Rheology Suspensions
-
Upload
marc-cornell -
Category
Documents
-
view
221 -
download
0
Transcript of Rheology Suspensions
-
8/2/2019 Rheology Suspensions
1/7
Progress in Organic Coatings 40 (2000) 111117
Rheology of sterically stabilized dispersions and latices
Jan Mewis, Jan VermantDepartment of Chemical Engineering, de Croylaan 46, Katholieke Universiteit Leuven, 3001 Leuven, Belgium
Abstract
Steric stabilization is a method that is often used to properly disperse small particles. It can be applied in aqueous as well as non-aqueous
media. The rheologicalproperties of sterically stabilized dispersions are discussed here. The various controlling parameters and the physical
mechanisms involved are reviewed. Brownian hard spheres are used as a reference. Scaling relations are presented that make it possible
to reduce data sets and to predict properties. Viscosity, yield stress, shear thickening and viscoelasticity are included. The rheological
properties are also related to the fundamental colloidal properties of the dispersions under consideration. Quantitative results are available
for monodisperse spherical particles, although the effects of particle size distribution can sometimes be predicted also quite well. In othercases the procedures presented here can be used qualitatively to predict viscosities. 2000 Elsevier Science S.A. All rights reserved.
Keywords: Rheology; Latex; Suspensions; Steric stabilization; Viscosity predictions; Viscosity scaling; Dynamic moduli
1. Introduction
Because of the presence of small particles most liquid
coatings can be considered colloidal suspensions. The col-
loidal stability of the system then determines whether the
particles will remain well dispersed or whether they will
flocculate. When flocculation is not desirable stability can
be induced by electrostatic repulsion between the particles,its application is mainly restricted to aqueous media. Steric
repulsion between layers attached to the particle surface can
provide stability in any suspending medium. Electrostatic
stabilization is very effective but makes the structure and
the rheology sensitive to variations in pH or ionic strength.
Steric, or polymeric, stabilization is not affected by these
parameters but, if the suspending medium is not a good sol-
vent for the stabilizer molecules, the stability might change
with temperature.
Steric stabilization is frequently used as a suitable and ro-
bust way of ensuring proper dispersion of the particles. The
stabilizer layer can be chemically grafted on the particle
surface or, more often, physically adsorbed. The formula-
tion of such materials would obviously be accelerated if the
rheology could be predicted or estimated rather accurately
on the basis of the composition. This is the problem which
is addressed here. Only stabilizer layers of grafted polymers
and adsorbed blockcopolymers or surfactants are consid-
ered, not homopolymers or statistical copolymers as such.
In the latter case the stabilizer layer consists of a complex
Corresponding author.
mixture of tails and loops of the stabilizing polymer,
whereas only tails are present in the other two cases. The
suspending medium can be aqueous or non-aqueous.
2. Brownian hard spheres
Various parameters affect the rheology of stable colloidalsuspensions. In the limiting case of spheres without any
interparticle interactions, only Brownian (thermal) forces
and hydrodynamic forces affect the flow behaviour. The
case of Brownian hard spheres is quite well documented,
experimentally and theoretically, at least for monodisperse
particles (e.g. Ref. [1]). At sufficiently low shear rates Brow-
nian motion will dominate the convective motion caused by
the flow. Under these conditions the equilibrium structure
of the particles that exist at rest is preserved during flow.
As a result the viscosity does not change with shear rate
and the contribution of the Brownian forces to the viscos-
ity is at its maximum. When increasing the shear rate the
Brownian motion will, at a certain stage, become slowerthan the convective motion. From then on the contribution
of the Brownian motion to the viscosity will gradually
decrease with increasing shear rate, whereas the hydrody-
namic contribution remains relatively constant. This causes
the viscosity to drop; a shear thinning region develops. At
still higher shear rates the Brownian contribution levels
off and becomes negligible, but an increase in hydrody-
namic effects can either compensate the decrease, causing a
pseudo-Newtonian high shear plateau, or overcompensate,
producing a shear thickening zone [2].
0300-9440/00/$ see front matter 2000 Elsevier Science S.A. All rights reserved.
PII: S 0 3 0 0 - 9 4 4 0 ( 0 0 ) 0 0 1 4 2 - 9
-
8/2/2019 Rheology Suspensions
2/7
112 J. Mewis, J. Vermant / Progress in Organic Coatings 40 (2000) 111117
The viscosity curves for all suspensions with monodis-
perse Brownian hard spheres of a given volume fraction
can be reduced to a single curve [3]. For that purpose the
viscosity has to be divided by the medium viscosity m,
i.e. the relative viscosity r is used, thus scaling for the
hydrodynamic effects of the suspending medium which are
proportional to m. The shear rate has to be substituted
by a dimensionless stress r, which expresses the ratio
between convective and Brownian effects,
r = a3
kT(1)
where a is the particle radius, k the Boltzmanns constant
and Tthe absolute temperature. The resulting representation
scales for the effects of particle size, medium viscosity and
temperature.
The limiting relative Newtonian viscosities at low and
high shear rates depend only on the volume fraction. These
relations are well documented by now [1]. The hydrody-
namic and Brownian contributions can be separated theo-
retically and experimentally [2,4]. A characteristic of the
hydrodynamic forces is that they drop instantaneously to
zero when the flow stops, the other contributions decay over
a finite time scale [5].
At very high volume fractions the situation becomes more
complicated as the details of the surface now become impor-
tant. These effects show up in the viscosities as well as in
the frequency dependence of the storage moduli [4]. Com-
puter simulations are also difficult for such systems because
of the divergence of hydrodynamic forces between particles
when the interparticle distance goes to zero [6]. Experimen-
tally, a sudden shear thickening can be observed in very
concentrated suspensions, at least when the particles are nottoo small. At the moment it is still not quite clear to what
extent the detailed surface conditions of the particles affect
the results.
3. Viscosity curves
The viscosity curves for sterically stabilized suspensions
of monodisperse, spherical particles are similar to those of
suspensions of Brownian hard spheres (see Fig. 1). There is
however a quantitative difference. This is most easily seen
when the limiting Newtonian viscosities are plotted as a
function of volume fraction. When the stabilizer layer is ei-
ther relatively thin with respect to the particle radius or rela-
tively rigid, the viscosity curves still coincide with those of
Brownian hard spheres, provided the stabilizer layer is in-
cluded in the particle volume. The effect of the stabilizer can
then be expressed by means of an effective volume fraction
eff, which can be calculated from the core volume fraction
of the particles themselves, c, the particle radius a and the
thickness of the stabilizer layer
eff = c
1 +
a
3(2)
Fig. 1. Viscosityshear rate curves for sterically stabilized PMMA sus-
pensions (a = 42nm) at different volume fractions, data from [7].
With a known, e.g. from transmission electron microscopy,
the layer thickness can be deduced from intrinsic viscosity
measurements or from dynamic light scattering data. Such
a value is called the hydrodynamic layer thickness. Other
measures for this parameter will be discussed later.
When the stabilizer layer becomes thicker and/or softer,
the previous procedure is not adequate anymore and re-
sults in overestimation of the viscosity, especially at higher
volume fractions [8,9]. This is illustrated in Fig. 2, where
the limiting viscosities at high shear rates are compared for
a number of sterically stabilized PMMA suspensions with
varying particle radius but similar thickness of the stabi-
lizer layer and silica suspensions with different layer thick-
nesses [10]. The lack of superposition could be expected.Indeed, the stabilizer molecules are dissolved by the sus-
pending medium and do not form a rigid layer. This layer
will be compressed whenever particles approach each other
with a certain force. In some cases the effective volume
Fig. 2. Limiting high shear viscosities for various sterically stabilized
PMMA and silica dispersions [10].
-
8/2/2019 Rheology Suspensions
3/7
J. Mewis, J. Vermant / Progress in Organic Coatings 40 (2000) 111117 113
fraction becomes even larger than unity, which is clearly
physically meaningless (see Fig. 2). The compression of the
stabilizer layer is determined by the molecular structure of
the layer, including molecular weight, grafting/adsorption
density of the stabilizing polymer and its solubility in the
suspending medium. A discussion on the molecular level is
outside the scope of the present discussion. The softness
of the stabilizer layer can be expressed by a potential for
the particle interaction force. It is important to note that
steric stabilization normally results in rather steep repul-
sion potentials, meaning that the softness of the layer is
limited.
Because of the relatively rigid nature of the stabilizer layer
the viscosity curves still could possibly be treated approxi-
mately on the basis of an hard sphere approach. For such an
approach to be useful it should reduce somehow the viscosi-
ties of different systems to a single curve that reflects hard
sphere behaviour. The viscosity curves of sterically stabi-
lized suspensions, e.g. those in Fig. 2, definitely differ in the
limiting volume fraction of the particles at which the viscos-ity goes to infinity, i.e. in the maximum effective packingeff,max, at low as well as at high shear rates. To compare
the intrinsic shape of the viscosityconcentration curves, the
viscosities can be plotted versus the ratio eff/eff,max. As
illustrated in Fig. 3 this procedure can often superimpose
curves for different dispersions. For very soft particles the
evolution of the viscosity with concentration should be more
gradual than for rigid particles. Clearly, in Fig. 3 the slopes
of the curves at the origin cannot be identical anymore as
they were made to coincide in the representation of Fig. 2.
Yet, the major part of the curves superimposes reasonably
well. It is concluded that some degree of similarity with
hard sphere suspensions still exists, provided a suitable mea-sure for the volume fraction is used. This can be obtained
in several ways. The maximum packing could be used for
this purpose as shown in Fig. 3. Alternatively, a critical con-
centration for phase transition could be used [11]. Below, a
Fig. 3. Scaling the viscosityvolume fraction curves using the maximum
packing, numbers indicate diameters (PMMA data of Fig. 2) [8].
third method will be presented that is based on the particle
interaction potential.
Varying temperature and medium viscosity can be taken
into account for sterically stabilized suspensions by means
of the scaling procedure used for Brownian hard spheres
[12]. When changing the suspending medium its solubility
for the stabilizer molecules could then change as well, thus
affecting the thickness of the layer. As this factor is not cov-
ered by the scaling for Brownian hard spheres, it should be
accounted for separately. When working with media which
are on the edge of solubility for the stabilizer molecules the
viscosity could become very sensitive to temperature be-
cause of weak flocculation setting in. Such a situation is
obviously not desirable in practice.
When the volume fraction reaches the maximum packing
value for zero shear rate the limiting low shear viscosity di-
verges and a yield stress appears. As the viscosity it depends
on volume fraction and the colloidal characteristics of the
system. This will be discussed together with the dynamic
moduli in the next section.
4. Dynamic moduli
Oscillatory measurements, in particular on concentrated
colloidal dispersions, can provide detailed information
about the material under consideration. In such experiments
the viscous and elastic contributions can be separated in,
respectively, the loss (G) and storage (G) moduli. In
Brownian hard spheres the Brownian motion is responsible
for the elastic part, whereas the high frequency limit of
G measures the pure hydrodynamic contribution in the
equilibrium structure. In concentrated, sterically stabilized,systems the stabilizer layers overlap and G measures the
interaction forces between layers on neighbouring particles
during the oscillatory motion. This requires the frequency
to be high enough to avoid particle diffusion, caused by
Brownian motion, during an oscillation. G should become
independent of frequency if this condition is satisfied. The
critical frequency at which this happens, i.e. the relaxation
frequency, depends on particle mobility, exactly as the
critical shear rate does in the viscosity curves. These two
parameters are therefore linked to each other as well as
to the zero shear viscosity which also depends on particle
mobility, of which particle diffusivity is the fundamental
measure. The modulusfrequency curves can also be scaledin a similar fashion as the viscosityshear rate curves.
The overlap of neighbouring layers and the resulting in-
teraction forces will depend on the relative distance between
particles, which will decrease with increasing volume frac-
tion. Hence, the change in moduli with volume fraction can
be used to probe the change of interaction potential with
distance. The ZwanzigMountain equation, derived in the
framework of molecular dynamics, relates the plateau mod-
ulus G to the interaction potential and the distribution
function g(r) of interparticle distances r [13]
-
8/2/2019 Rheology Suspensions
4/7
114 J. Mewis, J. Vermant / Progress in Organic Coatings 40 (2000) 111117
Fig. 4. Interaction potentials as a function of interparticle distance for
two PMMA dispersions and two aqueous latices, calculated from plateau
storage moduli (after Ref. [16]).
G = 2152
0g(r) d
dr
r4 d
dr
dr (3)
with the particle number density. Eq. (3) has been used for
electrostatically as well as sterically stabilized suspensions.
In electrostatically stabilized systems the particles can order
in a crystal-like lattice order in which the distance between
nearest neighbours has a well-defined value [13]. In steri-
cally stabilized systems often a less ordered glassy structure
exists during flow, but using suitable estimates for the av-
erage distance still makes it possible to calculate the inter-
particle potentials [8,14,15]. Some results for non-aqueous
PMMA suspensions and for aqueous latex suspensions with
adsorbed stabilizer are given in Fig. 4 [16]. Three of thefour systems in this figure have stabilizer layers with an hy-
drodynamic thickness of about 10 nm, which is typical for
industrial dispersions.
In the case of adsorbed blockcopolymers or surfactants,
steric stabilization is provided by the moiety of the stabilizer
molecule that is not adsorbed on the particle but is extended
in the suspending medium. Increasing the molecular weight
of this moiety obviously increases the layer thickness of
the stabilizer layer and consequently the repulsion force at
a given interparticle distance (compare the two latices in
Fig. 4). This does not imply that the dispersion becomes
more stable under all conditions, at least for adsorbed layers.
Changing the relative size of the adsorbed and non-adsorbedmoieties affects the strength of the adsorption. The change
that apparently increases the stability will actually reduce the
adsorption strength. At high shear rates this could result in an
irreversible, shear-induced, flocculation. Such a behaviour
has actually been observed in the latex system of Fig. 4
when increasing the length of the hydrophylic part of the
stabilizer molecules.
It is obvious that the relation between plateau storage
modulus and volume fraction is an important characteristic
of a sterically stabilized suspension. It reflects the softness
of the stabilizer layer and provides the means to calculate
the limiting viscosities. Empirically it has also be found
that the ratio between yield stress and plateau modulus is
between 0.02 and 0.04 for many suspensions, irrespective
of stabilizer softness, particles size or volume fraction [8].
Hence these two parameters are affected in the same fashion
by the stabilizer layer.
5. Viscosity predictions based on dynamic moduli
The particle interaction potential, as for instance deter-
mined from the plateau values of the storage moduli, can be
used to estimate the viscosities. Provided the particles are
not too soft, a perturbation theory, based on small devia-
tions from hard sphere behaviour can be applied. As was the
case for the expression of the plateau moduli, it is borrowed
from molecular dynamics theory. In essence it replaces the
real, steep, interaction potential by a hard sphere potential
(i.e. vertical line) at a suitable distance from the particlesurface (see Fig. 5). This distance provides another mea-
sure for the effective thickness of the stabilizer layer, which
is smaller than the hydrodynamic value. The ratio between
the new value, hs, and the hydrodynamic layer thickness
from Eq. (2) depends on the shape of the interaction poten-
tial, i.e. the softness of the stabilizer layer. An approximate
expression for the resulting particle diameter is used
2(a + hs) =
0
1 exp
kT
dr (4)
With Eq. (4) a value for the effective volume can be cal-
culated, hs, which is relevant in the case of non-dilute
suspensions. Using this value superimposes the limitingviscosity curves of various stericially stabilized dispersions,
as demonstrated in Fig. 6 [8,9].
Fig. 6 provides a rational basis for the effective hard
sphere approach in the case of sterically stabilized suspen-
sions, with either grafted or adsorbed stabilizer layers. It
also connects the rheological properties with the colloidal
parameters of the material and allows viscosities to be pre-
dicted over a wide range of conditions, at least for model
Fig. 5. Steric interaction potential (dotted line) and corresponding hard
sphere potential (full line).
-
8/2/2019 Rheology Suspensions
5/7
J. Mewis, J. Vermant / Progress in Organic Coatings 40 (2000) 111117 115
Fig. 6. Superposition of viscosity curves using the corrected volume
fraction hs, PMMA and latex suspensions (numbers indicate diameter)
[16].
systems. In practical formulation problems fundamental
characteristics as interaction potential and particle diffusiv-
ity are often not known in sufficient detail, although some
molecular scaling arguments could still be used. Neverthe-
less, the present approach can always be followed at least in a
semi-quantitative manner. Also, the results suggest that mea-
suring, e.g. the maximum packing is an adequate measure to
characterize a given stabilizer layer and to predict its effect
on the viscosity curves at various particle concentrations.
6. Particle size distribution
In real life systems the particles, even if they are spheri-cal, are seldom monodisperse. The particle size distribution
can have a pronounced effect on the rheology. For large,
non-colloidal particles various mixing rules are available,
as reviewed by Utracki [17]. They can give reasonable
predictions for the viscosity. As could be expected from
the discussion of the previous paragraph, the maximum
packing is still the governing characteristic parameter. A
mixture of different sizes can be packed more densely
than monodisperse particles, which increases the maximum
packing. For large particles the latter can be derived from
geometrical arguments. In colloidal suspensions the situa-
tion becomes more complex. The contribution of Brownian
motion has to be considered, which introduced a differentsize dependence. It reduces the efficiency of packing small
particles between larger ones. For mixtures of colloidal and
non-colloidal particles mixing rules have been proposed
that take the said phenomenon into account [1820]. An
example of such a prediction for the limiting viscosity is
shown in Fig. 7, where measured and predicted limiting
viscosities are compared for mixtures of latex (a = 63nm)
and polystyreen (a = 1545 nm) particles [16]. With each
size a shear rate region for shear thinning can be associated.
As the dimensionless stress contains the particle radius to
Fig. 7. Illustration of predictions for the viscosity in binary mixtures (25%
3m and 75% 127 nm diameter particles) [16].
the power three, Eq. (3), particle size distributions can giverise to a very broad shear thinning region (Fig. 8).
The whole discussion has been limited to spherical par-
ticles. In all other cases the shape has to be considered,
e.g. the aspect ratio (length over diameter) for axisymmetric
particles. For large particles the main effect is a reduction
in maximum packing. For smaller ones the relations given
above cannot be applied quantitatively but qualitatively sim-
ilar strategies can often still be followed.
7. Shear thickening
At sufficiently high volume fractions and shear rates shearthickening will occur in most suspensions. It normally lim-
its the concentration and shear rates that can be used, but
it also turns out to be important in understanding particle
interactions and flow in concentrated suspensions. General
Fig. 8. Broad shear thinning zones in dispersions with two particle sizes
[8].
-
8/2/2019 Rheology Suspensions
6/7
116 J. Mewis, J. Vermant / Progress in Organic Coatings 40 (2000) 111117
discussions on shear thickening are available [21]. This phe-
nomenon is not restricted to colloidal systems, it occurs even
more readily with larger particles. The shear rate or shear
stress at which shear thickening sets in is considered as the
most relevant parameter.
When discussing shear thickening it is important to dis-
tinguish between two different types. At moderate concen-
trations a gradual increase of the viscosity with shear rate
can often be noticed at high shear rates. No abrupt changes
in structure seem to accompany this kind of shear thick-
ening. Experimental as well as simulation results indicate
that gradual shear thickening is normal rather than excep-
tional at the upper limit of the shear thinning region for sus-
pensions with a liquid-like interparticle structure [2,22]. As
mentioned earlier it is caused by a stronger increase with
shear rate of the hydrodynamic contribution to the viscosity
than the simultaneous decrease in Brownian contribution.
The so-called high shear Newtonian plateau is actually a
limiting case of such a gradual shear thickening region.
Under more extreme conditions of volume fraction andshear rate a second type of shear thickening can be en-
countered. In motion-controlled rheometers it is difficult to
study because often the sudden stress jump accompanying
the increase in shear rate is too large to be measured. In
stress-controlled devices it can be seen that, at the onset of
sudden shear thickening, an increase in stress causes in fact
a decrease in shear rate, after which the latter changes errat-
ically (Fig. 9). When continuously increasing and decreas-
ing the shear stress the transition between the two regimes
shows an hysteresis. Both this and the erratic variations
suggest that a statistical process governs the transition.
The mechanisms responsible for the onset of shear thick-
ening are still under debate. Most likely more than onemechanism is possible. Hoffman [23] was the first to show
that at least in some suspensions with monodisperse spheres,
applying high shear rates caused the particles to order in lay-
ers with an hexagonal packing in each layer. This structure
Fig. 9. Sudden shear thickening in a sterically stabilized PMMA suspen-
sion (a = 170nm, eff = 0.636) [8].
would become unstable at a critical shear rate, signalling
the onset of shear thickening. The latter would then corre-
spond to an orderdisorder transition. The instability would
occur because of hydrodynamic effects dominating the sta-
bilizing effect of the interparticle repulsion. This approach
was extended by Boersma and Laven [24] who proposed a
scaling in which the critical shear rate for shear thickening
would be proportional to the product T/ma2. The existence
of such a scaling has been confirmed in systematic exper-
iments in which, however, not always an orderdisorder
transition could be detected at the onset of shear thicken-
ing [25]. Rheo-optical studies on such sterically stabilized
suspensions indicate a flow-induced, hydrodynamic aggre-
gation to be responsible for shear thickening [26]. A similar
result has been obtained in some computer simulations
[22]. As mentioned earlier, hydrodynamic interactions are
difficult to incorporate in such simulations and turn out to
be extremely important [6]. It should be mentioned that in
suspensions of relatively hard spheres the critical shear rate
might scale with a3
rather than with a2
[25].Polydispersity in particle size dramatically postpones
shear thickening. It can still occur although it is unlikely
that it would be preceded by shear layering. In bimodal
dispersions of big and small particles a first approximation
of the critical shear rate can be obtained by plotting this
parameter versus the volume fraction of the big particles
alone [8]. This proofs at least the strong effect of particle
size on shear thickening.
Finally the effect of particle volume fraction should be
considered. At moderate effective volume fractions, often to
about 0.50, shear thickening sets in at a constant shear rate.
At very high volume fractions the critical shear rate tends
to drop drastically and it is rather the critical shear stress cwhich now becomes constant. In that region the product ca
2
provides a scaling factor which takes into account particle
size and volume fraction. The extent of the range in volume
fractions over which the critical shear stress remains constant
seems to be quite variable and to depend on the nature of
the suspending medium.
8. Conclusions
Starting from the reference case of suspensions with
Brownian hard spheres, the rheology of sterically stabilized
suspensions can be quite well understood. The scaling lawsfor Brownian spheres can be used to predict the effect of
temperature and medium viscosity in sterically stabilized
systems as well. The stabilizer layer increases the effective
volume of the particles which results in a viscosity rise.
This could lead to overestimated values for the viscosity,
especially at higher volume fractions, as the stabilizer layer
is partially deformable. This deformability is expressed by
the interparticle potential, which can be used to calculate a
more suitable measure of the effective volume for non-dilute
suspensions. The interparticle potential is normally not
-
8/2/2019 Rheology Suspensions
7/7
J. Mewis, J. Vermant / Progress in Organic Coatings 40 (2000) 111117 117
known, but can be derived from the storage moduli obtained
in oscillatory experiments. On the whole, the rheology of
well characterized suspensions can be explained in terms
of fundamental colloidal parameters such as interparticle
potential and particle diffusivity.
A distribution of particle sizes reduces the viscosities,
especially in more concentrated suspensions. For bimodal
distributions some suitable mixing laws seem to be available.
Scaling relations have also be proposed for the onset of shear
thickening. Medium viscosity, temperature and particle size
can be taken into account. These relations do not describe all
possible conditions but can nevertheless be used to estimate
the effect of changing the composition.
References
[1] W.R. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions,
Cambridge University Press, Cambridge, 1989.
[2] J.W. Bender, N.J. Wagner, J. Colloid Interf. Sci. 172 (1995) 171.
[3] I.M. Krieger, Trans. Soc. Rheol. 7 (1963) 101.[4] R.A. Lionberger, W.B. Russel, J. Rheol. 41 (1997) 399.
[5] M.E. Mackay, B. Kaffashi, J. Colloid Interf. Sci. 174 (1995) 117.
[6] R.C. Ball, J.R. Melrose, Adv. Colloid Interf. Sci. 59 (1995) 19.
[7] W.J. Frith, Ph.D. Thesis, Katholieke Universiteit Leuven, Leuven
Belgium, 1986.
[8] P. DHaene, Ph.D. Thesis, Katholieke Universiteit Leuven, Leuven,
Belgium, 1992.
[9] J. Mewis, Ann. Trans. Nordic Soc. Rheol. 1 (1993) 5.
[10] G. Biebaut, Ph.D. Thesis, Katholieke Universiteit Leuven, Leuven,
Belgium, 1999.
[11] S.E. Phan, et al., Phys. Rev. E 54 (1996) 6633.[12] J. Mewis, et al., AIChE J. 35 (1989) 415.
[13] R. Buscall, et al., J. Chem. Soc., Faraday Trans. 78 (1982) 2889.
[14] R. Buscall, J. Chem. Soc., Faraday Trans. 87 (1991) 1365.
[15] L. Raynaud, et al., J. Colloid Interf. Sci. 181 (1996) 11.
[16] L. Raynaud, Ph.D. Thesis, Katholieke Universiteit Leuven, Leuven,
Belgium, 1997.
[17] L.A. Utracki, in: A.A. Collier, D.W. Clegg (Eds.), Rheological
Measurements, Elsevier Applied Science, Barking, 1993, p. 479.
[18] B.E. Rodriguez, E.W. Kaler, Langmuir 8 (1992) 2382.
[19] R.F. Probstein, et al., J. Rheol. 38 (1994) 811.
[20] P. DHaene, J. Mewis, Rheol. Acta 33 (1994) 165.
[21] H.A. Barnes, J. Rheol. 33 (1989) 329.
[22] J.F. Brady, Curr. Opinion Colloid Interf. Sci. 1 (1996) 472.
[23] R.L. Hoffman, Etrans. Soc. Rheol. 16 (1972) 155.
[24] W.B. Boersma, J. Laven, AIChE J. 36 (1990) 321.[25] W.J. Frith, et al., J. Rheol. 40 (1996) 531.
[26] P. DHaene, et al., J. Colloid Interf. Sci. 156 (1993) 350.