Excluded-volume effects in the diffusion of hard spheres

TL;DR

This paper derives a nonlinear diffusion equation accounting for excluded-volume effects in the diffusion of finite-sized hard spheres, showing these effects enhance collective diffusion, validated by stochastic simulations.

Contribution

It introduces a systematic derivation of a nonlinear diffusion equation incorporating excluded-volume effects for hard spheres using matched asymptotic expansions.

Findings

Excluded-volume effects increase the collective diffusion rate.

Derived an explicit expression for the effective diffusion coefficient.

Stochastic simulations agree well with the theoretical model.

Abstract

Excluded-volume effects can play an important role in determining transport properties in diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two or three dimensions is considered systematically using the method of matched asymptotic expansions. The result is a nonlinear diffusion equation for the one-particle distribution function, with excluded-volume effects enhancing the overall collective diffusion rate. An expression for the effective (collective) diffusion coefficient is obtained. Stochastic simulations of the full particle system are shown to compare well with the solution of this equation for two examples.