Self-diffusion in confined systems

TL;DR

This paper investigates the self-diffusion of hard sphere fluids confined between parallel plates, deriving a theoretical expression for the diffusion coefficient that matches Molecular Dynamics simulations across various confinement heights.

Contribution

It introduces a kinetic equation accounting for confinement effects and derives an explicit formula for the self-diffusion coefficient in confined systems.

Findings

Theoretical predictions agree well with Molecular Dynamics simulations.

The derived diffusion coefficient depends explicitly on the confinement height.

The approach is valid in the low-density limit.

Abstract

The self-diffusion process of a hard sphere fluid confined by two parallel plates separated by a distance on the order of the particle diameter is studied. The starting point is a closed kinetic equation for the distribution function that takes into account the effects of the confinement and that is valid in the low-density limit. From it, the Boltzmann-Lorentz equation that describes the dynamics of some tagged particles when the whole system is in equilibrium is derived. An equation that describes the diffusion in the directions parallel to the walls is deduced by applying the Zwanzig-Mori projection technique to the Boltzmann-Lorentz equation, obtaining an explicit expression for the self-diffusion coefficient that depends on the height of the system. A very good agreement between its theoretical prediction and Molecular Dynamics simulation results is obtained for the whole range of heights.