation.

Thus, Rp is proportional to N and Xn to N/Ri, so that an increase in N gives a simultaneous increase in both the rate of polymeri­zation and the polymer molecular weight. These "emulsion polymer­ization kinetics" are different from ehe inverse variation of Rg and Xn in the general kinetic equations for mass, solution, ana suspension polymerization:

kp[M] (Ri/kt)l/2

kp[M] (1/Rikt)l/2

(3)

( 4)

'l'hese emulsion polymerization kinetics obtain when two criteria are fulfilled: 1) the radicals are segregated; 2) the number of loci available for segregation is within a few orders of magni­tude of the number of free radicals. In emulsion polymerization, the growing polymer radicals segregated in adjacent particles cannot undergo termination with one another because of the inter­vening aqueous phase, and the values of N are within a few orders of magnitude of the number of existent free radicals over a wid~ range of temperature and initiator concentration.

EMULSION POLYMERIZATION PROCESSES

Industrial emulsion polymerizations are usually carried out in stirred-tank reactors using one of three types of processes: 1) batch polymerization, in which all ingredients are added to the

180

polymerization reactor, and the mixture is heated with stirring to the polymerization temperature; 2) semi-continuous or semi­batch polymerization, in which neat or pre-emulsified monomer (and sometimes initiator and emulsifier) is added continuously or incrementally to the reaction mixture at the polymerization tem­perature; 3) continuous polymerization, in which all ingredients are added continuously to one part of the polymerization system, and partially or completely converted latex is removed continu­ously from another part of the system; the polymerization system may comprise a single continuous stirred-tank reactor, a series or cascade of continuous stirred-tank reactors, a loop or tube reactor, or a combination of any of these systems.

Generally, batch polymerization is used only for those systems that polymerize sluggishly, e.g., poly(butadiene-co-styrene) or poly(styrene-co-butadiene). For other systems that polymerize more rapidly, e.g., acrylate ester copolymers, the rates of po­lymerization are too rapid for the heats of reaction of a batch polymerization to be removed by the cooling system of a large re­actor, and semi-continuous or semi-batch polymerization must be used; the monomer is added continuously or in increments so as to control the rate of polymerization. This process not only gives excellent control and reproducibility, but it is also extremely versatile and can make heterogeneous particles with unusual lay­ered morphologies (e.g., core-shell particles) as well as homoge­neous particles; however, the smaller concentration of monomer in the particles gives a greater propensity for radical transfer re­actions; nevertheless, the final latex properties can be adjusted precisely and reproducibly. In contrast, continuous polymeriza­tion has certain economic advantages, but it is difficult to con­trol and to adjust the properties of the final latex; often, the average particle size (and conversion) of the exit stream cycles.

SEEDED EMULSION POLYMERIZATION

Many of the difficulties in industrial emulsion polymerizations can be traced to a batch-to-batch irreproducibility in the number of particles nucleated. This particle nucleation stage can be ob­viated by "seeding," i.e., by polymerizing monomer in a previous­ly prepared latex with controlled amounts of emulsifier and ini­tiator, so that the "seed" particles grow to a larger size with­out the generation of a new crop of particles. Thus, the diffi­cult-to-reproduce particle nucleation stage is obviated, and the polymerization begins in the tractable particle growth stage.

In batch or semi-continuous polymerization, seeding ensures the batch-to-batch reproducibility of the final particle size; in continuous emulsion polymerization, it ensures the reproducibili­ty, not only of the final particle size, but also of the conver­sion of the exit stream. Seeded emulsion polymerization is equal­ly adaptable to emulsion homopolymerization and copolymerization; moreover, two-stage or multi-stage polymerizations can be used to produce core-shell particles. The variation of the process (e.g., batch, semi-continuous, continuous), as well as the parameters of the polymerization, can be used to control the extent of grafting by transfer between the different stages of the polymerization. The versatility of this seeding process has resulted in its wide use in industry, to give excellent batch-to-batch reproducibility and to "tailor" the latex to the specific application.

181

MECHANISMS OF PARTICLE NUCLEATION

Many mechanisms ha~e been proposed to explain the particle nucle­ation stage. These mechanisms can be divided into four main cate­gories according to the locus of particle nucleation.

ll Monomer-swollen emulsifier micelles (Harkins, 1947; Smith and Ewart, 1948; Smith, 1948, 1949), in which radicals generated in the aqueous phase enter the monomer-swollen micelles and initiate polymerization to form a monomer-swollen polymer particle. Only one out of every 100-1000 micelles becomes a polymer particle; the others give up their monomer and emulsifier to neighboring micelles which have captured a radical. The particle nucleation stage ends with the disappearance of the micelles. The particle growth stage begins with the formation of the first polymer par­ticle and becomes the sole stage after the disappearance of the micelles. The monomer droplets serve as reservoirs, feeding mono­mer to the micelles and polymer particles by diffusion through the aqueous phase; radical entry into monomer droplets does not occur to a significant extent because of their relatively small surface area.

2) Adsorbed emulsifier layer (Medvedev, 1955, 1957), which is conceptually similar to initiation in micelles: a radical gener­ated in the aqueous phase initiates polymerization in an adsorbed emulsifier layer whether it is on micelles, polymer particles, or emulsion droplets; however, the probability that the radical en­ters any of these depends upon their relative surface areas. At the beginning of the reaction, the surface area of the micelles is so much greater than that of the emulsion droplets that the radicals are likely to enter micelles to the exclusion of the mo­nomer droplets; the polymer particles, once formed, compete with the micelles for the radicals, according to their surface area.

3) Aqueous phase (Priest 1952; Jacobi, 1952; Patsiga et al., 1960; Roe, 1968; Fitch and Tsai, 1971), in which radicals genera­ted in the aqueous phase add monomer units until the oligomeric radicals exceed their solubility and precipitate; the precipita­ted oligomeric radic .:< ls form spherical particles which adsorb emulsifier and absorb monomer to become primary particles. These primary particles persist or flocculate with already-existing particles or other primary particles. The function of the emulsi­fier is to stabilize the particles precipitating from the aqueous phase. The rate of particle nucleation is initially the rate of radical generation, but shortly after the formation of mature la­tex particles this rate is decreased by the rate of capture of the oligomeric radicals Rc and the rate of flocculation of the latex particles Rf (Fitch and Tsai, 1971):

dN/dt (5)

This mechanism is generally more applicable to monomers that have significant solubilities in water.

4) Monomer droplets, in which the chance entry of a radical into a monomer droplet of 2,000-5,000 nm diameter gives a polymer par­ticle of about the same size (Durbin et al., 1979), to form a small weight fraction of microscopic particles separate from the main submicroscopic distribution. This mechanism becomes signifi­cant when the average droplet size is decreased, e.g., as in nmi­niemulsions,n monomer emulsions of only 100-300 nm diameter pre-

182

pared using mixed ionic emulsifier-fatty alcohol (Ugelstad g_t al., 1973, 1974) or ionic emulsifier-alkane (Azad et al., 1976) systems; the formation of these small droplet sizes is attributed to the very low solubility of fatty alcohols and alkanes in water (Higuchi and Misra, 1962) or to the formation of crystalline (Chou et al., 1982) or liquid crystalline (Lack et al., 1987) complexes between ionic emulsifiers and fatty alcohols; these two explanations are not mutually exclusive.

For initiation in micelles, the disappearance of the micelles is the end of the nucleation stage; the particle growth stage begins with formation of the first polymer particle and becomes the sole stage after the disappearance of the micelles. For initiation in the aqueous phase, the rate of particle nucleation is initially the rate of radical generation, but shortly thereafter a steady state is reached between the initiation of primary radicals and the capture of the oligomeric radicals and the flocculation of the latex particles. Thus, the nucleation of particles continues throughout the course of the polymerization, but is moderated by the capture of the precipitating oligomeric radicals and the flocculation of primary and mature particles. The duration of the particle nucleation stage differentiates between the initiation­in-micelles and initiation-in-the-aqueous phase mechanisms. Ini­tiation in micelles is generally applied to monomers which are only sparingly soluble in water, and initiation in the aqueous phase to monomers with significantly higher solubilities in wa­ter. Table 1 lists the water solubilities of monomers that have been studied extensively. Generally, the particle nucleation of the sparingly soluble monomers through butadiene is generally considered to proceed by initiation in the micelles for emulsifi­er concentrations that exceed the critical micelle concentration (erne) , and that of monomers from vinyl acetate onward, by initia­tion in the aqueous phase. For the intermediate ethyl acrylate, methyl methacrylate, and vinyl chloride, both mechanisms have been proposed in separate instances, but most consider initiation in the aqueous phase the more appropriate mechanism. Indeed, ini-

~able 1. Water solubility of vinyl monomers.

Monomer

n-octyl acrylate dimethylstyrene vinyl toluene n-hexyl acrylate styrene n-butyl acrylate chloroprene butadiene vinylidene chloride ethyl acrylate methyl methacrylate vinyl chloride -vinyl acetate ethylene methyl acrylate acrylonitrile acrolein

water Solubility (25-500CJ (mM)

0.34 0.45 1.0 1.2 3.5

11. 13. 15. 66.

150. 150. 170. 290.

200-600 650.

1600. 3100.

183

tiation in the aqueous phase has been proposed for such sparingly soluble monomers as styrene (Roe, 1968).

For initiation in micelles, the emulsifier concentration must ex­ceed the critical micelle concentration. The classical concept is that the erne represents the concentration at which micelles first form; at higher concentrations, more micelles form and, at lower concentrations, no micelles are present. The erne is usually de­termined by the inflection point in the variation of conductivi­ty, turbidity, equivalent conductivity, surface tension, or osmo­tic pressure with concentration. For sodium dodecyl sulfate, all five parameters showed an inflection point at ca. 8 mM (Hiemenz, 1977), the most common value for the erne of this emulsifier, and consistent with micelles forming above ca. 8 mM and not forming at lower concentrations. Recent measurements of the partial spe­cific volume of sodium lauryl sulfate solutions (Bonner, 1980), however, suggest that aggregates of lauryl sulfate ions are pre­sent at concentrations well below the erne. Figure 1 shows the variation of partial specific volume with sodium lauryl sulfate concentration in pure water, and in the presence of the potassium persulfate initiator and sodium bicarbonate buffer often used in emulsion polymerization. In both cases, the partial specific vol-

l.Or-----------------------------~--------------

7

"' " ~.,

u 0. s

.a·_. --o--- - -o- -- -o----- ---c- .. _ -c---

"' = 0

TEMP SOLVENT •c

> u

o. 6 D }0. 0

H20 : ~- ~ ~~: ~~~~g} -u 0 }0. 0 ~ .. ~

6 20. 0 H

20

.. :;; 0 .• .. ..

t

IC/oiC·HzO -I

ICMC·HzO•O. )/oi·NICI --• I

' 10 40 60 80 100

W[ IGHT FRACTION 1 10•

Fig. l. Variation of partial specific volume of solute sodium lauryl sulfate with concen­tration in pure water and electrolyte solution (Bonner, 1980).

ume was a constant ca. 0.85 cc/gm above the erne, but dropped off rapidly below the erne to values of less than 0.44 cc/gm. The val­ues of the erne were ca. 8 mM in pure water and ca. 0.8 mM in electrolyte solution. Similar results were observed in the pre­sence of polystyrene latex particles. The rapid downturn below the erne, with no apparent minimum value within the accuracy of measurement, suggested that, below the erne, the lauryl sulfate ions were aggregated to varying degrees and that, above the erne, additional increments of sodium lauryl sulfate resulted in the formation of more micelles. The corresponding definition of the erne would be that emulsifier concentration above which all addi­tional emulsifier formed micelles (constant partial specific vol­ume) and below which the emulsifier showed varying degrees of ag­gregation (partial specific volume decreasing with decreasing

184

concentration without reaching a constant value) • This concept is not necessarily inconsistent with the inflection points of the five parameters, but is different from the classical concept.

NUMBER OF PARTICLES

The most important parameter in determining the number of parti­cles is the type and concentration of emulsifier. Figure 2 shows that, for a given emulsifier, the variation of the log number of particles with log emulsifier concentration was sigmoidal; log N increased steeply from a low plateau at low log [El to a high plateau at high log [E], with the midpoint of the rising curve corresponding to the critical micelle concentration (van der Hoff, 1960; Okamura and Motoyama, 1962; Dunn and Al-Shahib, 1980; Dunn, 1982). The mechanism of nucleation at low log [E] was pos­tulated to be homogeneous nucleation in the aqueous phase; that at high log [E], to nucleation in monomer-swollen micelles. The initial low log [E] plateau was attributed to the limiting effect of Ri on the homogeneous nucleation. The high log [E] plateau was attributed to the value of rti limiting the rate of radical entry into the micelles. Polymerizations in which the value of N was independent of [E] gave good batch-to-batch reproducibility.

z

" 0 -'

LOG C

Fig. 2. Typical variation of number of particles with emulsifier concentration (van der Hoff, 1960; Okamura and Motoyama, 1962; Dunn and Al-Shahib, 1980; Dunn, 1982).

LATEX COLLOIDAL STABILITY

Latexes are colloidal sols; their stability is governed by the same principles as colloidal sols in general. The stability of a latex is determined by the balance between the electrostatic and steric repulsion forces and the London-van der Waals attraction forces. The electrostatic repulsion forces arise from adsorbed or chemically bound surface ions; these forces are affected strongly by the concentration and valence of the counterions. The steric repulsion forces arise from adsorbed or chemically bound hydrated uncharged surface groups; these forces are not affected signifi­cantly by the other parameters of the system. The London-van der Waals attraction forces arise from the difference in dielectric constant between the particles and the medium; these forces are not affected significantly by other parameters of the system. The combination of the electrostatic repulsion forces and London-van

185

der Waals attraction forces can be accounted for by the Verwey­Overbeek theory (Verwey and Overbeek, 1948), but there is no uni­fying theory for steric stabilization: neverthless, the effect of steric stabilization forces in combination with the other forces can be accounted for (Ottewill, 1967; Sontag and Strenge, 1972).

The stability of colloidal sols may also be affected by deple­tion flocculation (Asakura and Oosawa, 1954): the presence of soluble nonadsorbing polymer molecules in a colloidal sol affects the interaction between the stabilizing layers of the colloidal particles, so that the polymer molecules are excluded from the regions in which the stabilizing layers are in contact, and thus exert a force to form a more concentrated particle phase. Theore­tical explanations have been proposed for this depletion floccu­lation (Gast et al., 1983a, b) as well as for restabilization or depletion stabilization (Gast et al., 1983b; Gast, 1984).

Latex particles can be stabilized by three different mechanisms: 1) adsorbed ionic or nonionic groups; 2) chemically bound ionic or nonionic groups; 3) polar-but-uncharged groups.

The adsorbed groups may be conventional emulsifiers (e.g., sodium lauryl sulfate or nonylphenol-polyoxyethylene adducts) or polym­eric emulsifiers (e.g., methylcellulose). The adsorption of these emulsifiers is governed by an adsorption-desorption equilibrium, and the adsorbed groups may desorb if the composition of the la­tex serum is changed, the latex flocculates, or is dried. These equilibria are easy to recognize for conventional emulsifiers, but are more difficult to recognize for the polymeric emulsifi­ers, which desorb only difficultly; however, the addition of a fresh adsorbing surface usually results in the desorption of the polymeric emulsifier and its readsorption on the fresh surface, to meet a new adsorption-desorption equilibrium (Vanderhoff et al., 1977).

It should be emphasized that any polymeric emulsifier, ionic or nonionic, which adsorbs on the latex particles to increase their stability may also cause flocculation of the latex by "bridg­ing." Generally, very low concentrations of the polymeric emulsi­fier give flocculation whereas higher concentrations give stabi­lity; this phenomenon has been known for many years as the "sen­sitization-stabilization effects of protective colloids on col­loidal sols." Such polymeric emulsifiers may be prepared in situ when a functional monomer (e.g., acrylic acid, 2-sulfoethyl meth­acrylate, 2-hydroxyethyl acrylate) is used in the polymerization: in this case, the composition, molecular weight, and concentra­tion of the polymeric emulsifier determines whether it will floc­culate the latex or improve its stability.

The chemically bound groups may be sulfate endgroups ar1s1ng from the persulfate initiator), their reaction products (e.g, hydroxyl or carboxyl groups), or groups introduced by functional monomers (e.g., acrylic acid, 2-sulfoethyl methacrylate, 2-hydroxyethyl acrylate). These chemically bound groups cannot desorb without removing the surface layer of the particles and therefore remain fixed on the particle surface despite changes in the composition of the latex serum or drying the latex to form a continuous film. In particular, the surface sulfate endgroups contribute signifi­cantly to latex stability, comprising 1.0-1.6 surface sulfate endgroups/polystyrene molecule and surface concentrations as high as one group/nm2 (Vanderhoff et al., 1970).

186

The polar-but-uncharged functional groups of the monmer units that are oriented in the polymer-water interface have been postu­lated to improve the stability of the latex (Yeliseyeva, 1972), e.g., the ester group of methyl acrylate is oriented in the in­terface to a higher degree than that of n-butyl acrylate; this higher degree of orientation gives a lesser adsorption of conven­tional emulsifier. This concept has not yet been demonstrated for other monomers, but it offers a means of explaining hitherto un­explained latex stability data.

GENERATIONS OF LATEXES

Historically, the development of latexes for practical applica­tions can be divided in three generations of latexes.

The first-generation latexes used conventional emulsifiers as the polymerization emulsifier, steam-stripping stabilizer, and post­stabilizer. In the best cases, these latexes showed excellent stability to mechanical shear, added electrolyte, and freezing­and-thawing; however, their high surfactant concentration (often as high as 6%) gave low surface tensions and hence considerable foaming and, in some cases, poor adhesion to the substrate.

In the second-generation latexes, all or part of the conventional emulsifier was replaced with a functional monomer (e.g., acrylic acid, 2-sulfoethyl methacrylate, 2-hydroxyethyl acrylate). In the best cases, these latexes gave excellent stability to mechanical shear, added electrolyte, and freezing-and-thawing; their surface tensions, moreover, were usually higher than those of the first­generation latexes, so that they showed a lesser tendency to foam and the functional groups often improved the adhesion to certain substrates.

The third-generation latexes used a polymeric emulsifier. In the best cases, the development of the third-generation latex started with a good second-generation latex, which was characterized to determine the composition and molecular weight of the copolymer that was prepared in situ and adsorbed on the particle surface; this copolymer was then prepared in a separate reaction to the same composition and molecular weight, and the product was used as a polymeric emulsifier. The best of these latexes gave excel­lent stability to mechanical shear, added electrolyte, and free­zing-and-thawing; moreover, their surface tensions were high, sometimes approaching that of water itself, and the latexes show­ed little or no tendency to foam.

The transition from the first-generation to the second-generation to the third-generation latexes requires an increasing level of technology. The production of the first-generation latexes began in the mid-1940's, and some examples are still being produced to­day. The production of the second-generation latexes began in the late 1950's, and most of the latexes produced today are of this generation. The production of third-generation latexes began more recently, and -this generation represents the ultimate in latex development.

187

CHOICE OF EMULSIFIER

The function of the emulsifier in an emulsion polymerization is to generate the desired number of particles without forming coa­gulum. For a first-generation batch polymerization, several emul­sifiers or mixtures of emulsifiers can be used for the polymeri­zation emulsifier, steam-stripping stabilizer, and the post-sta­bilizer. The polymerization emulsifier selected is a compromise between the amount required and its cost, e.g., in styrene-buta­diene copolymerization, 20 mM Dowfax 2Al <c12-branched monoalkyl­ated diphenyl ether disulfonate) was required to give an average particle size of 185 nm, as compared with only 5.0 mM of the Cl6-linear monoalkylated analog; the latter emulsifier could cost twice as much as the Dowfax 2Al and still be less expensive to use (Vanderhoff ~., 1990). The molecular areas of the two emulsifiers were 0.81 and 0.94 nm2, and the surface coverages were only 12 and 13%, respectively.

These low surface coverages were insufficient to confer stability for the steam-stripping process. Generally, emulsifiers that con­tain sulfate groups (e.g., sodium lauryl sulfate) are susceptible to hydrolysis during steam-stripping; therefore, an emulsifier with sulfonate groups should be selected for the steam-stripping. After steam-stripping, the latex must be stabilized to give it the requisite stability to mechanical shear, added electrolyte, and freezing-and-thawing for the application. Generally, the re­quisite stability cannot be obtained by addition of more anionic emulsifier of the same type used for polymerization and steam­stripping (i.e., electrostatic repulsion is not enough); instead, nonionic emulsfier must be used (steric repulsion is required). For the foregoing example, the addition of more Dowfax 2Al or its C16-linear monoalkylated analog improved the latex stability somewhat, but the addition of Igepal C0-880 (nonylphenol-polyoxy­ethylene adduct) was required to give the requisite stability.

Second-generation semi-continuous polymerizations can be carried out using emulsifier or functional monomer to generate the requi­site number of particles. A small amount of seed latex can be added to furnish the seed particles, or a small part of the mo­nomer mixture can be polymerized in batch or the monomer feed can be started, to generate the seed particles in situ. The monomer can be added either continuously or in increments, and neat or pre-emulsified. The function of the emulsifier, if used, is the same as in first-generation batch polymerization, i.e., to nu­cleate the requisite number of particles. Generally, the copolym­erization of the functional monomer introduces sufficient func­tional groups to confer the requisite stability during the polym­erization; these functional groups may also be sufficient to sta­bilize the latex during steam-stripping and to post-stabiize the latex for the intended application. If this is not the case, an­ionic emulsifier can be added for the steam-stripping and nonion­ic emulsifier for the post-stabilization.

Third-generation polymerizations can be carried out by batch or semi-continuous polymerization. The key point is the use of a po­lymeric emulsifier, which may be one that has been used tradi­tionally (e.g., polyvinyl alcohol for poly(vinyl acetate) latex­es) or one that has been tailored for the application. The latter comprises the characterization of a good second-generation latex to determine the composition and molecular weight of the copolym­er that has been prepared in situ and adsorbed on the particle

188

surface; this copolymer is then prepared in a separate reaction and used as the emulsifier. The use of the proper polymeric emul­sifier can confer stability during polymerization, steam-strip­ping, and post-stabilization. If the polymeric emulsifier alone is not sufficient to confer the requisite stability for post-sta­bilization, nonionic emulsifier can be added.

FORMATION OF COAGULUM

Coagulum (defined here as polymer recovered in a form other than stable latex) is formed in all types of emulsion polymerizations. This coagulum decreases the yield of salable polymer, increases the reactor cycle time, and necessitates the cleanup of the reac­tor between polymerizations. The coagulum itself poses disposal problems and is often a health hazard. Moreover, its formation stifles the development of new latexes. There are three main types of coagulum (Vanderhoff, 1981, 1983):

ll Coagulum formed during polymerization and recovered from the latex by filtration or sedimentation, which may range in size from a single large lump (which occasionally fills the reactor) with little or no fluid latex to lumps in an otherwise stable la­tex to microscopic sand-like grains suspended in the latex. The lumps may be solid or porous, soft and sticky or hard and granu­lar in consistency, according to the polymer, the conversion at which the coagulum was formed, and the degree of plasticization by the monomer. The microscopic coagulum particles are difficult to remove by filtration or sedimentation, and may appear as a surface roughness or haziness in the dried latex films.

2) Coagulum deposited on the reactor surfaces during polymeriza­tion, which may take the form of lumps, accretions, or a surface skin on the reactor wall, bottom, or roof, the agitator shaft and blades, the baffles, thermowell, and cooling coils. This coagulum deposited on the reactor surfaces often resembles that recovered from the latex, but sometimes is of a different form, perhaps be­cause of a different mechanism of formation.

3) Coagulum formed in the latex after polymerization during stripping, storage, transfer, or transportation. Some coagulum may be formed during stripping of the residual monomer, particu­larly if the latex is sparged with steam. Coagulum may also be formed by flocculation of the latex by mechanical shear during pumping to transfer it from one container to another. The latex may also be flocculated by variations in temperature, e.g., by freezing or by heating to a high temperature or chilling to a low temperature. Accelerated storage stability tests are often run at 50-100°C. Also, microscopic particles may settle or cream dur­ing storage. Overbeek's criterion (Overbeek, 1952) states that a particle which settles only 1 mm in 24 hours according to Stokes Law will actually never settle because of the Brownian motion of the particles and the chance thermal convection within the sam­ple; using this criterion, the critical size for settling of po­lystyrene (density 1.050 gm/cm3) particles in water is 650 nm.

There are two main mechanisms for the formation of coagulum (Van­derhoff, 1981, 1983).

1) The failure of the colloidal stability, during or after polym­erization, to cause flocculation of the latex particles and even-

189

tually form microscopic or macroscopic coagulum. This mechanism can result in coagulum recovered from the latex, coagulum on the reactor surfaces, or coagulum formed during stripping, storage, transfer, or transportation. The factors affecting the stability include the polymerization recipe, type and intensity of agita­tion, temperature, and age and storage conditions. The important parameters of the polymerization recipe are the polymerization process, monomer/water phase ratio, solubility of the monomer in water, emulsifier type and concentration, initiator type and con­centration, electrolyte concentration, and impurities present in the system.

The stability of the latex to flocculation depends upon the in­teraction of the electrostatic and steric repulsion forces with the London-van der waals attraction forces. The electrostatic repulsion is greatest closest to the particle surface and decrea­ses exponentially with increasing distance; the rate of decrease depends upon the electrolyte concentration; the higher the con­centration and the higher the valence of the counterions, the more rapid is the decrease. The London-van der waals attraction forces are greatest closest to the particle surface and decrease with increasing distance according to a power law; the rate of decrease is unaffected by the electrolyte concentration. The net interaction for a stable colloidal sol is a deep primary well of attraction at very small distances, rising to a repulsion peak at greater distances, followed by a decrease to zero. The presence of a steric stabilization layer gives a mechanical barrier to flocculation; the net interaction for a stable colloidal sol is a high repulsion at very small distances, decreasing to a shallow minimum at greater distances, followed by a rise to a second low­er repulsion peak and a decrease to zero.

2) Polymerization of the monomer by a mechanism other than emul­sion polymerization, to give polymer of a form other than latex particles. The coagulum which is recovered from the latex may re­sult from polymerization of the monomer in large droplets or in a monomer layer; coagulum deposited on the reactor surfaces may re­sult from polymerization of large monomer droplets or a monomer layer, surface polymerization on the reactor surfaces, or polym­erization of monomer in the vapor space. The surface polymeriza­tion is nucleated by the polymer wetting and sticking to the re­actor surfaces, which is enhanced by sur face scratches, rough­ness, or other discontinuities.

FLOCCULATION OF LATEX PARTICLES

There are three main mechanisms for the floculation of colloidal sols.

1) Diffusion-controlled flocculaton, in which each particle acts as a center to which the other particles diffuse and flocculate (von Smoluchowski, 1916, 1917); for latex particles, the stabili­zing layer presents a potential energy barrier to flocculation.

2) Agitation-induced flocculation (von Smoluchowski, 1917; Tuo­rila, 1927; Mueller, 1928), which depends upon the collision ra­dii of the particles and the rate of mechanical shear. For col­loidal particles of 100 nm diameter and typical parameters, dif­fusion-controlled flocculation is predominant; at 1,000 nm diame­ter, the diffusion-controlled flocculation and agitation-induced

190

flocculation are equivalent, and agitation-induced flocculation is predominant at larger sizes (Overbeek, J. Th. G., 1952).

3) Surface flocculation (Heller and Peters, 1970, 1971; Peters and Heller, 1970; Heller and De Lauder, 1971; De Lauder and Hel­ler, 1971; Diep S. et al., 1979), in which colloidal particles adsorb at the water-air interface according to a Langmuir adsorp­tion isotherm and flocculate there, according to the mechanism of diffusion-controlled flocculation; agitation renews the particle concentration at the surface.

The formation of coagulum during emulsion polymerization was cor­related with the agitation parameters (Lowry et al., 1984, 1986); at low Reynolds numbers, the average shear rate was assumed to be proportional to the rotational speed of the impeller, which was corroborated by experiments with polystyrene latexes; for high Reynolds numbers, the Kolmogorov theory of locally isotropic flow was used to relate the average shear rate to the power consump­tion, which was corroborated by experiments with polyvinyl chlor­ide latexes (Rubens, 1958).

REFERENCES

Asakura, s. and F. Oosawa (1954). J. Chern. Phys. 22 1255. Azad, A. R. M., J. Ugelstad, R. M. Fitch and F. K. Hansen (1976).

ACS Symp. Ser. 24 1. Bonner, F. J. (1980). Prepr. Org. Coatings Plastics Chern. 42 181. Chou, Y. N., M. s. El-Aasser and J. w. Vanderhoff (1982). ACS

Symp. Ser. 197, 399. De Lauder, w. B. and w .• Heller (1971). J. Coll. Inter. Sci. 35

308. Diep s., W. Heller and s. Kalousdian (1979). J. Coll. Inter. Sci.

70 328. Dunn, A. s. and w. A. Al-Shahib (1980). Polymer Colloids II (R.

M. Fitch, ed.), p. 619, Plenum, New York. Dunn, A. s. (1982). Paper, International Latex Conference London,

June 13-16. Durbin, D.P., M. s. El-Aasser, G. W. Poehlein and J. W. Vander­

hoff (1979>. J. Appl. Polym. Sci., 24, 703. Fitch, R. M. and c. H. Tsai (1971). In Polymer Colloids (R. M.

Fitch, ed.l p. 73, Plenum, New York. Gast, A. P., C. K. Hall and W.B. Russel (1983al.J. Coll. Inter.

Sci. 96 251. Gast, A. P., c. K. Hall, and w. B. Russel (1983bl. Disc. Far.

Soc. 76 189. Gast, A~P. (1984). Ph.D. dissertation, Princeton Univ. Harkins, w. D. (1947). J. Am. Chern. Soc. 69 1428. Heller, W. and w. B. De Lauder (1971). 5:" Coll. Inter. Sci. 35

60. Heller, W. and J. Peters (1970). J. Coll. Inter. Sci. 32 592. Heller, w. and J. Peters (1971). J. Coll. Inter. Sci. 35 300. Hiemenz, P. C. (1977). Principles of Colloid and Surface Chemis-

1£¥, p. 284, Dekker, New York. Higuchi, W. I. and J. Misra (1962). J. Pharm. Sci. 51 459. Jacobi, B. (1952). Angew. Chern. 64 539. Lack, C. D., M. S. El-Aasser, C. A. Silebi, J. W. Vanderhoff and

F. M. Fowkes (1987). Langmuir 1 1155. Lowry, v., M.s. El-Aasser, J. W. Vanderhoff and A. Klein (1984).

J. Appl. Polym. Sci. 29 3925.

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Lowry, V., M. S. El-Aasser, J. w. Vanderhoff, A. Klein and C. A. Silebi (1986). J. Coll. Inter. Sci. 112 521.

Medvedev, S. s. (1955). Ric. Sci. Suppl. 25 897. Medvedev, S. s. (1957). International Symposium on Macromolecular

Chemistry, Prague, p. 174, Pergamon, New York. Mueller, H. (1928). Kolloidchem. Beihefte ll 223. Okamura, S. and T. Motoyama (1962). J. Polym. Sci, 58 221. Ottewill, R. H. (1967), In Nonionic Surfactants (M, Schick, ed.),

p, 627, Dekker, New York. Overbeek, J, Th, G. (l952a), In Colloid Science (H. R. Kruyt,

ed,), Vol. 1, p. 80, Elsevier, New York. Overbeek, J, Th. G, (l952b) , In Colloid Science (H, R. Kruyt,

ed,), Vol . 1, p. 290, Elsevier, New York, Patsiga, R., M. Litt and V. Stannett (1960). J, Phys, Chern, 64

801. Peters, J. and W, Heller (1970), J, Coll, Inter. Sci. 33 578. Priest, W. J. (1952) . J. Phys. Chern. 561077. Roe, C. P. (1968), I&EC 60 20. Rubens R. w. (1958). M.S. thesis, Newark College of Engineering. Smith, W. V. (1948). J, Am. Chern, Soc. 1..Q. 3695. Smith, W. V, (1949), J. Am, Chern. Soc, 71 4077, Smith, w. V. and Ewart, R. H. (1948), J, Chern. Phys. 16 592. Sontag, H. and K. Strenge (1972), Coagulation and stability of

Disperse Systems (R. Kondor, translator), p. 27, Halsted, New York.

Tuorila, P. (1927). Kolloidchem. Beihefte 24 1. Ugelstad, J,, M. S. El-Aasser and J. W. Vanderhoff (1973), ~­

lym. Sci., Polym. Lett. Ed, 11 505. Ugelstad, J,, F. K. Hansen and s. Lange (1974), Makromol. Chern.

175 507. van der Hoff, B. M, E. (1960). J, Polym. Sci. 48 175. Vanderhoff, J, w., H. J. van den Hul, R. J. M. Tausk andJ, Th,

G. Overbeek (1970), In Clean Surfaces: Their Preparation and Characterization for Inter facial Studies (G. Goldinger, ed,) , p. 15, Dekker, New York.

Vanderhoff, J. w., F. J, Micale and P, H. Krumrine (1977). ~ Pur. Methods i 671. ·

Vanderhoff, J, w. (1981), ACS Symp. Ser. 165 199, Vanderhoff, J. w. (1983), NATO/AS! Bristol, UK, Science and Tech­

nology of Polymer Colloids (G. W. Poehlein, R. H. Ottewill, J. W. Goodwin, eds.), Vol. I, p. 167, Martinus Nijhoff, Boston.

Verwey, E. J. W. and J. Th. G. Overbeek (1948) • Theory of Stabi-lity of Lyophobic Colloids, Elsevier, New York.

von Smoluchowski, M. (1916), Physik. Al7 557, 585. von Smoluchowski, M. (1917), z. physik , Chern . 92 129. Yeliseyeva, V. I. (1972), Acta. Chim, Acad. Sci. Hung. 2li!L 465,

192

THE FUNCTION OF SURFACTANT MICELLES IN LATEX PARTICLE NUCLEATION.

F.K Hansen

Department of Chemistry, University of Oslo , P .O. Box 1033 Blindern , 0315 Oslo 3, Norway

ABSTRACT

193

The molecular mechanisms involving the surfactant micelles in the nucleation interval of an emulsion polymerization are described. Quantitative expressions for the rate of radical capture in micelles are given, and from these the conclusion is drawn that for ionic surfactants, the micelles must play an important part in the particle nucleation process, also for more water soluble monomers. Modifications to the nucleation mechanism in the case of nonionic emulsifiers are discussed and a possible decrease in radical absorption rate due to a dense diffusion barrier on the aqueous side of the surface is proposed.

KEYWORDS

Emulsion polymerization; micelles; particle nucleation; diffusion; absorption

INTRODUCTION

The theory for particle nucleation in emulsion polymerization has traditionally been described by the Smith-Ewart (S-E) theory (Smith and Ewart, 1948). In this theory the emulsifier (surfactant) micelles are recognized as the sole locus for particle nucleation. The well known Smith-Ewart expression for the particle number is

(1)

Here p is the rate of radical generation, ~ is the (constant) rate of particle volume growth, a

5 is the specific surface area of the emulsifier, and S is the

total amount of emulsifier (e.g. in micelles) . This expression gives good agreement for systems characterized by monomers of relatively low water solubility and low chain transfer constant, combined with surfactants with low critical micelle concentrations (CMC). For other systems the particle numbers found experimentally show strong deviation both in absolute magnitude and in the surfactant and initiator dependency (orders). The S-E expression have been rederived by Roe (1968) on the basis of a homogenous mechanism disregarding micelles as nucleation loci , exchanging the CMC with a "critical stabilization concentration".

The homogenous nucleation theory has been generally extended by the work of Fitch and Tsai (1972; Fitch, 1973; Fitch and Shih, 1975) and by Hansen & Ugelstad (1978, l979a-d) . The latter concludes that micelles may play a mayor part above the CMC for many monomers. These ideas and derivations have

194

eventually been labeled "HUFT" theory and the main conclusion is that particles may be formed by 3 different mechanisms, alone or in combination . These are 1) Precipitation of growing oligomers from the water phase (homogenous nucleation), 2) Nucleation from emulsifiers micelles as in theS-E-theory , and 3) Nucleation in monomer droplets. The theory also includes the possibility for limited coagulation of the small primary particles, especially in emulsifier-free and low emulsifier cases.

Even if nucleation takes place exclusively in micelles, the S-E expression (1) is changed if chain transfer to monomer and radical desorption/reabsorption is important . It has been shown (Nomura et al., 1976; Hansen and Ugelstad, 1979d) that a general expression for the particle number in this case is

(2)

where 0 . 6<z<l .O depending on the chain transfer constant and water solubility of the monomer. The details in the nucleation work up to 1980 has been extensively reviewed by this author earlier (Hansen and Ugelstad, 1982).

In the last decade, Gilbert, Napper and coworkers (Lichti et al ., 1983; Feeney et al., 1984, 1987; Richards et al., 1989) have done considerable work in order to discriminate between the nucleation mechanisms. Especially the amount of experimental data has been considerably increased, and quantitative calculations on limited coagulation seem to confirm the theory of homogenous nucleation. However there still seems to be some controversy over the role of the emulsifier micelles, the main question being if and to what degree these are the main locus for nucleation at supermicellar surfactant concentrations. Also the role of water phase termination and the magnitude of the termination constant have been questioned . Another question that has been raised by these authors is the possibility for limited coagulation also above the CMC. This mechanism has been proposed on the background of the positively skewed particle size distributions, which do not agree with a decreasing rate of nucleation during Interval I . This mechanism does not, however, definitely exclude the possibility for nucleation in micelles .

On this background, there is a need for a more thorough investigation into the role of the micelles in particle nucleation . In this paper some of the main features of the HUFT theory regarding radical absorption are reviewed, and some further ideas are discussed that may serve as a basis for future work.

ABSORPTION RATE OF RADICALS IN MICELLES

When evaluating the role of emulsifier micelles the main question is if micelles capture (absorb) radicals ( oligomers or monomer radicals) or not, or more precisely , at what rate this capture takes place . The traditional argument for capture is that the micelles are so numerous, 1019 - 1021 per drol, that they have to dominate the absorption process . Arguments against micellar capture have been of a phenomenologic type, looking more at the consequences of the mechanism than at the mechanism itself. As this procedure is a good initial approach, it is clearly desirable also to understand why a nd how the results can be explained, and the outcome of this process may call for reevaluation of experimental procedures and results .

A derivation of the net rate of radical absorption into spherical particles has been performed by this author earlier (Hansen and Ugelstad , 1978) and will not be r e peated here . However it may be worthwhile to go into some detail in t he absorption process in order to evaluate the different steps that are involved:

The oligomeric radica l s tha t stem from the i nitiator are surface active, while

195

the monomer radicals or oligomers grown from these are not . When the radicals are to be adsorbed on a micelle (or on any particle) they must first diffuse through the bulk phase to the surface. This process is often considered to occur in two steps and has been treated quantitatively in the famous work by Ward and Tordai (1946). The first step involves pure diffusion to the "subsur­face" (i.e . just outside the "true" surface) while the second step involves an adsorption process which may involve an activation energy connected to desol­vatization and/or stearic effects . The first step is completely described by Fick's second law for a non steady-state process which gives a time dependent adsorption rate . In an emulsion polymerization process, however , it is usually justified to use a steady-state approximation with Fick's 1st law. The second step is very dependent on the adsorbing molecule and on the surface compos i tion . Several workers (Ward and Tordai, 1946 ; Joos and Serrien, 1988) have found that the adsorption of small molecules (up to C-7 alcohols) is transfer controlled, whi le larger molecules are diffusion controlled. Also the rate constant for surfactant adsorption in micelles that is equal to the rate constant, k±, for the fast relaxation process (Wennerstrom and Lindman, 1979) show that this is mostly a diffusion controlled process, at least when the surfactant form gaseous or liquid expanded layers. It should be kept in mind, however, that emulsifiers or mixed emulsifier systems that form condensed surface layers may significantly slow down the adsorption process .

When the radical has arrived at the surface, it can either stay adsorbed, desorb again into the bulk, or diffuse further into the micellejparticle. In the case of small micelles of surfactants such as sodium dodecyl sulfate ( SDS) the question of further diffusion is rather irrelevant, because it is usually believed that the solubilized monomer is present close to the interphase (in the palisade layer) and the micelle is in any case very small . The rate of desorption can be deduced from the desorption rate constant, k~. for the above mentioned fast relaxation process. When the micelles are larger (especially nonionic micelles) or converted to polymer particles , the question of further diffusion becomes important . Even if the molecules are surface active , they may be truly absorbed , at least the radical end may be buried because of the propagation process . In the last case, the radical will hardly desorb again. The engulfment of surface active radicals may possibly be described by a similar 2-step process as in the aqueous phase. The equations for simple diffusion from the interphase into a particle with simultaneous chemical reaction have been derived by Danckwe~s (1951) both for steady-state and non steady-state condi­tions .

The Hansen and Ugelstad absorption equation is based on steady state diffusion, and describes the combined adsorption to the interphase as a process of diffusion against a potential energy barrier. The energy change at the interphase is represented simply by the r a tio, a, between the solubility in oil and water , and further diffusion is calculated by the Danckwerts steady state equation. A key issue of the combined process is that radicals are captured in the particles only if they react there , otherwise they will diffuse out again and back to the bulk phase . The total net rate of absorption is given by

where

aDP(X coth X - 1) PA - 4~D~r[RJw --~-----------------­

Dw + W'aDp(X coth X - 1) (3)

(4)

Here r is the particle radius, Dw and Dp are the diffusion constants in water and particles, respectively , a is the equilibrium distribution constant for radicals between particles and water, and [Rlw is the bulk concentration of radicals . The parameter k is the first order rate constant for reaction of a

196

radical inside a particle and consists of the sum of the propagation and termination rate constants (1st order) as shown in Equ . (4) (vis the particle volume) . W' is the electrostatic factor (2:1) analogous to Fuchs' stability ration. The fraction, denoted by F, is the "efficiency factor", describing to what degree absorption is lowered compared to irreversible diffusion. The equation may seem complex, but it can often be simplified to some limiting cases where the true physical processes can be easily understood. These are:

1) Diffusion control in the water phase when the water solubility of the radicals is very low andjor the particles are large : ->Absorption rate is proportional to the particle radius.

10.,2

F 104

10"'

10 ..

10 .. 1

F 104

10"'

v v v v

v v v v

v v

v

v_... v

/

/'

/ /'

/ /'

vv vv v v v v v v v v v

/ v -

~ 10 100

(nm)

v/ ·v /

v v v /

v -

% 10 100

r (nm)

-r-

'r--.

I'--

10"' I

10""'

1000

I /

/

F 104 //

/ 7

10"'

/ L

/

1000

10

vv v v

I

"-

~ 100

(nm)

__....-i--- .---1-

/

/

/

/

10

/

/

/

"-

~ 100

(nm)

1000

1000

Fig. 1. Absorption efficiency, F , as a function of particle radius, r , and the distribution constant , a, for radicals between the oil and water phase . The curves are for a=l, 10 , 102 , 103, 104 , and 105 respec­tively , beginning at the bottom. A: Ordinary conditions : n- 0 , 7mk [M]p=l500 s-1, W' - 1, Dw=lo-7 dm2;s,

D -lo-B dm2;s k -1oB dm3 mol s p ' tp . B: Particles with 1 radical, n-1. C: With electrostatic repulsion, W'=lO. D: With diffusion constant in the particles, Dp- lo-12 dro2js.

197

2) Diffusion control in the oil phase when the diffusion constant in this phase is very low: ->Absorption rate is proportional to the particle surface.

3) Reaction control in the oil phase when the particles are small andjor the water solubility of the radicals is medium to high: ->Absorption rate is proportional to the particle volume.

Also by plotting F as a function of particle radius r and the distribution constant a, the true implications of this equation appear, as shown in Fig. 1. Figure lA represents micelles and particles without any radicals (n-0) and B the same conditions for particles which contain 1 radical (n=l). Figure lA shows that for relatively small particles, all other than very water insoluble molecules are absorbed at a much lower rate than by irreversible diffusion. The slopes +2 (A) or -1 (B) in the logjlog plots correspond to case 3) above, meaning that

and (5)

The slope +2 corresponds to the case where k ~ kp[M]p, the rate constant for propagation in particles, whereas the slope -1 corresponds to k- ktnfNAv , so that F becomes proportional to ljr and pA becomes independent of particle size. Case 3) means that radicals are absorbed at a gross rate equal to the diffusion rate (with F-1), but are desorbed again at the same rate, if they do not react inside the particle. In Fig. lC is shown the effect of a potential energy barrier (W'-10), revealing that such an effect is only expected when the diffusion rate is high, close to case 1) (for values of W' is referred to Hansen and Ugelstad, 1978). The exact magnitude of W' is difficult to calculate, but it is generally believed that it is quite small (<10).

Figure lD shows case 2), the effect of a strongly decreased diffusion rate in the particles (reduced from 10-8 to lo-12 dm2js). It is seen that even this very strong decrease in Dp is not expected to have importance for the radical absorption in micelles, as the effect is only noticeable for larger particles . A stronger effect of a diffusion barrier is expected, however, if this barrier is on the aqueous side of the surface . The barrier may have the form of a dense layer of low diffusion coefficient or an a ctivation energy barrier that slows down the absorptio~ from the subsurface to the surface as mentioned above. This barrier must efficiently hinder the radicals to contact the solubilized monomer; a layer of water soluble polymers as in many nonionic micelles may be expected to behave this way . The quantitative effect of this sort of barrier may be easier explained ifF from Equ.(3) is written on the form

U- ljF- Dw/[aDp(X coth X - 1)) + W' (6)

The parameter U may be looked upon as the resistance to mass transfer. It may then be easily shown that additional diffusion barriers will appear as addition­al terms to this resistance . If we visualize a thin diffusion layer at the surface with thickness 6 and diffusion constant D

5 we will have

(7)

If D5

is several orders of magnitude lower than Dw and if the particles are small (low r) this additiona l resistance may become several orders of magnitude high, and therefore will have important influence on the upper limit of F . This is illustrated in Fig . 2, where the value of 6-1 nm and D

5-lo-10 dm3js. We see

that the additional diffusional resistance sets · an uppe r limit of F for all chains. This is very important, because even the water insoluble long oligomers will be slowed down, and possibly even more that the short chains, because they will have a lower diffusion constant. The slope +1 of the upper limiting curve

198

means that the absorption rate will be proportional to Nr2, i.e. the total particle surface. This sets the conditions for the collision theory. Because the resistance is on the aqueous side, the solubility ratio, a, does not enter Equ . (7); this will be the case, however, if the resistance is on the "oil" side. U will then be lowered by this factor in the denominator, which will mean that the upper limit of F will probably still be close to 1 .0 as in Fig. lD.

1 o-1

10-2

F 10-3

10-4

10-5

...,. ~~ ,_ .. y v,.... , / v / /

..... ~ / ./ / / v vv v

/ / /

v vv v / v y

10-6 / v

10 100 1000 r (nm)

Fig. 2. Absorption efficiency , F, as a function of particle radius, r, and the distribution constant, a, as in Fig. 1, but with additional diffusion resistance expressed by Equ . 7 with 6-1 nm and D5~lo-10 dm3; s . The curves are for a-1, 10, 102, 103 , 104 , and 105 respectively, beginning at the bottom.

THE NUCLEATION PROCESSES

The most probable situation during the particle nucleation period of any monomer where micelles are present, may be visualized using the ideas outlined above: Radicals are created by splitting of the water soluble initiator and add monomer in the aqueous phase because they are not oil soluble (a<<l). Soon the radicals will become partly oil soluble (a~l) and may absorb into micelles at a net rate proportional to a and proportional to the propagation rate kp[Mlp· Reaction in the micelle will lead to an oligomer with one extra monomer unit . The value of a for this chain will be larger , but as ·long as say a <l05 (deduced from Fig. lA), it will desorb again. We will therefore have a situation where radicals pass through the micelles at a high rate, and eventually increase their chain length by propagation both in the aqueous an in the oil phase. Micelles may therefore be visualized not only as a source of surfactant, but as a source of apparent increase in the monomer concentration in the aqueous phase leading to increased propagation . The ratio between the rate of particle nucleation in micelles and that in the aqueous phase may then simply be taken as the ratio between the propagation rates in these two phases of an oligomer of one l ess the critical chain length. When this oligomer propagates in the aqueous phase it l eads to homogenous nucleation of a primary particle, and when it propagates in

199

the micelle, it cannot desorb again. This simple picture will be considerably more complex if these new particles, called primary particles, are not stable (see below).

For monomers of low water solubility such as styrene, having a low critical chain length in the region 2-5, the difference in a between the different chains is very large, and this model is applicable . For monomers of higher water solubility, such as MMA, VAc or VC, the simple picture becomes cluttered when a is increasing and F approaches 1 for several oligomers . However, still the qualitative picture stays the same. For these monomers also desorption of monomer (or similar) radicals produced by chain transfer becomes important for the nucleation, and these will probably have a lower critical chain length because of the lack of an ionic end group .

We can calculate the ratio between the propagation rate, Ppm• in micelles and Ppw in water as long as there is an equilibrium distribution between the phases both of monomer and of radicals when case 3) is valid:

(8)

Here aR and aH are the distribution constants for radicals and monomer , respectively and Vm is the volume fraction of micelles . If Vm=O . Ol (1%) and a~l300 (styrene) we see that p m(P >>1 for all radicals except the smallest , and increases with increasing clfain ~ngth . Therefore , it seems highly probable that the dominating place for particle nucleation is the micelles. For more water soluble monomers like VAc with a~28, the picture becomes somewhat different. A radical with equal solubility in water and oil (a-1) will have the ratio 1.0 x 28 x 0.01 = 0.28 , meaning that this radical will propagate mainly in the aqueous phase. Oligomers closer to the critical chain length will have much higher values of a (the exact value is still uncertain). Also a monomer radical with the same value of a as the monomer will have a propagation rate ratio of 28 x 28 x 0.01 = 7.8 . Therefore it seems that even for these monomers micelles should be the dominating source for nucleation as indicated by seed experiment with MMA (Hansen and Ugelstad, 1982) . From the considerations above, it would appear that the most probable explanation of a lower capture efficiency of micelles would be a dense diffusion barrier on the aqueous "side" of the micelle surface. For surfactants like SDS this seems highly improbable, but nonionic surfactants and polymeric surfactants may show such behavior. With these surfactants, homogenous nucleation also above the CMC may seem possible, especially in the case of partly water soluble monomers that also have a relatively low chain transfer constant to monomer, like for instance MMA.

THE PARTICLE NUMBER

The final particle number is reached both as a result of competition between nucleation and absorption of radicals in particles already formed, as a result of adsorption of surfactant on the new particles and the possibility for limited coagulation of the particles. The depletion of surfactant due to particle growth is described in the Smith-Ewart theory . The new particles that contain 1 radical will terminate rapidly because of the increased adsorption rate as shown in Figure lB , and this will hinder the maximum in rate that is predicted by the Smith-Ewart theory. The expression for the particle number as given in Equ.(l) and Equ.(2) may be expected to be approximately valid except for the magnitude of the constant k that will be lower than that predicted by Smith and Ewart. However, these expressions are only valid if all the primary particles that are formed are stable. It has been argued by Lichti et al. (1983) that the primary particles are not stable , because this does not agree with the measured particle size distributions that are positively skewed. The reason for and probability of such a coagulation mechanism above the CMC are currently

200

discussed, but will be beyond the scope of this article. It is important to observe, however, that a coagulation mechanism and micellar nucleation are not mutually exclusive.

REFERENCES

Danckwerts, P. V. (1951). Absorption by Simultaneous Diffusion and Chemical Reaction into Particles of Various Shapes and into Falling Drops. Trans.Faraday Soc., 47, 1024.

Lichti, G., R.G. Gilbert and D.H. Napper (1983). The Mechanism of Latex Particle Formation and Growth in the Emulsion Polymerization of Styrene Using the Surfactant Sodium Docedyl Sulfate. J.Polymer Sci., Polymer Chem.Ed . , 21, 269 .

Feeney, P.J., D.H. Napper and R. Gilbert (1984). Coagulative Nucleation and Particle Size Distributions in Emulsion Polymerization . Macromolecules 17, 2520.

Feeney, P.J., D.H. Napper and R. Gilbert (1987). Surfactant-Free Emulsion Polymerizatios: Predictions of the Coagulative Nucleation Theory . Macromole­cules 20, 2922.

Fitch, R.M. and C.H . Tsai (1971). Particle Formation in Polymer Colloids, III: Prediction of the Number of Particles by a Homogeneous Nucleation Theory. Polymer Colloids (R.M . Fitch, Ed.), Plenum press , p.73 .

Fitch, R.M. (1973) The Homogenous Nucleation of Polymer Colloids. Br.Polymer J., 5, 467 .

Fitch, R.M. and L.-B. Shih (1975) Emulsion Polymerization: Kinetics of Radical Capture by the Particles. Progr.Colloid Polymer Sci., 56, 1-11.

Hansen, F .K. and J. Ugelstad ( 1978). Particle Nucleation in Emulsion Polymeriza­tion. I. A Theory for Homogenous Nucleation. J.Polymer Sci., Polymer Chem.Ed., 16, 1953.

Hansen, F .K. and J . Ugelstad (1979a) . Particle Nucleation in Emulsion Polymeri­zation. II. Nucleation in Emulsifier-Free Systems Investigated by Seed Polymerization. J.Polymer Sci., Polymer Chem.Ed., 17, 3033 .

Hansen, F.K. and J . Ugelstad (1979b) . Particle Nucleation in Emulsion Polymeri­zation. III. Nucleation In systems with Anionic Emulsifiers Investigated by Seeded and Unseeded Polymerization. J.Polymer Sci., Polymer Chem.Ed., 17, 3047.

Hansen, F.K. and J. Ugelstad (1979c). Particle Nucleation in Emulsion Polyme~i zation . IV. Nucleation in Monomer Droplets. J.Polymer Sci., Polymer Chem.Ed., 17' 3069.

Hansen, F.K. and J. Ugelstad (1979d).The Effect of Desorption in Micellar Particle Nucleation in Emulsion Polymerization. Hakromol.Chem., 180, 2423.

Hansen, F.K . and J . Ugelstad (1982). Particle Formation Mechanisms. Emulsion Polymerization (I.Piirma Ed.), Acad.Press., pp . 51 - 92.

Joos, P. and G. Serrien (1989) . Adsorption Kinetics of Lower Alkanols at the AirjWater Interface: Effect of Structure Makers and Structure Breakers. J.Colloid Interface Sci., 127 , 97.

Lichti, G. , R. Gilbert and D.H. Napper (1983) . J .Polymer Sci., Polymer Chem.Ed., 21, 269.

Noumura, M., M. Harada , S. Euguchi and S. Nagata (1976). Kinetics and Mechanism of the Emulsion Polymerization of Vinyl Aceta te. ACS Symp.Ser. , 24, 104.

Richards, J.R., J.P. Congalidis and R. Gilbert (1989). Mathematical Modeling of Emulsion Copolymerization Reactors . J.Appl.Polymer Sci., 38, 2727.

Smith, W.V . and R.H. Ewart (1948). J.Chem.Phys. , 16, 592. Roe, C.P. (1968). Ind.Eng.Chem. , Sept., p.20 Ward, F.H. and L~ Tordai (1946). Time-Dependence of Boundary Tensions of

Solutions. I . The Role of Diffusion in Time Effects. J.Chem.Phys . , 14, 453 . Wennerstrom, H. and B. Lindman (1979). Micelles . Physical Chemistry of Surfac­

tant Association. Physics Reports, 52, No.1, 1-86.

201

THE PREPARATION OF COLLOIDAL PARTICLES HAVING (POST-GRAFTED) TERMINALLY-ATTACHED POLYMER CHAINS

BRIAN VINCENT

School of Chemistry, University of Bristol, Cantock's Close Bristol BS8 lTS, U.K.

ABSTRACT

The terminal grafting of various monodisperse polymers, which may be prepared by ionic or group-transfer polymerisations, to two types of colloidal particle (oxides and polymer latices) is described. Polymers considered include poly(ethylene oxide), polystyrene, poly(dimethylsiloxane) and poly (methylmethacrylate).

KEYWORDS

Polymer grafting; terminally-attached chains; steric-stabilisation; surface modification; polymer end-functionalisation.

INTRODUCTION

Steric stabilisation of particulate dispersions occurs widely in nature (e.g. micro-organisms, blood cells) and is much used in industrial formulations and processes. It involves the presence of a continuous sheath of solvated polymer chains arotmd the particles , such that the net attractive (van der Waals) forces between the particles become ineffective.

Although physically adsorbed polymers (in particular, block or graft copolymers) may well be effective in this respect, solvated chains, t e rminally grafted (i .e . chemicaly bonded) to the particle surface , offer the advantage that the possibility of desorption, especially during particle collisions, is eliminated. Moreover, with regard to fundamental studies of interparticle forces and colloid stability, terminal grafting of polymer chains offers advantages over physically adsorbed copolyemrs, in particular:

i) the structure of the adsorbed polymer sheath is well-defined .

ii) good control of M.W. (and M. W. distribution) and also coverage may be achieved.

In this paper attention will be focussed on the pos(-grafting (chemisorption) of long-chain polymers to particles. Short chains e.g. n-alkyl) are not cons idered. No discussion will be given either of in situ grafting, which may be achieved with latex particles, for example, by copolymeris ing the latex monomer with a suitable macromonomer i n the preparation stage. This subject is reviewed adequately elsewhere (Barrett, 1975); nor will grafting by surface initiation at active sites on the solid surface be considered This subject has been previous ly reviewed by Laible and Hamann ( 1980) . In

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general, less control over chain density and chain molecular weight distribu­tion are achieved using this route.

General Features

There are several general steps involved in the post-grafting of polymers to colloidal particles. These are summarised below:-

a) The preparation of a stable dispersion of the particles, carrying a surface-reactive group (X), in a suitable solvent (A). "Dry stages" during the incorporation of X are best avoided, if possible, since complete redispersion is generally difficult. Since steric stabilisation cannot be used at this stage, charge stabilisation is required (i.e. A needs to be a reasonably polar solvent). Alternatively, stirring/ultrasonics may be used to help prevent coagulation/settling; low particle concentrations are then preferable.

b) The preparation of a stable solution of the polymer chains having a reactive (terminal - for end grafting) group (Y). Again, a suitable solvent must be chosen , i.e. either A, or B which ilust be ·miscible with A and not lead tD coagulation of the particles on mixing). Generally, ionic or group-transfer polymerisation is invoked, both to give control over M.W . (and narrow M.W. distribution) and to yield the necessary end-group functionality, Y. Y may be the "living" end itself, or a functionality achieved by terminating the polymerisation with a suitable molecule.

c) Reaction of X + Y leads to the grafting process on mixing. It is desirahle to follow the grafting kinetics (coverage with time). In situ, spectroscopic methods (e.g. FTIR, NMR) are generally preferable. If the kinetics are sufficiently slow (~ hours or longer) sampling procedures may be used. Here, the partic les are separated from the unreacted polymer solution (e.g. by centrifugation), and either the amount of unreacted polymer determined or , more directly, the amount of grafted polymer on the particles determined , e.g. by thermal gravimetric analysis, in the case of non-combustible particles.

Grafting kinetics has not been analysed theoretically in detail, but clearly a number of factors are important:-

i) the M.W. of the chains (the react ive Y functionality will tend to be more "buried" in a higher M. W. chain).

ii) the existing coverage at any point; the higher the coverage the more difficult it will be for a Y group to locate a surface X group.

d) After preparation, 'clean-up' and characterisation of the grafted-polymer layer are required. The latter includes: determination of the final grafted amount; the thickness of the grafted layer; detection of any physisorption of chain segments (especially a t low coverages); segment density profiles normal to the surface. Various techniques are available to determine these parameters, and have been reviewed by Cohen Stuart et al. (1986).

In this article the grafting of polymer chains to two classes of colloidal particles will be ~onsidered: metal oxides and polymer latices.

GRAFTING TO OXIDE PARTICLES

Laible and Hamaan (1980) have reviewed the grafting of terminally-activated polystyrene (and, to a lesser extent, of poly 4-vinylpyridine) onto various pre-treated oxide surfaces: Si02 , Ti02 , Fe2o3 , ZnO, Cr2o3 . The polymers

203

were prepared by living anionic polymerisation, in tetrahydrofurane at -78°C, using n-BuLi as the catalyst. The living polymer may then be directly reacted with the activated oxide particles dispersed in a suitable solvent, under conditions where care is taken to avoid extraneous Oz, COz and HzO. This involves using break-seal equipment or, alternatively, a high-vacuum rig oper­ating under a dry Nz or Ar atmosphere, as described for example, by Bridger et al. (1979). The oxide surface may be activated in several ways. In the case of SiOz, one way is to thermally treat the particles, not only to remove surface adsorbed water, but also to condense neighbouring surface silanol groups to siloxane bridges. This invovles heating to about 700°C to effect the removal of the last, isolated silanol groups whose presence should be avoided since they 'kill' the living polymer. Around this temperature the siloxane bridges remain sufficiently strained to be readily ring-opened by the living polystyrene anions; higher temperatures lead to some relaxation of the strain in the siloxane bridges. This method has been described by Clarke and Vincent (1981). An alternative route is to treat the Si02 particles, preheated to ~ 120°C to remove surface adsorbed water with, say, a chlorosilane (Bridger et al. 1979) or SOClz (Laible and Hamann), to convert surface Si-OH groups to Si-Cl groups; these Si-Cl groups also react readily with polystyryl anions. Both of these routes involve the formation of a direct Si-C bond between the particle surface and the terminally-grafted polymer chains; such bonds are very stable to possible hydrolysis. This is in contrast to the less stable Si-0-C bonds, formed, for example, in the direct reaction of methoxy­terminated polystyrene chains with the native surface Si-OH groups (see later). Lenon(l979) has described similar methods for grafting polystyrene to alumina and titanium particles, as well as freshly-cleaned mica.

All of the routes described above involve a "dry stage" for the oxide particles, and, as mentioned previously, this is best avoided, since complete redispersion of the aggregated particles into the necessary solvent is extremely difficult, especially for sub-micron particles.

Bridger and Vincent (1980) described two methods for the terminal grafting of poly(ethylene oxide) (PEO) chains to silica surfaces. In both cases a diisocyanate coupling route was employed. In the first method isocyante­capped PEO chains were reacted directly with surface silanol groups of the silica particles dispersed in a suitable solvent, such as carbon tetrachloride. Although a dry stage can be avoided here, by utilising a series of centrifu­gation/redispersal cycles through intermediate solvents, the dispersion of (hydrophilic) s ·ilica particles in carbon tetrachloride is not particularly stable and vigorous stirring much be maintained to avoid particle aggregation at this stage. The second method described by Bridger and Vincent (1980) was an attempt to prepare aqueous dispersions of silica particles with terminally­grafted PEO chains. This method bears certain similarities to the in s itu grafting method for latex particles, referred to .in the Introduction. It involves reacting the isocyanate-capped PEO chains withy-amino n-propyl triethoxysilane. The resultant triethoxysilane-capped PEO chains are then added dirctly to the silica dispersion during the latter stages of its formation (by hydrolysis of tetraethylsilicate in water/methanol mixtures). A surface condensation reaction between the ethoxy groups on the polymer chains and the silanol groups on the particles leads to grafting. It was found to be necessary to add ~ 0.57. isopropanol to the system to prevent oxidative degradation of the PEO chains. However, even then, long-term stability (> ca . 1 month) of the dispersions was difficult to achieve; this was thought to be due to the slow dissolution process of silica itself in aqueous solution.

Meals (1966) has described the basis of an alternative method for grafting PEO to silica, which is based on pre-activation of the silica surfaces and, hence, a dry stage. The surface activation involves reacting the surface silanol groups on the dried particles with methyldichlorosilane leaving an Si-H

204

functionality on the surface. PEO is generated by anionic polymerisation and terminating with allyl bromide to yield a terminal alkene group, which reacts readily with the Si-H group. Grafting of the PEO chains is effected in an aprotic solvent such as DMF.

Edwards et al. (1984) developed methods for terminally-grafting polystyrene (PS) and polydimethylsiloxane (PDMS) to silica particle in non-aqueous media, avoiding both a dry stage and also the potential aggregation difficulties, discussed by Bridger and Vincent (1980) and referred to above. The silica dispersions remain stable throughout, by maintaining a surface charge and hence electrostatic repulsion between the particles; this necessitates the use of reasonably polar solvents or solvent mixtures.

In the case of PS, the polymer is prepared anionically in toluene/THF mixtures and then reacted with a large excess of trichlorosilane, leaving each chain, in principle, with two terminal chloro groups. These are reacted with excess methanol. The methoxy-terminated PS may then be freeze-dried from dioxan and later redissolved in some suitable solvent, e.g. DMF. The silica particles are also re-dispersed in DMF, in which they are stable. The PS solution and silica dispersions in DMF are then mixed, at a predetermined mass ratio of PS:Si02, and heated at 120° for varying periods up to 2 days. Figure 1 shows a plot of grafted amount (A) versus time (t) for one such Si02-g-PS system. A values were determined by thermo-gravimetric analysis. For this system the maximum grafted

3 A

2

1

0

Fig. 1.

20 40 t I h -2 Grafted amount A (mg m versus time (t)

for polystyrene (Mn=25,600) onto silica particles (diam = 105 nm); PS:Si02 ratio= 4.1 (w/w).

amount is about 3 mg m-2. This corresponds to an area per adsorbed polymer chain of <v 14 nm2. The subtented area of a random coil (11 r~, where rg is the solution radius of gyration of an equivalent chain) at the surface would be <v 78 nm2, indicating that the grafted chains are strongly extended normal to the surface .

For the grafting of PDMS chains to silica a somewhat different route was employed, since this polymer is not soluble in DMF. PDMS was prepared by the anionic polymerisation of hexamethylcyclotrisiloxane, in a solvent mixture of cyclohexane and THF, using n-butyllithium as the initiator. Termination was effected by the addition of acetic acid, .leaving terminal hydroxyl groups on the chains. Grafting was then effected by adding a solution of this polymer in heptane to a dispersion of the silica particles in ethanol, such that the

205

final solvent ratio heptane:ethanol was 1:1 (by volume); this proved to be sufficiently polar to maintain charge-stabilisation of the particles. After 24 h at ambient temperature (to achieve physisorption of the chains), the d i spersion was diluted with a three-fold excess of heptane, and then evaporated leaving the silica partic les in the PDMS melt. This was then heated at 150o, under nitrogen, for about 5 h (to effect chemisorption), before being redispersed in heptane, and a series of centrifugation/redispersal in heptane cycles undertaken to remove excess (ungrafted) polymer. Much higher grafted amounts (typically, A=10 - 15 mg m-2) could be obtained with PDMS, compared to PS, possibly reflecting the greater flexibility of the PDMS chains.

Milling and Vincent (unpublished results) have recently grafted polymethyl­methacrylate (PMMA) chains to silica particles, by extending the method introduced by Wu et al. (1989) for the grafting of polybutylacrylate chains to silica surfaces. This involves using group transfer polymerisation of methyl methacrylate monomer, at room temperature, in THF solvent, with methyltrimethy­silyl-1.1-dimethylacetal as the initiator and tetrabutylammonium cyanide as the catalyst. Termination was effected by adding methanol, to yield a cluster of three terminal methoxysilyl functionalities, each of which is capable of condensation onto adjacent surface silanol groups on silica. This grafting reaction was achieved by dispersing the silica particles in a (polar) solvent mixture of ethanol and ethylene glycol diacetate (1:4 by wt.), which is also a good solvent mixture for the PMMA chains. The mixture was heated at 80° for about 3 days.

GRAFTING TO LATEX PARTICLES

As mentioned previously, there is a rich literature on the preparation of latex particles with terminally attached chains such as PEO, by in situ polymerisation methods. Examples are the polymerisation of the latex monomer in the presence of preformed block or graft copolymer (containing PEO chains) or co-polymerisation with an alkene-terminated PEO chain (Cowell and Vincent, 1982). The chain coverage obtained in this type of· system is usually self­adjusting such that the maximum amount (pertinent to the solvent conditions used, etc.) is normally obtained; in fact, the average particle size depends on the monomer:stabiliser ratio. Also, with the copolymerisation method referred to only PEO chains up to ~ 5000 in M.W. can usually be successfully grafted . This is because the reactive terminal alkene group tends to be "buried" in the PEO coil, sterically hindering copolymerisation with styrene monomer.

Both Ryan (1988) and, more recently, Ploehn and Goodwin (1991) have described the post-grafting of PEO chains to performed polystyrene latex particles. In order to achieve this surface -COOR groups on the latex particles are co~sed with terminal -NH2 groups on the PEO chains. In Ryan's method the surface -COOR groups are produced by copolymerising styrene with polymethacrylic acid in forming the latex, whilst in Ploehn and Goodwin's method a normal styrene emulsion homopolymerisation is carried out, but using 4,4'-azobis-4-cyanopent­anoic acid as the initiator. The route chosen to the -NH2 terminated PEO chains in both studies was similar. OR-terminated PEO chains (at one end) are commercially available, or are readily prepared by anionic polymerisation of ethylene oxide, followed by termination with e.g. water or an alcohol. The OR-terminated PEO chains are dissolved in warm toluene. A tenfold molar excess of toluene-4- sulphonyl chloride, plus some pyridine, are added, thereby replacing each terminal -OR groups with a tosylate leaving group (with insoluble pyridinium hydrochloride being precipated). Bubbling ammonia gas through the warm solution for 3-5 h gives the required -NH2 terminated PEO chains. The coupling of the PEO chains to the latex surface, can be achieved at room temperature, by first activating the surface carboxylic acid groups with N-hydroxybenzotriarole, in the presence of a water-soluble carbodi -

206

imide, to yield active ester groups on the surface. The latices may be cleaned-up by repeated centrifugation/redispersal in water cycles.

CONCLUSIONS

The terminal-grafting of polymer chains to colloidal particles provides one of the most effective means of achieving steric stabilisation of the dispersions concerned: well-anchored, extended chains, giving thick sheaths, even at moderate coverages, are obtained. Possible extensions to the work described here for aqueous systems would be:

(a) to put a terminal charge group (say -oso) or COO at the free end of the PEO chain. This could be achieved using PEO chains functionised at both ends: one to achieve grafting, the other leading to the terminal charge group .

(b) to directly graft polyelectrolyte chains to particles, thereby extending the work of Buscall (1981), who investigated the properties of polystyrene latex particles carrying absorbed layers of poly(acrylic acid)/poly(methyl methacrylate) graft copolyemrs. Such systems would be of considerable academic interest, as well as potential practical use.

ACKNOWLEDGEMENTS

I should like to thank my graduate student colleagues who have, over the years, contributed to this work. These include: Keith Bridger, Jane Clarke, Stephen Lenon, John Edwards, Andrew Jones, Keith Ryan and Andrew Milling .

REFERENCES

Barrett, K.E.J. (1975). Dispersion Polymerisation in Organic Media, Wiley­Interscience, London.

Bridger, K., D. Fairhurst and B. Vincent (1979). Non-Aqueous Silica Dispersions Stabilsied by Terminally-Grafted Polystyrene Chains .. J .Colloid and Interface Sci., 68, 190-195.

Bridger, K. and B. Vin~nt (1980). The Terminal Grafting of Poly(ethylene oxide) Chains to Silica Surfaces. European Polymer J;, 16, 1017-1021.

Buscall, R. (1981). Properties of Polyelectrolyte-stabilised Dispersions. J.Chemical Society Faraday Transaction I, 77, 909- 917.

Clarke, J. and B. Vincent (1981). Non-Aqueou~Silica Dispersions Stabilised by Terminally-Anchored Polystyrene: The Effect of Added Polymer. J.Colloid Interface Sci., 82, 208 - 216.

Cohen Stuart M.A.,-r. Cosgrove and B. Vincent (1986). Experimental Aspects of Polymer Adsorption at Solid/Solution Interfaces. Advances in Colloid and Interface Sci., 24, 143-239.

Cowell, C. and B. Vincent (1982). Temperature-Particle Concentration Phase u1agrams for Dispers ions of Weakly-Interacting Particles. J.Colloid Interface Sci., 87, 518-526.

Edwards, J., S. Lenon, A.F. Toussaint and B. Vincent (1984). The Preparation and Stability of Polymer-Grafted Silica Dispersions. In Polymer Adsorption and Dispersion Stability (E.D. Goddard and B. Vincent, ed .), American Chemical Society Sympossium Series, 240, 281-296.

Laible R. and K. Hamann (1980). Formation of Chemically Bound Polymer Layers on Oxide Surfaces and Their Role in Colloid Stability. Advances in Colloid and Interface Sci., 13, 65-99.

Lenon, S. (1979). Grafting of Polystyrene to Inor ganic Oxide Particles. M.Sc. thesis, Bristol University.

Meals, R.N. (1966). Hydrosilation in the Synthesis of Organosilane. Pure and Applied Chern., !J, 141 -147.

Ploehn, H. and J.W. Goodwin (1991). Rheology of Aqueous Suspensions of Polystyrene Latex Stabilised by Grafted Pol y (ethylene oxide). Faraday Discussions Chemical Society, in press.

Ryan, K. (1988). The Post-Grafting of Polymers to Colloidal Particles . Chgemistry and Industry, pp . 359-364.

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Wu, D.T., C.Y. Wang and R.L. Settlerquist (1989). Grafting of Polybutyl­acrylate to Silica . In Po lymer Late x III, Proc .of the Plas tics and Rubber Institute pp. 12-18.

208

CATAPHORETICALLY APPLICABLE FILM-FJRMING DISPERSE S~STEMS

MINODORA LECA

Department of Physical Chemistry, University of Bucharest Facul ty of Chemistry, Bucharest 70346,

Blvd. Republ icii No . 13, ROMANIA

ABSTRACT

209

Dispersions of a LO.) J isopropanol ~clutio~ of a cataphor~tic ~ilm-forming copolyme r with the tert1ary am1ne groups part1ally to completely neut t'Rliz~d to obtain a 1~ ~ copolymer content, required by the indus tr1al electrod0pos1t1on, were prepared. Dispersions obtained in this way had a level of isopropanol o~ 3 .68 ~ and were characterized by turbidity, conductivity, vis­cosity, surface tens i on 1 pH, and film-form~ng properties • . The influence of some oreGnlc solvents, added 1n a concentrat1on of 1 . 32 %, on the above mentioned properties were determined f or a degree of neutraliza ti on of 0.6 for which the most convenient filrns we re obtained.

KSYWORDS

Polymer disp0rsiom>; polymer colloids, cataphoresis .

Ir\TRODUCTIVN

As a r esul t of the environmental, fire and economic pressures of the past quarter of century water thinned paints become very used in c.oatings technoloe;Y. These lead also to a new paint process named e l ec trodeposi t lon , electropainting or electrocoating (Machu, 197d) which consists in migration of electrically charged pigmented coating particles under the action o~ a difference o~ potential between the object to be coated and a counter-electrod~ tha t is in electrophoresis process.

The stability of aqueous disperse systems is bring about by the electrical charge of the disperse phase particles. This can be obtained both by changing the amine groups o~ the copolymer into quaternary ammonium salt and by adsorption of ions existing in the system. The particles are not of uniform size and they do not all bear the same number of charges so they have widely differ­ing rates of migrntion. Consequently one of the requirements is tp produce as nearly as possible uniformly sized and charged par­ticles whi ch migrate at a uniform rate.

The colloid s t a te of the system is of esential importance for the s t ability of the bath, the kinetics of the electrodeposition i. e . the performr.mce o.f the e l ectrophore tic deposition process,

210

the throwine power of the paint, and the building-up of paint film. Therefore a special care must be paid to the preparation of dispersions.

Dispersions of a quatern:1r.v copolymer with tertiary ~mine groups neutralized to various degree were prepared and the 1nfluence of the method of preparation as well as of some organic solvents on their properties were established . The properties of the dis­persions were correlated with the properties of the electrode­posited films.

EXPERIMENTAL

The copolymer was obtained by solution copolymerization of 2-hydroxyethyl methacrylate (30% by weight), 2-dimethylamino­ethyl methacrylate (20 %), butyl acrylate (25 %), and styrene (25 %) in isopropanol as solvent, AIBN as initiator and tert-do­decyl mercaptan as chain regulator at a content of dry substance of 67 %, concentrated then to 80.3 %. Copolymer characteristics, part of the organic solvents added, and stability measurements were described in the previous papers (Leca et al., l)J~, Leca et al., 11)90). ---

The tertiary amine groups, with a content of 1.272 milieQuiva­lents per gram, were neutralized to various degrees usin£ 50 % acetic acid aqueous solution.

Two different procedures to obtain 15 % copolymer dispersion re­quired by the industrial electrodeposition were used: addition of water to the :isopropanol c.opolymer solution neutralized to various degrees and addition of water and the calculated amount of neutralizing acid all together to the copolymer solution. All the operations were made under vigorous stirring until the co­polymer was swept into the aqueous phase and continuated for another 15 minutes. The surface tension, conductivity, viscosity, rllld turbidity in terms of disperse phase concentrGtion were measured for neu­t~alizati?n levels ranging.between 0.35 and l using a du Nouy r1ng tens1ometer, a Radel~1s conductometer, a Schott viscometer and a S~ekole spe~tr?pho~ometer.equiped with turbidity TK annex respect1vely. Var1at1on 1n pH wlth the degree of neutralization of copolymer was measured using a MVb4-type pH ~eter.

Dispersion were electrodeposited on phosphatized stainless steel sheets for 90 seconds at a voltage of 70 v.

RESVLTS

Isoprop~nol copolymer solutions of 67 and GO.)~ were dispersed to o?taln a.content of 15% copolymer which leads to a concen­t~atlon of lsop~openol in .d ~spersion~ of 7.34 and 3.68% respec­tlvely. D1spers1ons co~ta1n~nf less 1sopropanol prepared by the ~e~ond proce~ure descr1bed 1n the.experimental part are the most ...,table ~nd Bl'(e the most smooth f1 l rns. It is why the results for these d1spers1ons are presented .

The lowest degree of neutralization for which the copolymer was

211

dispersible was 0.35% for a concentration of copolymer of 15 ~ by weight.

Dispersions containing 1.32 ~ some other organic solvents were also prepared and their properties were compared with the dis­persion containing 15 % isopropanol.

Surface tension merlsurements, represented in Fig. 1, for disper­sions with different levels of neutralization show a surf~ct~t­lik~ behaviour. This demonstrates that a small amount of 10n~zed copolymer dissolves molecularly in all the cases ru:d t~at th1s quantity is so much the less the degree of neutral1zat1on (DN).

50

f L.5

E ~ E ~

40

35 0

Fi[. l.

1;2

5 10 15 C,

0 /o ----­Dependence ofsurface tension of disper­sions on concentration of the dispersed phase for the degrees of neutralization: 1 - 0.35; 2 - 0.4; 3 - 0.5; 4 - 0.6; 5 - o.7; 6 - o.s; 7- 1.o.

Kinematic viscosities of dispersions in terms of the degree of neutralization show an increase with the degree of neutralization until a value of 0.8 then the increase diminishes because the site-binding Jf counterions becomes larger and a greater number is kept inside the copolymer particles - Fig. 2.

The consequence of dilution on the viscosities of dispersions having different levels of neutralization is represented in Fig. 3 as relative viscosities in terms of the volume fractions of the copolymer to be able to compare the experimental rezults with ~he ca~culeted ones obtained using the relationships given for d1spers1ons. The calculation of the volume fractions assumed no volume change on mixing and that the acetic acid and iso­propanol were present in the aqueous phase.

212

(j) v. '>

6

5

.4

3WL--~----~----~~ 0.3 0.5 0.7 1.0

ON--Fig. 2. Dependence of kinematic viscosity on the

DN for 15 % copolymer dispersions with 3.68 % isopropanol.

6

5

4

2

0

-­... -

0.30

/ ,A"

./

/

0.35

~/ /

/

/

/ /

-- -o4() __ ... ----0.05 010 015

volume fraction Fig. 3. Variation of relative viscosities with

~oncentration of the disperse phase with the DN: 1 - 0.)5; 2 - 0.4; 3 - 0.5; 4 -0.6; 5 - 0.7; 6 - 0.8; 7 - l.O; 0 and 0' -- Thomas equation.

213

The results show a non-lineGr increase of rel:ttive viscosities when the concentration rises for all the degrees of neutraliza­tion used; this increase diminishes when the degree of.neutal­ization decrease. To compare the res~lts, Thom?s equa~1on was selected (Thomas, l 9o5) because it g1ves the.h1ghest 1ncrease of relative viscosity on concentr8tion of the d1sperse ~has~. Sv~n the dispersion having the smallest degree of neutral1zat1on d1d not follow the above mentioned relation.

The pH values of 15 1 copolymer dispersions range batveen 5 and 7 when the degree of neutralization decreases from l.vO to o. ".55 - Fig. 4 curve 2 - and they are smaller than that of the mono­mer at the same molar concentration of the amine groups and degree of neutraliz2tion - curve 2.

3L_ __ ~-----L----~--~~--~ 0.6 0.8 0.2 0.4

ON Fig. 4. Variation in pH of the amine monomer­

- curve l and of copol~ner- curve 2 -with the degree of neutralization.

Figure 5 gives the dependence of turbidities on the degree of neutralization immediately after prep3ration - curve l - and after 24 hours - curve 2 . Turbidities were measured at .<1 w[lve­length of 497 nm for which the most of the dispersions have mAx­imum values. As can be seen, there is a linear decrease in tur­bidity when the degree of neutralization rises from 0.35 to 0.70, then tt1is slows down and became very small for colllpletely neu­t!'alized copolymer. li.fter 24 hours the curve has the same aspect but.the.values are smaller which shows that the process of ma­tur1zat1on takes place.

Electrical conductivity of disperse systems being the sum of electrical conductivity of disperse phase particles and electri­cal conductivity of small ions present in the system, it increa­ses with the degree of neutralization until a value of 0.8 then the increase diminishes because more counterions form ionic pairs with the amine groups - Fig. 6.

214

Fig. 5.

ol_ _ _____.~ __ __L ___ ---::-'

0.3 0.5 0.7 ON~

Varir:tion of' turtJidi ty with the degree of n~utrulization for 15 ~ co~olymer dispclr­sions with }.6d I isopropanol: l - im­mediately after ~reparation; 2 - after 24 hours.

0.3 0.5 0.7 1.0 ON-

Fig. 6. Variation of conductivity with the degree of neutrelization for 15 ~ copolymer dis­persion with ) • ..Sb 'i> isopropanol.

DISCUSSION

There are three methods to obtain aqueous polymer dispersions: emulsion polymerization, dispersion of water insl..luble polymer solutions in the presence of suitable surfactants, and dispersion of concentrated hydro~hilic polymer solutions. The most conven­i ent way to ~repare resin dispersions applicable by electro­phoresis is the third one, because it has the following advent­apes: thu co~olymer design principles which have been developed f'or solution resins r emain valid, the solvent levels required for disp~ rsion are low, and the obtained films are water resist­ent containing no surfactant.

A polymer may be d ispersed in water when it contains hydrophilic groups so it is a polymeric surfactant which dissolves or dis­perses in water to give micelle-like particles. Such a dispersion may be potentially thermodynamically stable, its particles reach-

215

ing an equilibrium size if enough ionic groups ?re present, a slow process due to the high viscosity of the d1sper~e phase. Solubility and dispersability of ioniz~bl~ polymers 1n wate~ are caused by their structure: content of lOnlzable.Fro~ps, th~lr distribution alonf the chain, deeree of neutral1zat1on of lon­izable grou~s as ~ell as by t he ir mo~ecular weight. A level o~ about one miliequivalent per gram ionic rroups is fenerally suf­ficient to make dispersion possible for the ordinary copolymers and molecular wei,shts used by the paint industry. However the copolymer must be hydrophilic in the disperse~ ~tate and water resist8r,t :in a finnl film so tha t the hydroph1l1c groups must be convertible during film formation.

Th~ copolymer is prepared or dissolved in a coupler s olvent which has appreciable so~ubility both in the copolymer a~d water and serves several purposes (Machu, 1978, Brown, l9LO): 1t re­duces polymer viscosity to facilitate handling and dispersioni it influences the viscosity of the dispersion depending upon 1ts distribution between the disperse and eontinuous phases; it im­proves the stability of the dispersion, ac t ing as a weak, vola­tile surfactant; it !)lasticizes the polymer and makes the fi l m smooth and uniform.

The co-m(.mo.ners were selected according to the above require­ments us well as to the film-forming ones and the coupler s ol­vent accord in{~ tu the solubility parameter of the copolymer.

The two procedures used to prepare copol~ner dispersions are funll c11uentnlly different: in the focmation of dispersions by stir­ring water with partially neutralized isopropanol solution of copolymer the interfaces are created mechanically and must be stabilized by the migration of stabilizing species to the inter­fnc~s ; in the formation of dispersions by the stirring of all the w8ter und acid with the copolymer isopropanol solution the acid diffuses into the surface layer of the polymer phase gener­at int: ionizublc SDlt which makes the copolymer more hydrophilic. Such a layer s wel ls readely with water and in this softened s t ate it is more quicly swept into the aqueous phase.

~t is very yroba?le that the first portion of copolymer taken up 1nto the water 1s completely neutralized and dispersed as indi­vidual molecules or as micelles. The curves in Fig. l show that this is the situation: the higher the level of neutralization the larger the quantity dispersed in these states. At higher con­centrations the irre€ular shape water-swollen micelles aggregate or separate as a distinct phase. Surface tensions for the oagrees of neutralization of 0.8 and 0.7 are very close to thst of t he complete ly neutra lized copolymer which shows that there is enough fully neutralized copr;>lyrner in th~ s~ systems brought about by the !)rocedure of pre!)aratlon. In c ond1t1ons of partial neutralizat ion the copolymer f~n~tions both as_insoluble material to be disper­sed and as stab1l1zer for the d1spersion . When the ratio is sui~able chosen, instead of dissolving the quantity of copolyme~ equ1~alent to the _umount of acid added, the excess acid over that re qu1red for the 1nterfacial l~er continues to diffuse into the copolymer and ac tua lly all of it form$ salt with the base i n t~e CO!)ulymer phase . Thus the whole copolymer is softened Gnd d~spers~d. Th~ st~b i l i~in£ s~ecies redistribute quickly ond the f1nnl d1spers1on 1s qu1te un1form. ·

216

The swelling of disperse phase particles with water is supported by the relative viscosity dat~ of Fig: 3: the relative visco~ity increases when the concentrat1on of d1sperse phase becomes h1gher for all the levels of neutralization, the increase being the more so as the degree of neutralization is higher. ThG increase of relative viscosity Ni~h the degree of neutralization can also be assirned to the electroviscous effect. Both the 2bsorption of water and the electrical charge of the particles increase when the level of neutralization becomes higher.

pH measurements for the 15 \6 copolymer dispersion neutralized to different levels show smaller values compared to those of the monomer dispersions having the same content of amine groups and degree of neutralization (Fi£. 4). In two phase systems the pH values characterize only the aqueous phase as conductivity do~s. Thus the results demonstrate that the largest part of the neu­tralizing acid is present into the disperse phase retained by the .amin~ groups. This conclusion is also supported by the dilu­tion of the dispersions with water for all the degrees of neu­traliz8tion: at the be[inning the pH decreases with dilution, than it increases tendinr to the pH of distilled water. pH de­creasinr indicates an e<lUilibrium partition of the acid between the diSperse and aqueous phases with the most of the acid in the copolymer phuse.

It was observed (Palluel, 1969, Delcour, 1988) that other organic solvents, also soluble in the resin and water, added in small quanti ties improve the solubili tyjdispersibili ty of resin in wa­ter, lower the resistivity of the bath and the electrical re­sistance of the film which increases the throwing power of the paint, facilitate the control of deposition of paint films, and affect the surface properties of deposited films. The less hydro­philic the'solvent the more co-deposition with resin and the big­ger the plasticization and throwing power effects. The solvents u~ed: dia~etonealcohol, dimethyl formamide, butyl glycol and the m1xture dlacetonealcohol/cyclohexanone = 1/1 were selected ac­cordinr to their solubility parameters and their capability to form hydrogen bondine.

The b~st fi~m-fo~ing properties were obtained electrodepositing the d1spers1on w1th the degree of neutralization of 0.6. The in­fluence of ~he above solvents, added ill proportion of 1.32 ~ on the propert1es of the dispersions are given in Table 1. '

Table 1. Properties of dispersions with the degree of neutrHlization 0.6, 3.68% isopropanol and 1.32 I other solvents. '

s 0 l v e n t "'f, mN/m )), eSt pH Turbidity .:\xl03, S/cm

Isopropanol 35.90 4.97 6.'10 38 3. r5 Dime thyl formarr~de 36.41 4.bl 6.75 40 3.78 Diac.etone alcohol 36.70 4.98 6. '(5 44 3.65 Butyl glycol 35.76 5.43 6.T) 46 3.'79 Diacetonealcohol/ 36.26 5.03 6.'75 42 3.74 cyclohexanone =1/1

217

As cnn be seen, such properties as conductivity, surface tension, and pH are not influenced by the addition of solvents as expected, because they are not a~fected practically by the size of the dis­perse phase par>ticles. But other proper>ties, as turbidity and viscosity, are sensible to the modification of particle size. The inc1'ease of visC:osi ty and tur>bidi ty for the same concen­tration of the disperse phase snows that butyl glycol and the mixture diaceton0~lcohol/cyclahexanone = l/1 decrease the parti­cle size. The same solvents pre.ctic;~lly double the thickness of the films comp<.l!'ed to the dis~ersion containin£ only iso propanol.

In conclusion it cart be stated that there is a complex distri­bution of the components between the disperse and continuous phases: water and the added solvents distribute between the two phases, the coupler solvent - also present in the both phases -sorbs moderately nt the interfaces and the ionized runine groups are predominantly arranged at the interface but Hre 1:1lso present in the interior.

Brown, G. L. (1930). Water dispersible polymers. In: llth Short Course Advances in Emulsion Polymerization and Latex Technol­~. vol. II, Emulsion Polymer Institute, Lehigh ~n1vers1ty, Bethlehem.

Delcour, J, (l9b8). Electrodeposable paint in the automobile industry. Double Liaison- Chim. Feint ., 35, XXVIII- XXXII.

Leca, M., M. Olteanu, R. Serban and N. Mogall989). Characteri­zation of some film-forming cationic resins. Mat. Plastice, 26, 91-96.

Leca, M., R. Serban and A. Velicu (19~0). Dispersion of a cata­phoretic resin in view of electrodeposition. Rev. Roumaine Chim., 35, 967-972.

Machu, W.ll978). Handbook of Electropainting Technology. Elec­troc'hemicHl Pub] 1cnt1ons Ltd.

Pal~uel, A.L. (1969). Symposium Electropainting for the Seven­t1es, London, Paper ) .

218

Preparation of (non-)aqueous dispersions of colloidal boehmite needles

Paul A. Buining, Chellappah Pathmamanoharan, Albert P. Philipse*,

and Hendrik N.W. Lekkerkerker

Van 't Hoff Laboratory for Physical and Colloid Chemistry, University of Utrecht,

Padualaan 8, P.O.Box 80.051, 3508 TB Utrecht, The Netherlands

(*Author for correspondence)

Abstract

219

A novel hydrothermal alkoxide method is presented for the preparation of stable, aqueous

dispersions of fairly monodisperse, charged colloidal boehmite needles. A polymer coating

procedure for the needles is described which leads to sterically stabilized dispersions in organic

solvents.

Keywords

Boehmite; aluminium alkoxides; colloidal needles; organic coating.

Introduction

This contribution summarizes our recent work on the preparation of stable dispersions of colloidal

boehmite (AIOOH) needles in various solvents.

We investigate this preparation because of our interest in a fundamental study of anisotropic

colloids (Lekkerkerker, 1989). For a quantitative study of, say, diffusion or sedimentation of

colloidal rods, the panicles have to meet a list of requirements. Ideally the rods are monodisperse,

with a controllable size and shape, and able to form stable, non aggregated dispersions. Moreover,

the interactions between the rods should be adjustable by appropriate surface modifications which

allow, for example, a comparison between charged and sterically stabilized rods. An analogous

comparison is possible for colloidal silica spheres (van Heiden~. 1981; Philipse and Vrij,

1989). Last, but certainly not least, we are see!Gng for a relatively simple synthesis which yields at

least a few gram within a few days.

220

There are some well-known types of rod-like colloids, such as tobacco mosaic virus (Lauffer,

1944) and ~-FeOOH particles (Zocher and Heller, 1930). All anisotropic colloids we are aware of,

however, have some serious drawbacks with respect to the requirements mentioned above.

Probably TMV is the best model system available at present. Yet it does not allow variation of

particle length or application of surface modifications. Moreover, sample preparation is a laborious

task.

We therefore develope an alkoxide route for the synthesis of boehmite needles to be used as model

colloids. After an outline of this synthesis, we briefly describe in this communication the coating

of the needles with polymer after which they form stable dispersions in organic solvents. Some

observations are mentioned which confirm the needle shape, and the colloidal stability, of the

boehmite.

Boehmite synthesis

First we attempted to improve a boehmite preparation described by Bugosh (Buining et al, 1990;

Bugosh, 1959). His method comprises the hydrothermal treatment of basic aluminium chloride

solutions. We were able to prepare stable dispersions of fairly monodisperse boehmite fibrils. The

fibril length (- 300 nm, aspect ratio of ten), however, was difficult to vary systematically for

reasons explained by Buining et al (1990). Another drawback of the Bugosh method is the time

consuming dissolution of aluminium powder in hot AICI3 solutions.

Afterwards we found a method which avoids these disadvantages (Buining sa...ill, 1991). This

method employs the hydrothermal treatment of a 1:1 molar mixture of aluminium sec-butoxide and

aluminium iso-propoxide, acidified with an excess aqueous HCI solution. The mixture

composition which produces the most needle-like boehmite particles (Fig.l) was determined more

or less by trial and error. A scheme of the synthesis is given in Fig.2. The average needle length,

which lies in the range 100-500 nm, can be controlled with reagent concentrations in the initial

synthesis mixture, as is illustrated in Fig.3. Some representative characterization results for

dispersions of the (polycristalline) boehmite particles are given in Table I.

Coating with polymer

The aqueous dispersions are stabilized by electrostatic repulsions between the (positively) charged

needles. When transferred to weakly polar solvents such as toluene, the particles flocculate. To

attain stability in such solvents, a protective polymer layer on the needles is required. However,

attaching polymer on the surface of the needles without loosing colloidal stability is not a straight

221

Fig. 1 Transmission micrographs of boehmite needles with (A) average length 137 nm (code

ASBS) and (B) 306 nm (code ASBIPl). Bar is 1 ~J.m.

forward procedure. One has to change the solvent composition gradually from water, which is a

good solvent for uncoated boehmite, to an appropriate polymer solvent for the needles coated with

polymer. The polymer grafting procedure has to take place during this gradual solvent change.

This coating process was developed recently for the surface coating of silica spheres with

polyisobutene (M- 1500 g moi-l) modified with a polar anchorgroup (Pathmamanoharan, 1988).

We used a similar process for attaching the polyisobutene to boehmite, which comprises the

following steps (Buining tl.lll, to be published).

First the boehmite needles are transferred from water to propanol by a distillation procedure. Then

a solution of the modified polyisobutene in tetrahydrofurane is added to the dispersion in propanol.

During distillation of tetrahydrofurane toluene is slowly added to further lower the solvent polarity.

Distillation is continued until the needles are dispersed in pure toluene.

The resulting needles are indeed stable in toluene and other solvents of comparable or lower

dielectrical constant, such as cyclohexane. This clearly points to the presence of the polymer on the

boehmite surface. This polymer cannot be removed from the surface by repeated sedimentation­

redispergarion procedures. The polymer attachment was also corroborated by other techniques,

such as infrared and element analysis (Buining et al, to be published).

222

AI (OBu')J

+ HCI

IM~ ~gmg for - one day T= 25'C

.j.

I Hydrothermal treatmenl for 20 h T= !50'C

.j.

Removal of alcohols and ions from

boehmi1e dispersions by

dialysis againsl deionized H~O

.j.

Boehmite transfer 1o propanol

by disLillaLion

.j.

Addition polyisobutene in tetrahydrofurane

.j.

Fig.2 Scheme of the hydrothermal synthesis of boehmite needles and the subsequent polymer

coating procedure.

Dispersion properties

The following qualitative observations illustrate the marked difference between ungrafted and

grafted needles.

Dialyzed dispersions of the boehmite in water exhibit permanent birefringence at boehmite volume

fractions as low as 0.3%. The permanent (partial) alignment of needles at these low concentrations

requires long range electrostatic forces, which indeed must be present in deionized water because

of the large Debye length (see Table 1). Grafted needles in cyclohexane only exhibit flow-induced

streaming birefringence at volume fractions roughly above 10%. This must be due to the fact that

these uncharged needles have a much smaller effective interaction volume.

A similar difference between grafted and ungrafted needles was (visually) observed for the

relaxation time of streaming birefringence in dispersions with no permanent alignment of particles.

At a given concentration this time is clearly much longer for the needles in water, than for the

coated boehmite needles in cyclohexane. This points to a relatively slow rotational diffusion of the

needles in water, which probably also manifests the presence of significant electrical double layer

interactions. We note here that these observations on birefringence properties of the various

dispersions indicate non-aggregated needles.

e .s .c Q, c: ~ Q)

0 € "' a. Q)

g> Q; > <

500

400

300

200

100

0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Initial AI:CI molar ratio

'AI (OBu5 )3

!AI (OPri)J

'AI (0Bu5)J+AI (OP~)J

223

Fig.3 Average boehmite needle length as a function of the alkox.ide type and the initial aluminium

concentration and aluminium/chloride ratio in the synthesis sketched in fig.2.

Table I. Some properties of representative boehmite dispersions

solvent

(average) needle length

spread in length

needle thickness

Debye length

particle mass density

1) laboratory code ASBIP8

2) laboratory code ASBIP8g

3) deionized dispersion

4) literature value

ungrafted I)

water

281 nm

46%

12nm

"""" 100 nm 3)

3.01 g/cm3 4)

grafted 2)

toluene, cyclohexane

191 nm

28%

12nm

2.10 g/cm3

224

The viscosity of aqueous boehmite dispersions is high. Dispersion ASBIP 8 at a volume fraction

of only 0.3%, for example, has a (zero-shear) viscosity relative to water of about 600. The grafted

(ASBIP8g) needles in cyclohexane produce a much lower viscosity at comparable concentrations.

We attribute this viscosity difference, again, to a difference in interaction between the needles.

Conclusions

Stable dispersions of fairly monodisperse, charged boehmite needles with a controllable length can

be prepared by a simple and rapid hydrothermal treatment of an aqueous acid aluminium alkoxide

mixture. The needles can be modified with polyisobutene to form stable dispersions in organic

solvents such as toluene and cyclohexane.

Preliminary observations on the viscosity and optical properties of the various dispersions confirm

their stability and the needle shape. It is clear that the boehmite synthesis and modification can be

further improved. For example, a further decrease in polydispersity of needle length would be

profitable. It is also clear that a quantitative study is needed for a more accurate evaluation of

particle and dispersion properties.

The results so far, nevertheless, clearly indicate that the boehmite dispersions are promising

candidates for a future study of sterically stabilized and charged rod-like colloids, as referred to in

the introduction.

Acknowledgements

Monique Bosboom and Yvonne Veldhuizen are thanked for their contribution to this work. We

also acknowledge the support of Dr. Ben Jansen and his group of the Geochemistry department of

the Utrecht University.

References

Buining, P.A., Pathmamanoharan, C., Bosboom, M., Jansen, J.B.H. and Lekkerkerker,

H.N.W. (1990). Effect of hydrothermal conditions on the morphology of colloidal boehmite

particles: implications for fibril formation and monodispersity. J. Am. Ceram Soc., TI., 2385-

90.

Buining, P.A., Pathmamanoharan, C., Jansen, J.B.H. and Lekkerkerker, H.N.W. (1991).

Preparation of colloidal boehmite needles by hydrothermal treatment of aluminium alkoxide

precursors. To appear in J. Am. Ceram. Soc., H.

225

Buining, P.A., Veldhuizen, Y., Pathmamanoharan, C. and Lekkerkerker, H.N.W. Preparation of

a non-aqueous dispersion of sterically stabilized boehmite rods. (To be published).

Bugosh, J. (1959). Fibrous alumina monohydrate and its production. U.S. Patent no . 2915475.

Heiden, A.K., Jansen, J.W. and Vrij, A. (1981). Preparation and characterization of spherical

monodisperse silica dispersions in nonaqueous solvents. J. Colloid Interface Sci., .81, 354-

368 .

Lauffer, M.A. (1944). The size and shape of tobacco mosaic virus panicles. Am. Chern. Soc ., Q.Q 1188-1194.

Lekkerkerker, H.N. W. (1989) . Crystalline and liquid crystalline order in concentrated colloidal

dispersions: an overvieuw. In : Phase transitions in soft matter (T. Riste and D. Sherrington,

eds.), pp. 165-177. Plenum Press, New York.

Pathmamanoharan, C. (1988) . Preparation of monodisperse polyisobutenen grafted silica

dispersions. Colloids and Surfaces, 31_, 81-88.

Philipse, A.P. and Vrij, A. (1989). Preparation and properties of nonaqueous model dispersions

of chemically modified, charged silica spheres. J. Colloid Interface Sci ., ill, 121-136.

Zacher, H. and Heller, W.Z. (1930) Z. Anorg. Chern., .lliQ, 75.