Interplay between polydispersity, inelasticity, and roughness in the freely cooling regime of hard-disk granular gases

TL;DR

This paper develops a kinetic theory for polydisperse granular gases of inelastic, rough disks, analyzing energy distribution and uncovering a mimicry effect where polydisperse systems resemble monodisperse ones in energy nonequipartition.

Contribution

It provides a detailed kinetic-theory derivation of energy rates and reveals a novel mimicry effect in polydisperse granular gases of disks.

Findings

Disks show stronger rotational-translational nonequipartition than spheres.

A mimicry effect allows polydisperse disks to mimic monodisperse energy distribution.

Energy nonequipartition patterns depend on particle size and mass relationships.

Abstract

A polydisperse granular gas made of inelastic and rough hard disks is considered. Focus is laid on the kinetic-theory derivation of the partial energy production rates and the total cooling rate as functions of the partial densities and temperatures (both translational and rotational) and of the parameters of the mixture (masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution). The results are applied to the homogeneous cooling state of the system and the associated nonequipartition of energy among the different components and degrees of freedom. It is found that disks typically present a stronger rotational-translational nonequipartition but a weaker component-component nonequipartition than spheres. A noteworthy "mimicry" effect is unveiled, according to which a polydisperse gas of disks having common values of the coefficient of restitution and of the reduced moment of inertia can be made indistinguishable from a monodisperse gas in what concerns the degree of rotational-translational energy nonequipartition. This effect requires the mass of a disk of component $i$ to be approximately proportional to $2\sigma_i+\langle\sigma\rangle$, where $\sigma_i$ is the diameter of the disk and $\langle\sigma\rangle$ is the mean diameter.