Energy production rates in fluid mixtures of inelastic rough hard spheres

TL;DR

This paper develops a theoretical framework to analyze how polydispersity and roughness affect energy dissipation and temperature ratios in granular fluid mixtures of inelastic rough spheres.

Contribution

It introduces a method to compute energy production rates and temperature ratios considering polydispersity and roughness in granular mixtures.

Findings

Energy production rates depend on partial temperatures and mixture parameters.

Roughness and inelasticity significantly influence temperature ratios.

Theoretical predictions align with expected behaviors in granular cooling states.

Abstract

The aim of this work is to explore the combined effect of polydispersity and roughness on the partial energy production rates and on the total cooling rate of a granular fluid mixture. We consider a mixture of inelastic rough hard spheres of different number densities, masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution. Starting from the first equation of the BBGKY hierarchy, the collisional energy production rates associated with the translational and rotational temperatures ($T_i^\text{tr}$ and $T_i^\text{rot}$) are expressed in terms of two-body average values. Next, those average values are estimated by assuming a velocity distribution function based on maximum-entropy arguments, allowing us to express the energy production rates and the total cooling rate in terms of the partial temperatures and the parameters of the mixture. Finally, the results are applied to the homogeneous cooling state of a binary mixture and the influence of inelasticity and roughness on the temperature ratios $T_1^\text{tr}/T_1^\text{rot}$, $T_2^\text{tr}/T_1^\text{tr}$, and $T_2^\text{rot}/T_1^\text{rot}$ is analyzed.