Kinetic theory of a confined quasi-one-dimensional gas of hard disks

TL;DR

This paper derives a Boltzmann-like kinetic equation for a dilute quasi-one-dimensional gas of hard disks confined between two lines, demonstrating its monotonic approach to equilibrium and validating predictions with molecular dynamics simulations.

Contribution

It introduces a new kinetic equation accounting for limited scattering angles in a confined quasi-one-dimensional system, with theoretical and simulation validation.

Findings

The kinetic equation satisfies an H theorem, ensuring approach to equilibrium.

Equilibrium properties are analytically derived for the confined gas.

Theoretical predictions match molecular dynamics simulation results.

Abstract

A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like kinetic equation, that takes into account the limitation in the possible scattering angles, is derived. It is shown that the equation verifies an $H$ theorem implying a monotonic approach to equilibrium. The implications of this result are discussed, and the equilibrium properties are derived. Closed equations describing how the kinetic energy is transferred between the degrees of freedom parallel and perpendicular to the boundaries are derived for states that are homogeneous along the direction of the boundaries. The theoretical predictions agree with results obtained by means of molecular dynamics simulations.