Tagged particle in a sheared suspension: effective temperature determines density distribution in a slowly varying external potential beyond linear response

TL;DR

This paper demonstrates that in a sheared colloidal suspension, the tagged particle density distribution under a slowly varying external potential can be described using an effective temperature, extending the concept beyond linear response, supported by theoretical derivation and simulations.

Contribution

The study derives a steady state equation for the tagged particle density in sheared suspensions and shows the effective temperature governs its distribution beyond linear response.

Findings

Tagged particle distribution matches equilibrium form with effective temperature.

Effective temperature relates to Einstein relation violation.

Simulation results support theoretical predictions.

Abstract

We consider a sheared colloidal suspension under the influence of an external potential that varies slowly in space in the plane perpendicular to the flow and acts on one selected (tagged) particle of the suspension. Using a Chapman-Enskog type expansion we derive a steady state equation for the tagged particle density distribution. We show that for potentials varying along one direction only, the tagged particle distribution is the same as the equilibrium distribution with the temperature equal to the effective temperature obtained from the violation of the Einstein relation between the self-diffusion and tagged particle mobility coefficients. We thus prove the usefulness of this effective temperature for the description of the tagged particle behavior beyond the realm of linear response. We illustrate our theoretical predictions with Brownian dynamics computer simulations.