Tagged-particle motion in glassy systems under shear: Comparison of mode coupling theory and Brownian Dynamics simulations

TL;DR

This study compares mode coupling theory and Brownian Dynamics simulations to understand the motion of a tagged particle in glassy systems under shear, revealing new dispersion phenomena and stress-related dynamics.

Contribution

It extends mode coupling theory to include tagged particle correlators under shear and compares predictions with detailed simulations.

Findings

Transient correlation functions show stress overshoot effects.

Discovery of a new type of Taylor dispersion in glassy states.

Qualitative agreement between theory and simulations with some quantitative deviations.

Abstract

We study the dynamics of a tagged particle in a glassy system under shear. The recently developed integration through transients approach based on mode coupling theory, is continued to arrive at the equations for the tagged particle correlators and the mean squared displacements. The equations are solved numerically for a two dimensional system, including a nonlinear stability analysis of the glass solution, the so called beta-analysis. We perform Brownian Dynamics simulations in 2-D and compare with theory. After switch on, transient glassy correlation functions show strong fingerprints of the stress overshoot scenario, including, additionally to previously studied superexponential decay, a shoulder-like slowing down after the overshoot. We also find a new type of Taylor dispersion in glassy states which has intriguing similarity to the known low density case. The theory qualitatively captures most features of the simulations with quantitative deviations concerning the shear induced timescales. We attribute these deviations to an underestimation of the overshoot scenario in the theory.