Can we understand and model non-colloidal suspensions?

Abstract

This talk is about the rheological behaviour of non-colloidal suspensions. 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 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 for the model is 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 the new experiments with reversing flows, I suggest it is so difficult to find a linear response (G' and G") region for such suspensions because with a sinusoidal strain input there are always strain reversals leading to nonlinearity, at least down to strains of order of the roughness ratio of the spheres, which is here about 10−4.