Nonlinear microrheology of dense colloidal suspensions: a mode-coupling theory

TL;DR

This paper develops a first-principles mode-coupling theory to describe the nonlinear microrheology of dense colloidal suspensions under strong external forces, extending understanding of probe dynamics in fluid and glass states.

Contribution

It introduces a novel mode-coupling framework for nonlinear probe motion in dense colloids, including force thresholds for delocalization and a schematic model for analytical insights.

Findings

Identified a force threshold for probe delocalization in glasses

Derived nonlinear velocity-force relations for dense colloids

Validated the theory with simulations and experiments on hard sphere systems

Abstract

A mode-coupling theory for the motion of a strongly forced probe particle in a dense colloidal suspension is presented. Starting point is the Smoluchowski equation for $N$ bath and a single probe particle. The probe performs Brownian motion under the influence of a strong constant and uniform external force $\Fex$. It is immersed in a dense homogeneous bath of (different) particles also performing Brownian motion. Fluid and glass states are considered; solvent flow effects are neglected. Based on a formally exact generalized Green-Kubo relation, mode coupling approximations are performed and an integration through transients approach applied. A first-principles theory for the nonlinear velocity-force relations of the probe particle in a dense fluid and for the (de-) localized probe in a glass is obtained. It extends the mode coupling theory of the glass transition to strongly forced tracer motion and describes active microrheology experiments. A force threshold is identified which needs to be overcome to pull the probe particle free in a glass. For the model of hard sphere particles, the microscopic equations for the threshold force and the probability density of the localized probe are solved numerically. Neglecting the spatial structure of the theory, a schematic model is derived which contains two types of bifurcation, the glass transition and the force-induced delocalization, and which allows for analytical and numerical solutions. We discuss its phase diagram, forcing effects on the time-dependent correlation functions, and the friction increment. The model was successfully applied to simulations and experiments on colloidal hard sphere systems [I. Gazuz et. al., Phys. Rev. Lett. 102, 248302 (2009)], while we provide detailed information on its derivation and general properties.