Partitioning of energy in highly polydisperse granular gases

TL;DR

This paper models a highly polydisperse granular gas with a continuous size distribution, analyzing its temperature profile, velocity distributions, and decay behavior under various driving mechanisms, supported by simulations.

Contribution

It generalizes previous binary and multicomponent models to continuous size distributions, providing approximate analytical solutions for temperature profiles and velocity distributions.

Findings

Stationary temperature profiles depend on driving mechanisms and size distribution variance.

Polydispersity causes non-Gaussian velocity distributions with size-dependent tail behavior.

Decay rates in free cooling vary continuously with particle size, following Haff's law.

Abstract

A highly polydisperse granular gas is modeled by a continuous distribution of particle sizes, a, giving rise to a corresponding continuous temperature profile, T(a), which we compute approximately, generalizing previous results for binary or multicomponent mixtures. If the system is driven, it evolves towards a stationary temperature profile, which is discussed for several driving mechanisms in dependence on the variance of the size distribution. For a uniform distribution of sizes, the stationary temperature profile is nonuniform with either hot small particles (constant force driving) or hot large particles (constant velocity or constant energy driving). Polydispersity always gives rise to non-Gaussian velocity distributions. Depending on the driving mechanism the tails can be either overpopulated or underpopulated as compared to the molecular gas. The deviations are mainly due to small particles. In the case of free cooling the decay rate depends continuously on particle size, while all partial temperatures decay according to Haff's law. The analytical results are supported by event driven simulations for a large, but discrete number of species.