Thermal properties of an impurity immersed in a granular gas of rough hard spheres

TL;DR

This paper investigates the thermal behavior of an impurity in a granular gas of rough spheres, developing an approximate kinetic theory solution and validating it against molecular dynamics and Monte Carlo simulations.

Contribution

It introduces an approximate analytical solution for the kinetic equations of a granular impurity in a rough gas, accounting for energy non-equipartition and validating it with simulations.

Findings

The analytical solution captures translational/rotational energy non-equipartition.

Simulation results from MD and DSMC agree reasonably with the theory.

The model effectively describes impurity dynamics in granular gases.

Abstract

We study in this work the dynamics of a granular impurity immersed in a low-density granular gas of identical particles. For description of the kinetics of the granular gas and the impurity particles we use the rough hard sphere collisional model. We take into account the effects of non-conservation of energy upon particle collision. We find an (approximate) analytical solution of the pertinent kinetic equations for the single-particle velocity distribution functions that reproduces reasonably well the properties of translational/rotational energy non-equipartition. We assess the accuracy of the theoretical solution by comparing with computer simulations. For this, we use two independent computer data sets, from molecular dynamics (MD) and from Direct Simulation Monte Carlo method (DSMC). Both approach well, with different degrees, the kinetic theory within a reasonable range of parameter values.