Velocity Distribution in a Viscous Granular Gas

TL;DR

This paper studies how velocities in a viscous one-dimensional granular gas relax over time, revealing non-Maxwellian distributions with distinct relaxation behaviors through analytical and numerical methods.

Contribution

It introduces a detailed analysis of velocity relaxation in viscous granular gases, highlighting the non-Maxwellian nature of the distribution and comparing different approximation methods.

Findings

Velocity distribution develops two peaks that relax as 1/t.

Numerical simulations confirm the two-peaked relaxation behavior.

Maxwell approximation predicts a single-peaked, exponentially narrowing distribution.

Abstract

We investigate the velocity relaxation of a viscous one-dimensional granular gas, that is, one in which neither energy nor momentum is conserved in a collision. Of interest is the distribution of velocities in the gas as it cools, and the time dependence of the relaxation behavior. A Boltzmann equation of instantaneous binary collisions leads to a two-peaked distribution with each peak relaxing to zero velocity as 1/t while each peak also narrows as 1/t. Numerical simulations of grains on a line also lead to a double-peaked distribution that narrows as 1/t. A Maxwell approximation leads to a single-peaked distribution about zero velocity with power-law wings. This distribution narrows exponentially. In either case, the relaxing distribution is not of Maxwell-Boltzmann form.