Time-dependent active microrheology in dilute colloidal suspensions

TL;DR

This paper analytically investigates the time-dependent response of a probe particle in dilute colloidal suspensions under strong external forces, revealing exponential relaxation, nonanalytic force dependence, and transient superdiffusion.

Contribution

It provides an exact first-order analytical solution for the time-dependent microrheological response in dilute suspensions, highlighting nonanalytic behavior and transient superdiffusion.

Findings

Exponential approach to stationary velocity for small forces.

Nonanalytic dependence of steady-state behavior on driving force.

Transient superdiffusive fluctuations in the force direction.

Abstract

In a microrheological set-up a single probe particle immersed in a complex fluid is exposed to a strong external force driving the system out of equilibrium. Here, we elaborate analytically the time-dependent response of a probe particle in a dilute suspension of Brownian particles to a large step-force, exact in first order of the density of the bath particles. The time-dependent drift velocity approaches its stationary state value exponentially fast for arbitrarily small driving in striking contrast to the power-law prediction of linear response encoded in the long-time tails of the velocity autocorrelation function. We show that the stationary-state behavior depends nonanalytically on the driving force and connect this behavior to the persistent correlations in the equilibrium state. We argue that this relation holds generically. Furthermore, we elaborate that the fluctuations in the direction of the force display transient superdiffusive behavior.