From Equilibrium to Steady-State Dynamics after Switch-On of Shear

TL;DR

This paper explores the relationship between equilibrium and steady-state dynamics in dense glass-forming liquids under shear, deriving an approximate relation using ITT and validating it with simulations, revealing insights into shear thinning and relaxation behaviors.

Contribution

The paper introduces an approximate relation connecting equilibrium and steady-state correlation functions under shear, validated by simulations, within the mode-coupling theory framework.

Findings

Good qualitative and semi-quantitative agreement between theory and simulations.

Excellent quantitative agreement for short waiting times.

Predicted faster decay of correlations at intermediate waiting times.

Abstract

A relation between equilibrium, steady-state, and waiting-time dependent dynamical two-time correlation functions in dense glass-forming liquids subject to homogeneous steady shear flow is discussed. The systems under study show pronounced shear thinning, i.e., a significant speedup in their steady-state slow relaxation as compared to equilibrium. An approximate relation that recovers the exact limit for small waiting times is derived following the integration through transients (ITT) approach for the nonequilibrium Smoluchowski dynamics, and is exemplified within a schematic model in the framework of the mode-coupling theory of the glass transition (MCT). Computer simulation results for the tagged-particle density correlation functions corresponding to wave vectors in the shear-gradient directions from both event-driven stochastic dynamics of a two-dimensional hard-disk system and from previously published Newtonian-dynamics simulations of a three-dimensional soft-sphere mixture are analyzed and compared with the predictions of the ITT-based approximation. Good qualitative and semi-quantitative agreement is found. Furthermore, for short waiting times, the theoretical description of the waiting time dependence shows excellent quantitative agreement to the simulations. This confirms the accuracy of the central approximation used earlier to derive fluctuation dissipation ratios (Phys. Rev. Lett. 102, 135701). For intermediate waiting times, the correlation functions decay faster at long times than the stationary ones. This behavior is predicted by our theory and observed in simulations.