Can we understand and
model non-colloidal suspensions?
Roger Tanner
University
of Sydney, Australia
Abstract
This talk is about the rheological
behaviour of non-colloidal suspensions and my favourite rheological pastime,
model building. There are applications (for example injection moulding
modelling) where a better suspension model than a simple generalized Newtonian
fluid would be useful, and here we report progress in this direction.
In order to construct models one
needs a set of experimental data. For the simplest kind of suspensions, rigid
spheres of equal size in a Newtonian matrix, we now have data on:
(i)
Steady shear viscosity.
(ii)
Normal stress differences-
N1 and N2.
(iii)
Uniaxial elongational flow. (Planar extensions are too difficult).
(iv)
Unsteady shear flows : we will consider the reversing kind [2] and
sinusoidal strains.
One could use the Criminale-Ericksen-Filbey (CEF) model to describe steady
shear flows (i,ii) but such
a model fails for rapidly reversing shear flows. Because the suspensions are
completely inelastic one needs a model without a time constant. Such an
inelastic model, due to Thompson and Souza Mendes (TSM model) can describe
steady viscometric flows and with a modification it
can also describe sudden reversals of shearing, where strain from the reversal
point is important.
A more crucial test is for uniaxial
extensional flow- here the TSM model behaves reasonably well. (Planar
extensions can be computed, but there are no experiments to compare with; the
model gives a Trouton ratio of 4, in agreement with computations).
Finally following some new
experiments with reversing flows, I suggest a reason why it is so difficult to
find a linear response (G¢ and G¢¢) for such suspensions.
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