The structural model discussed in Part I of the present
work is applied to "true" behavior – i.e. shear thinning
followed by shear thickening (sometimes followed by shear thinning) –
very often observed in complex fluids as
the applied shear is increased. This model states
that the viscosity η of these fluids – described as concentrated
dispersions of several classes of Structural Units (SUs) – is a unique
function of a flow-dependent effective
volume fraction, φeff. The latter is expressed in terms of
Si = fraction of "aggregated" particles contained in all
the SUis (as SUs of i-class) and Ci = (ϕi−1−1)=
"compactness factor", directly related to the mean
compactness ϕi of SUis.
Shear induced flocculation (SIF) is the more obvious
process capable to explain the shear thickening
behavior of partially flocculated suspensions (obviously,
another process should be required for stabilized
dispersions). After progressive reduction of SUs submitted
to shear forces (i.e. leading to a decrease of Si), such
a behavior should be observed if SIF
occurs beyond a critical shear rate ${\dot {\gamma}_{\rm C}}$,
then resulting in re-increase of Si,
thus of φeff and η. The simplest "SIF-model" will
introduce only one class of SUs, with only one variable S
governed by a kinetic equation in which the kinetic rate
for SU-formation increases with shear, thus giving the
expected shear-thickening behavior if ${\dot {\gamma}}>{\dot {\gamma}_{\rm C}}$.
However, at high shear rates, SIF is limited by a (Smoluchowski-like)
shear decreasing sticking probability. Effects of varying
model parameters on predictions of the resulting
SIF-model are discussed. Finally, this model is tested by
comparison with observed rheological behavior, namely
viscosity change vs. pH in aqueous styrene-ethylacrylate
dispersions, from Laun's data [2].