Integration through transients for Brownian particles under steady shear

TL;DR

This paper derives exact microscopic expressions for steady-state properties of interacting Brownian particles under shear, using generalized Green-Kubo relations involving transient dynamics, providing a foundation for approximations of non-equilibrium states.

Contribution

It introduces a microscopic framework with exact expressions and equations of motion for steady shear, enabling better modeling of dense colloidal dispersions under flow.

Findings

Exact Green-Kubo relations for shear-dependent averages

Derived equations of motion with memory effects

Framework for approximating non-equilibrium steady states

Abstract

Starting from the microscopic Smoluchowski equation for interacting Brownian particles under stationary shearing, exact expressions for shear-dependent steady-state averages, correlation and structure functions, and susceptibilities are obtained, which take the form of generalized Green-Kubo relations. They require integration of transient dynamics. Equations of motion with memory effects for transient density fluctuation functions are derived from the same microscopic starting point. We argue that the derived formal expressions provide useful starting points for approximations in order to describe the stationary non-equilibrium state of steadily sheared dense colloidal dispersions.