Mobility and Diffusion of a Tagged Particle in a Driven Colloidal Suspension

TL;DR

This study investigates how density and strain rate affect the diffusion and mobility of a tagged particle in a sheared colloidal suspension, revealing a weak strain rate dependency and an effective temperature concept that restores the Einstein relation.

Contribution

It introduces a novel method to measure response functions and demonstrates the applicability of an effective temperature in nonequilibrium colloidal systems.

Findings

Diffusion coefficient depends on strain rate.

Mobility exhibits weak strain rate dependence.

Effective temperature concept aligns response and correlation functions.

Abstract

We study numerically the influence of density and strain rate on the diffusion and mobility of a single tagged particle in a sheared colloidal suspension. We determine independently the time-dependent velocity autocorrelation functions and, through a novel method, the response functions with respect to a small force. While both the diffusion coefficient and the mobility depend on the strain rate the latter exhibits a rather weak dependency. Somewhat surprisingly, we find that the initial decay of response and correlation functions coincide, allowing for an interpretation in terms of an 'effective temperature'. Such a phenomenological effective temperature recovers the Einstein relation in nonequilibrium. We show that our data is well described by two expansions to lowest order in the strain rate.