First-Principles Constitutive Equation for Suspension Rheology

TL;DR

This paper derives a first-principles tensorial constitutive equation for dense colloidal suspensions under arbitrary homogeneous, incompressible, time-dependent flows, capturing slow structural relaxation and glass transition effects.

Contribution

It introduces a detailed derivation of a first-principles approach using mode-coupling theory for suspension rheology under complex flow conditions.

Findings

Captures slow relaxation and glass transition in dense suspensions.

Provides a tensorial framework for arbitrary homogeneous flows.

Applicable to systems with time-dependent shear and extension.

Abstract

We provide a detailed derivation of a recently developed first-principles approach to calculating averages in systems of interacting, spherical Brownian particles under time-dependent flow. Although we restrict ourselves to flows which are both homogeneous and incompressible, the time-dependence and geometry (e.g. shear, extension) are arbitrary. The approximations formulated within mode-coupling theory are particularly suited to dense colloidal suspensions and capture the slow relaxation arising from particle interactions and the resulting glass transition to an amorphous solid. The delicate interplay between slow structural relaxation and time-dependent external flow in colloidal suspensions may thus be studied within a fully tensorial theory.