Self-diffusion in a quasi-two dimensional gas of hard spheres

TL;DR

This paper derives a theoretical self-diffusion coefficient for a quasi-two-dimensional hard sphere gas confined between plates, validated by molecular dynamics simulations, advancing understanding of confined particle transport.

Contribution

It introduces a modified Chapman-Enskog approach to derive the self-diffusion coefficient in an inhomogeneous, confined system, bridging kinetic theory and simulations.

Findings

Good agreement between theory and molecular dynamics results.

Self-diffusion coefficient depends on plate separation.

Inhomogeneous equilibrium state considered in the model.

Abstract

A quasi-two-dimensional system of hard spheres strongly confined between two parallel plates is considered. The attention is focussed on the macroscopic self-diffusion process observed when the system is looked from above or from below. The transport equation, and the associated self-diffusion coefficient, are derived from a Boltzmann-Lorentz kinetic equation, valid in the dilute limit. Since the equilibrium state of the system is inhomogeneous, this requires the use of a modified Chapman-Enskog expansion that distinguishes between equilibrium and non-equilibrium gradients of the density of labelled particles. The self-diffusion coefficient is obtained as a function of the separation between the two confining plates. The theoretical predictions are compared with molecular dynamics simulation results and a good agreement is found.