The contribution of Brownian motion to the stress in a colloidal suspension

TL;DR

This paper critiques the traditional method of calculating stress in colloidal suspensions, highlighting inconsistencies, and proposes a new expression that better accounts for particle motion.

Contribution

It introduces a revised expression for colloidal suspension stress that addresses the limitations of the classical thermodynamic force approach.

Findings

The classical stress expression is inconsistent with colloid motion.

A new stress expression aligns better with particle dynamics.

The proposed model improves understanding of suspension mechanics.

Abstract

The deviatoric stresses of colloidal suspensions are routinely calculated using the expression introduced by Batchelor [J. Fluid Mech. 83, 97--117 (1977)]. We show by example that the central feature in its derivation, the thermodynamic force driving particles down the density gradient, is inconsistent with the motion of the colloids. A new expression for the stress is proposed.