Energy nonequipartition in gas mixtures of inelastic rough hard spheres: The tracer limit

TL;DR

This study investigates energy nonequipartition in inelastic rough hard sphere gas mixtures, combining theoretical analytical solutions with numerical simulations to understand temperature ratios of tracer particles in the homogeneous cooling state.

Contribution

It provides explicit analytical expressions for temperature ratios and validates them through DSMC and molecular dynamics simulations, highlighting the reliability of the Maxwellian approximation.

Findings

Good agreement between theory and simulations.

Molecular chaos assumption has limited impact on temperature ratios.

Maxwellian approximation reliably predicts temperature ratios.

Abstract

The dynamical properties of a tracer or impurity particle immersed in a host gas of inelastic and rough hard spheres in the homogeneous cooling state is studied. Specifically, the breakdown of energy equipartition as characterized by the tracer/host ratios of translational and rotational temperatures is analyzed by exploring a wide spectrum of values of the control parameters of the system (masses, moments of inertia, sizes, and coefficients of restitution). Three complementary approaches are considered. On the theoretical side, the Boltzmann and Boltzmann--Lorentz equations (both assuming the molecular chaos ansatz) are solved by means of a multitemperature Maxwellian approximation for the velocity distribution functions. This allows us to obtain explicit analytical expressions for the temperature ratios. On the computational side, two different techniques are used. First, the kinetic equations are numerically solved by the direct simulation Monte Carlo (DSMC) method. Second, molecular dynamics simulations for dilute gases are performed. Comparison between theory and simulations shows a general good agreement. This means that (i) the impact of the molecular chaos ansatz on the temperature ratios is not significant (except at high inelasticities and/or big impurities) and (ii) the simple Maxwellian approximation yields quite reliable predictions.