ELSEVIER Desalination 150 (2002) 155-164

DESALINATION

www.elsevier.com/Iocate/desal

Concentration and diafiltration of aqueous fluorescent whitener solution by nanofiltration

Gang Yang, Weihong Xing, Nanping Xu* Membrane Science and Technology Research Center, Nanjing University of Technology~ No. 5 Xinmofan Rd., Nanjing,

Jiangsu 210009, China Tel. + 86 (25) 331-5980; Fax + 86 (25) 330-0345; emaik npxu@njuct, edu. cn

Received 7 September 2001; accepted 25 February 2002

Abstract

Concentration and desalination of NT dye solutions by nanofiltration were studied experimentally with a spiral- wound nanofiltration membrane element. The decrease of permeation flux and increase of the observed NaCI rejection were observed due to the formation of the gel layer and possibly the precipitate layer on the membrane surface due to the high bulk NT concentration. By analyzing concentration polarization of NaC1 at the membrane-solution interface, a simple empirical correlation between the permeation flux and the interfacial mass transport coefficient was obtained and coupled with a simplified S-K model for prediction of concentration and desalination of NT solutions. The concentration polarization was investigated using the simplified model that complied with the theoretical understanding. Several operations were compared, which resulted in an optimized technology for potential field implementation.

Keywords." Nanofiltration; Model; Desalination; Dye; Whitener

1. Introduction

Much literature has reported applications of nanofiltration technology in dye waste treatment, and some concerned desalination and/or concen- tration of dye products [1-7]. Based on experimental investigations of the nanofiltration behaviors of the dye-salt solutions, the authors tried, respect- ively, with their different models to simulate the

*Corresponding author.

membrane processes. The concerned dye concen- trations in the literature are generally much lower than 0.1 mol.L -~, which is higher than that of the dyeing effluent but inadequate compared with those of most dye solution products. For example, the highest concentrations of both dye and salt investigated by Bowen and Mohammad [6] were 0.035 and 0.05 mol.L -t, respectively. Therefore, the formerly proposed models are challenged when the dye and salt (NaCI) concentrations are

0011-9164/02/$- See front matter © 2002 Elsevier Science B.V. All rights reserved PII: S 0 0 1 1 - 9 1 6 4 ( 0 2 ) 0 0 9 4 0 - 2

156 G. Yang et al. / Desalination 150 (2002) 155-164

much higher, such as the concentrations of 0.30 and 1.0 mol.L -~, respectively, in the dye-NaCi solutions that will be reached in the nanofiltration experiment of this article.

Based on experiments with a spiral-wound nanofiltration membrane element, the aim of this article is to establish a model to describe the concentration and desalination processes of an industrially synthesized dye solution (a fluore- scent whitener, called NT). Some phenomena that occur in the experiment are given and analyzed, then a simplified description &the concentration polarization at the high-pressure side of the mem- brane is given, a simplified S-K model is applied for prediction of the nanofiltration process for further discussion and an optimized technology for concentration and desalination of NT solution is finally obtained for the field operation.

2. Theoretical model

When the net driving force in the nanofiltration process is weak enough, solute transport in the membrane is mainly contributed by diffusion, and the convective flux can be neglected. Therefore, the solute permeation flux in the S-K model can be simplified. This makes the numerical computation in simulation much easier. Within a relatively wide permeation flux range, where the solute transport in the membrane through diffusion and convection may co-exist, Levenstein et al. [4] experimented with dye-NaCl solutions and simulated the pro- cesses using the simplification with a satisfactory agreement. They coupled the simplification with the Donnan effect, assuming that the average CI- diffusion coefficient Ds was only affected by CI- concentration at the interface, and gave real rejection of CI- as

r~eol 1 B

m

B=DsK.~ X,,, = BoC2cl- ( l a )

13=(1+ vCx / °s

\ Clcl- j (lb)

where 13 is the enhancement factor, n is the valence of the dye anion of concentration C2~ at the membrane surface, K is the partition coefficient of NaC1 between the boundary layer solution and the membrane at the interface and X is the mem- brane thickness. B 0 and n are the model parameters.

Eqs. (I) and (la) can be rewritten as follows:

LI3 + -1J (2)

Constants B 0 and n are obtainable based on necessary experimental data. Levenstein et al. experimented with NaC1 solutions and plate membranes to regress B 0 and n for predicting nanofiltration process of the H20-NaCl-dye-PNa solution system. The results proved consistent with their experiments. In this article, however, B o and n will have to be obtained using the NT-NaCI solution directly because concentrations of the dye and salt are much higher and the dynamic interactions between the dye and salt components are complex and will change greatly during the nanofiltration process.

A description of concentration polarization in the spiral-wound module should be considered. On the other hand, a gel layer and/or a precipitate layer are likely to be formed and accumulate at the membrane surface. The layers are appro- ximately of the same thickness along the axial direction due to the enhanced flow disturbance of the fabric grid assembled in the flow channel at the high-pressure side of the membrane. The gel layer may cause the permeation flux to decrease and the observed rejection of NaC! to rise. If so, a secondary membrane is virtually formed on the primary polymer membrane surface. In this case, the membrane process is usually modeled with filtration or according to hydrodynamic theories [8,9], and the mathematical

G. Yang et aL / Desalination 150 (2002) 155-164 157

treatment using solution thermodynamics seems to be valid where only concentration polarization occurs [10]. However, if the secondary layer is closely compacted with the primary membrane, then the two layers may be treated together as a "black box," and concentration polarization of the NaCI relates to the concentration at the interface of the solution with the surface of the secondary membrane as depicted in Fig. 1. One can then use the film theory expression to relate the concen- trations of NaCl in the bulk feed, at the interface and in the permeate:

C2c'--C3c' = exp(-~-) Clc ~_ - C~c I_

(3)

where k is mass transport coefficient of NaCI at the interface. Therefore, real rejection of NaC1 is

C2C 1 - - C3C I_ _ _

~'eal - -

C2CI

(4)

A boundary mass transport correlation often used is Deissler's expression, which results in mass transport coefficient k. However, value o f k is difficult to dynamically describe in experiments of this article. Eriksson [11 ] obtained, through an experiment with spiral-wound modules, a different empirical equation, which suggested that rather large deviations might be introduced in the de- scription if Deissler's expression were adopted for a complicated solution system. Schock and Miquel [ 12] thought that, because the local gradients of pressure and concentration were complicated in the spiral-wound membrane element, it was difficult to obtain the empirical constants in Deissler's equation. Special considerations for the concentration polarization are therefore necessary, which will be further discussed later in this article.

3. Experiment 3.1. Apparatus and chemicals

The experimental apparatus is shown in Fig. 2. The water used is treated with a reverse-osmosis membrane and ion-exchange resin. The aqueous NT solution is sampled from the industrial pro- duction line, prefiltered with ceramic membranes of an average pore diameter of 0.8 x 10 -6 m. NaC1 and NT concentrations are 1.05 and 0.14 mol.L -1,

CtNaCI

C3_..~_NaC I

r ; C~NaCI

i "

T layer

T T T T Bulk Polarization Second Primary Permeate

Solution membrane membrane solution

Fig. 1. NaCI concentration in the concentration polarization layer, the secondary membrane layer and the primary membrane layer.

i '°i i

Fig. 2. Nanofiltration apparatus flowchart. 1, tank; 2, cooler; 3, pump; 4,6, pressure gauges; 5,7, temperature meters; 8, membrane module; 9,10, sampling points; 11,12, flow meters; 13, feeding point.

158 G Yang et aL /Desalination 150 (2002) 155-164

respectively. In the solution, fluorescent whitener NT is dissociated into a tetravalent anion and four Na + ions. The viscosity of the parental solution increases with the NaCi concentration, and NT may coagulate due to the high concentration of NaCI. The solution contains a small fraction of low molecular-weight organic matter. Analytical grade NaCi is used for calibration of the chlorine ion-selective electrode.

3.2. Analyses

NT concentration is determined using a spectro- photometer at the wavelength of 346 nm. The NaC1 component is determined with a chlorine ion-selective electrode at a temperature 303.2 K.

3.3. Nanofiltration membrane

A spiral-wound cellulose acetate membrane element is used. The module is 40 in. in length and 4.0 in. in diameter. Its pure water permeation flux is 1.06× 10 -5 m.s-~.MPa -I at temperature 308 K. Under feeding pressure of 1.4 MPa, its nominal rejection to 8.6x 10-6 mol'L -~ (0.5 mg.L -~) NaCI solution and 4.2× 10 -6 mol.L -~ (0.5 mg.L -~) MgSO 4 are 50 and 98%, respectively. The module configuration and membrane area are chosen so that the pilot process best represents the potential field application.

3.4. Experimental procedures

Under the feeding pressure of 1.8 MPa and the bulk flow rate of 0.13 m.s -1 tangential to the membrane surface, the bulk solution is concen- trated to approximately half of its volume. An appropriate volume of water is then added into the tank. The bulk solution is cycled at a high tangential flow rate for 5 min at the interval of the concentration terms. The process is designed in this way so that different solute concentrations can be acquired. At the beginning, middle and end of each concentration turn, the bulk solution and the permeate are sampled simultaneously. It is necessary to point out that the system temperature

increases slightly during every concentration turn. Therefore, the pilot conditions are very similar to the potential industrial working conditions.

4. Results and discussion

4.1. Permeat ion f luxes and observed NaCI rejection

Because the concentration of NaCl in the NT solution has decreased, a higher permeation flux in the next nanofiltration turn is anticipated. However, as is seen from Fig. 3, the trend is not always so. At a given bulk NT concentration, the permeation flux J, increases among the first three concentration turns but decreases among the rest of the turns. On the other hand, observed rejection of NaC1 rob s (= 1- C3cJC~cv) increases with the number of the concentration turns, as is shown in Fig. 4. In the first nanofiltration turn, rob s is very low and, in the end, drops to the lowest point. Negative rejection of NaC1 appears to be due to the Donnan effect [13] as tetravalent NT anions are almost completely rejected. However, when

4.0

,?

3.0

2.0-

1.0-

0.0

~) 1st

L~~ [] 2rid 3rd 4th

~ t h

\ -q 0.15 0.20 0.25 0.30 0.35

Clsr / mol'L -1

Fig. 3. Permeation flux J changes as the bulk NT concentration C~N- r in each turn of the processes.

G Yang et aL / Desafination 150 (2002) 155-164 159

1.0

0,8-

0.6--

0.4

0.2

0.0

\

' ' ' ' t ' ' ' I '

40 80

\

i i [ i i J i

120 160

t min

Fig. 4. Observed rejection of NaCI during the nanofiltration process of the NT solution.

C,c ~ is down to 0.03 mol-L -1, rob s is up to 83%, although the enhancement factor 13 [according to Eq. (lb)] is high.

4.2. Formation of the boundary layer

In order to better discuss the changes of the permeation flux and the observed NaCl rejection, let us suppose that the NT component is com- pletely dissolved and no type of secondary mem- brane formulates. The changes of the difference of the salt osmotic pressures at both sides of the polymer membrane contribute to changes of the permeation flux. At the same bulk NT concen- tration, a negative rejection of NaCI facilitates the permeation flux as NaCI concentration on the high-pressure side of the membrane is lower than its bulk concentration. In this case, the real NaCi rejection is supposed to decrease monotonously in the previous successive concentration terms, which is expected to be similar with the trends described with NaCI-Na2SO 4 solutions in early reports [14]. Subsequently, the permeation flux is expected to rise. Slight temperature variation should not divert the trends. However, the experi-

mental result seems counterintuitive. One possible reason for the phenomena is the inadequate dissolving of the NT component due to its accu- mulation at the membrane surface and the existence of the NaCI component. Inadequate dissolving of NT suggests that the molecules lose degrees of freedom and tend to be more structured, and changes of NaC1 concentration exert a relevant salt effect on the NT component, which tend to facilitate NT molecules to agglomerate and preci- pitate. To partly support this assumption, it is found that the viscose parental sample containing 0.33 mol-L -1 NT and 1.05 mol.L-' NaCI contains a small proportion of fine NT particles, which is part of the reason that the salt is required to be washed out for industrial purposes. A gel layer and/or a precipitate layer are considered in this article to have formed according to the literature [15], but the gel-phase transition from a true solution to a stiff construction is not necessarily apparent. Under the same interfacial NT concen- tration, the thickness of the NT precipitation layer and the gel layer increases with NaCI concen- tration. Transport of NaC1 in the boundary layer is therefore hindered and possibly dominated by the secondary membrane layer. Under the same feeding pressure, the net pressure driving force is affected by the osmotic pressure difference across the membrane and the resistances of the primary and secondary membranes, while the osmotic pressure at the parental side is contributed by NT dissolubility and NaCI concentration just outside the gel layer. As the parental NaCI concentration decreases, NT dissolubility increases, and thus the osmotic pressure difference across the membrane changes. The resistances of the secondary membrane also vary simultaneously. Therefore, the complicated changes of the permeation flux occur.

The variation of the observed NaCI rejection can be explained in terms of the S-K model and Donnan exclusion [ 13 ]. The reflection coefficient is expected to rise due to the formation of the secondary membrane. On the other hand, as the parental NaC1 concentration decreases, the

160 G Yang et al. / Desalination 150 (2002) 155-164

reflection coefficient increases together with the NaC1 passage enhancement factor b. With a low reflection coefficient, a negative NaC1 rejection occurs within a wide permeation flux range (starting from 0). However, when the reflection coefficient rises, the range is quickly shortened so that negative NaCI rejections do not appear at the tested permeation flux. Such are the cases in the experiment of this article.

It is easy to accept that the extremum of NaCl concentration is reached at the surface of the secondary membrane. It seems difficult to deter- mine the local NT concentration that contributes to the Donnan effect because the gel layer and the true solution do not show abrupt phase transition. As the NT concentration at the surface is always slightly higher than the bulk NT solution, the bulk NT concentration may be taken as that which exerts the Donnan effect at the gel surface, and the subsequent deviation is thought to be balanced by the thickness modification of the virtual gel layer. This treatment generally complies with the principle of simplicity.

The concentrations and diffusivities of NT and NaC1 as well as the viscosity of the solution all influence the thickness of the gel layer and therefore the thickness of the polarization layer, which in turn link the mass transport coefficient of NaC1, k, and the permeation flux, J,, in a com- plicated manner. As the permeation flux concerned in this article is limited from 1.0xl0 -6 to 3.0x 10 -6 m.s -~, it may be assumed that k and J, can be correlated into an empirical expression so that the Eqs. (1), (la) and (lb) are adoptable for a com- paratively accurate description.

When k/J,. is assumed to be a constant, its value can be regressed from Eqs. (2), (3) and (4). As is seen in Fig. 5, when k/J, is set to 1.4, even though the system temperature slightly changes and the concentrations are variable, ln(C2cl_) vs. In[J, (1- r,~o~)/([5-1+r~) ] shows approximately a linear relationship. Eq. (1 a) can be expressed as

~6 1.45 B = 4.24x10 C2c r (5)

-12.0

I "-- -13.0 -

+ -14.0 -

I

" " -15.0 - 7- " ~ -16.0 -

I

,_,~ -17.0 - _=

/ / ./"

- 1 8 . 0 ' I ' I ' I ' I '

-4.00 -3.00 -2.00 -1 .00 0.00 1.00

In (Cm-) / -

Fig. 5. Regression of the experimental data according to Eq. (2) when k/J is set at 1.4.

With the fixed value of k/J,, a simple approach is reached for the description of the diffusion transport-dominated nanofiltration process where a gel layer may formulate at the membrane surface. By using empirical Eq. (5), the simulated NaC1 concentration C3c t_ in the permeate can be compared with the experiment in Fig. 6. It can be seen that the results are in good agreement.

Using the numerical model, concentration polarizations in the nanofiltration of NT solutions under several typical conditions are shown in Fig. 7. From Fig. 7a it can be seen that, when the bulk NT concentration, CmT, increases or the per- meation flux, J,, decreases, the degree of polari- zation (=1- Clcr/C:cr) decreases; when the bulk NaC1 concentration, Cmr, decreases, the polariza- tion increases. A more apparent Donnan effect can be observed at lower permeation fluxes, as is seen from Fig. 7b. This explains why negative rejections at low NaCI concentrations discussed in the previous section do not occur in the experiment. It can be seen that, although negative rejections are obtained at low permeation fluxes, the operation period would be too long.

G. Yang et al. / Desalination 150 (2002) 155-164 161

o B

1.20

0.80

0.40

0.00

0

0.0 1.0 2.0 4.0

Q~ II 0

3.0

Jv / 10-6m's -1

Fig. 6. Calculated NaCI concentration in the permeate is compared with the experimental data. - - : Calculated; O: experimented.

4. 3. Description and comparison o f the nanofil- tration processes

Calculated observed rejections of NaCl under different conditions are given in Fig. 8. When the bulk NT concentration, CtNT, increases from 0.15 mol.L ' to 0.3 mol.L -' but a constant permeation flux, J , is maintained, observed rejection of NaCl, rob.,, decreases. The trend is more obvious when bulk NaC1 concentration, C~N,a, is high and a negative observed rejection shows. When Cma a increases even more, a decrease of ro~ + tends to cease, which shows that, over a relatively wide range of NaCI concentrations, effective desali- nation may be obtained. At a fixed permeation flux, an increase ofCjN v facilitates the desalination. Although rob s can be lowered by decreasing J , the amount of permeated NaCI decreases; there- fore, the nanofiltration equipment should be designed with a greater membrane area.

One example from field implementation is given for an application of the model; 25m 3 of NT solution that contains 0.14 mol.L -~ NT and

0.20

i

'c

0.15

0.10

0.05-

t 0.00

0.20 ~ ~ Quv Z,

mol-L 1 10 '~ 6ms-I 0.15,3.0

0.30.3.0 0.15, 1.0

0.20 0.40 0.60 0.80 1.00

Clc r / mol .L -I

0.00 -

I ~. -0.20 -

~ -0.40 - r,o

I " -0.60 -

-0.80 " 0 , 0 5 I I I I I [ l [' I

o.oo 0.00

~/" l m°l'Ll 10? 8m'sl

£ / o +! o.3o.3o

/ ,~ o.3o, 1.o /

d 0.15, 30

' 1 ' I ' [ ' I '

0.20 0.40 0.60 0.80 1.00

C/c r / mol.L -I

Fig. 7. Degree of concentration polarization of NaCl component (1- C,c,JC2c r) affected by bulk NaCI concentration, C~cv, at a certain NT concentration, CmT , and permeation flux, J .

162 G. Yang et aL /Desalination 150 (2002) 155-164

1 . 0 0 ]

0 . 8 0 -

~,,_ Clm" J,. \\ ~ mol'L "1 10" 6m'sl \\ + 015,30

[ ] 0.30,3.0 0.60_ - \ \ o

~ . ~ . 0.40- ' ' "

0 . 2 0 -

0 .00 -

-0.20 ' i ' I ' I ' I '

0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

Clc r / mol.L -t

Fig. 8. Observed rejection of the NaCI component, rob,, affected by bulk NaCI concentration, C~ct. at certain NT concentration, C~N T, and permeation flux, J.

1.0 moI.L -t NaC1 is to be desalinated and concen- trated within 30 h. NT and NaC1 concentrations in the end product are required to be 0.25 and 0.085 mol.L -~, respectively. The literature [6] usually considered a two-step approach for the purpose. However, the method is not best in this article as an additional dilution process is other- wise needed. Two other approaches are considered to compare the needed membrane areas and amounts of effluent:

1. The nanofiltration equipment is generally fit for operation under a constant feeding pressure.

The bulk NT concentration, C1NT, is fixed and the feeding pressure is 1.8 MPa. Although the perme- ation flux, J , rises first and then decreases as NaCI concentration decreases, as is shown in Fig. 3, the linear expression, Eq. (6), is obtained from the experiment to simplify the relationship between permeation flux, J,, and the driving pressure. The original NT solution is concentrated to and fixed at 0.25 mol.L -1 for desalination, as is illustrated in Table 1. For comparison, the originalNT solution is also considered to concentrate to and fixed at 0.30 mol.L -~ for desalination. In the end, the NT concentration is adjusted down to 0.25 mol.L -~.

J, = -9.19C~N T + 4.15 (6)

2. The permeation flux is fixed as shown in Table 1. When the NT concentration reaches 0.25 mol.L -1, de-ionized water is added to keep a constant NT concentration. In choosing the per- meation flux as 3.0x10 -6 m's -1, more deviation may occur because the needed driving pressure in the ending period is larger; however, the result is obtained for a rough comparison.

Variations of the observed rejection of NaCI, robs, and the separated amounts ofNaC1, Q~, during the desalination under several conditions are given in Fig. 9. All rob s decrease to their respective minimum values when the bulk NT concentrations arrive at the summit, as is shown in Fig. 9a. Then rob s increases as NaCI concentration decreases. When the fixed permeation flux, J,, is low, rob s is also low. However, it can be seen from Table 1

Table 1 The needed membrane area A and the amount of effluent Qp under different conditions

Parameters Fixed permeation flux Fixed feeding pressure -9.19 C1 NT + 4.15

Jr, 10~m's -~ 3.0 1.57 1.0 Concentrated to 0.25 mol'L -~ Concentrated to 0.30 mol.L -~ A, m 2 210" 322 452 275 260 Qp, m 3 68 55 49 58 44

*The real value should be larger because k cannot be as high as is used in the calculation in the late desalination when the driving pressure is much larger than 1.8 MPa.

G Yang et al. / Desalination 150 (2002) 155-164 163

0.80 (a)

0.60

0.40 -

0.20

0.00

- 0 . 2 0 ' I ' I '

0 10 20 30 t/min

25

2O

.~ 15.

Q)j~ 10.

5.

' I ' I '

0 10 20 30 t/min

Fig. 9. Variations of observed rejection of NaCl rob s and the separated amount during the desalination. O , J = 3.0x 10 -6 m-s-J; ~ , J--1.57× 10 -6 m.s-~; [ ] , J=l .0× 10-rm's-~;/~, concentrated to 0.25 moI.L-J; -I-, concentrated to 0.30 mol.L-L (a) Trends that rob ' changes. (b) Trends that Q, changes.

that the necessary membrane area, A, increases despite reduction of the effluent amount, Qp. Fig. 9b shows that the desalination lasts longer when the NaC1 concentration becomes lower. Desalination at an NT concentration of 0.30 mol-L -~ needs the least membrane area and produces the least effluent, as is shown in Table 1. This is achieved as the target bulk NaCI concentration is raised to 0.102 mol.L -~.

5. Conclusions

Special variations of permeation flux and observed rejection of NaCl are observed in nano- filtration of the NT solution, which are thought to be due to formation of the gel layer and possibly the precipitate layer. The process is characterized with the diffusion-dominated transport and a thickness-changeable secondary membrane layer and concentration polarization layer. This article links the interfacial mass transport coefficient of NaCI with the permeation flux to simplify descrip- tion of the concentration polarization. The empirical

relationship is coupled with the simplified S-K model and well represents the experiment. Simu- lation of the desalination and concentration pro- cesses of NT solution under different conditions shows that required membrane area and effluent amount both decrease if the bulk NT concentra- tion is raised moderately higher than the require- ment. It may be expected that the model proposed here is promising for desalination and concentra- tion of aqueous dye solutions that have features as stated in this article.

Symbols

A - - B 0 - - C - - q -

O s - -

K -

Membrane area, m 2 Empirical constant defined in Eq. (1 a) Solute concentration, mol.L -~ Dye concentration in the bulk solution, mol.L-~ Average diffusion coefficient of NaCI in the membrane, m2.s -1 Permeation flux, m.s -1 Partition coefficient of NaCl

164 G. Yang et al. / Desalination 150 (2002) 155-164

n - - Empirical constant defined in Eq. ( lb ) Q~, - - Volumetric amount o f the permeate, m 3 r,h ~ - - Observed rejection o f NaCl r a ~ - - Real rejection o f NaCl t - - Time, min X - - Membrane thickness, m 13 - - Enhancement factor v - - Valence o f the dye anion

Subscr ip ts

1 - - Bulk solution 2 - - Membrane-bu lk solution interface 3 - - Permeate solution

R e f e r e n c e s

[1] P. Schirg and F. Widmer, Desalination, 89 (1992) 89. [2] (2 Christian, Inf. Chim., 382 (1996) 115. [3] G. Venkidachalam and S.K. Verma, Indian J. Chem.

Technol., 3 (1996) 131.

[4] R. Levenstein, D. Hasson and R. Semiat, J. Membr. Sci., 116 (1996) 77.

[5] X. Xu and H.(2 Spencer, Desalination, 114 (1997) 129.

[6] W.R. Bowen and A.W. Mohammad, AIChE J., 44 (1998) 1799.

[7] W.R. Bowen andA.W. Mohammad, Desalination, 117 (1998) 257.

[8] W.B. Russel, The Dynamics of Colloidal Systems, University of Wisconsin Press, Madison, WI, 1987.

[9] M.R. Mackley and N.E. Sherman, Chem. Eng. Sci., 47 (1992) 3067.

[10] M. Elimelech and S. Bhattacharjee, J. Membr. Sci., 145 (1998) 223.

[11] P. Eriksson, J. Membr. Sci., 36 (1988) 297. [12] (2 Schock andA. Miquel, Desalination, 4 (1987) 339. [13] M. Perry and C. Linder, Desalination, 71 (1989) 233. [14] T. Tsuru, M. Urairi, S. Nakao and S. Kimura, J. Chem.

Eng. Jpn., 24 (1991) 518. [15] W.B. Russel, D.A. Saville and W.R. Schowalter,

Colloidal Dispersions, Cambridge University Press, Cambridge, 1989.