A First-Principles Constitutive Equation for Suspension Rheology

TL;DR

This paper develops a comprehensive constitutive equation for the nonlinear rheology of dense colloidal suspensions under arbitrary flow, linking microstructure deformation to stress response using mode-coupling theory.

Contribution

It generalizes previous shear-specific models to arbitrary flows, revealing the tensorial structure and microstructure-stress relationship in colloidal suspensions.

Findings

Flow curves for steady elongation are presented and compared to shear.

Non-linear Trouton ratios indicate a tensorially nontrivial yield condition.

The theory connects microstructure deformation directly to stress response.

Abstract

Using mode-coupling theory, we derive a constitutive equation for the nonlinear rheology of dense colloidal suspensions under arbitrary time-dependent homogeneous flow. Generalizing previous results for simple shear, this allows the full tensorial structure of the theory to be identified. Macroscopic deformation measures, such as the Cauchy-Green tensors, thereby emerge. So does a direct relation between the stress and the distorted microstructure, illuminating the interplay of slow structural relaxation and arbitrary imposed flow. We present flow curves for steady planar and uniaxial elongation and compare these to simple shear. The resulting non-linear Trouton ratios point to a tensorially nontrivial dynamic yield condition for colloidal glasses.