Dense colloidal suspensions under time-dependent shear

TL;DR

This paper develops a theoretical framework to analyze the nonlinear rheology of dense colloidal suspensions under time-dependent shear, deriving exact relations and a mode coupling approximation for stress response.

Contribution

It introduces a formalism based on the Smoluchowski equation to compute time-dependent averages and derives a generalized Green-Kubo relation for shear stress.

Findings

Derived a generalized Green-Kubo relation for shear stress.

Developed a mode coupling approximation for the constitutive equation.

Numerically solved for the stress response of a hard sphere glass under step-strain.

Abstract

We consider the nonlinear rheology of dense colloidal suspensions under a time-dependent simple shear flow. Starting from the Smoluchowski equation for interacting Brownian particles advected by shearing (ignoring fluctuations in fluid velocity) we develop a formalism which enables the calculation of time-dependent, far-from-equilibrium averages. Taking shear-stress as an example we derive exactly a generalized Green-Kubo relation, and an equation of motion for the transient density correlator, involving a three-time memory function. Mode coupling approximations give a closed constitutive equation yielding the time-dependent stress for arbitrary shear rate history. We solve this equation numerically for the special case of a hard sphere glass subject to step-strain.