Nonlinear Hydrodynamics of a Hard Sphere Fluid Near the Glass Transition

TL;DR

This paper numerically investigates the nonlinear hydrodynamics of dense hard sphere fluids near the glass transition, revealing glassy behavior, relaxation dynamics, and their dependence on density and wavenumber.

Contribution

It introduces a numerical approach using Langevin equations and a free energy functional to study glassy dynamics in hard sphere fluids, connecting theory with experiments.

Findings

Glassy behavior with stretched exponential decay

Two-stage relaxation of density correlation functions

Relaxation times follow Vogel-Fulcher law

Abstract

We conduct a numerical study of the dynamic behavior of a dense hard sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free energy functional of the Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as evidenced through stretched exponential decay and two-stage relaxation of the density correlation function. The characteristic times grow with increasing density according to the Vogel-Fulcher law. The wavenumber dependence of the kinetics is extensively explored. The connection of our results with experiment, mode coupling theory, and molecular dynamics results is discussed.