Homogeneous Free Cooling State in Binary Granular Fluids of Inelastic Rough Hard Spheres

TL;DR

This paper analyzes the energy dissipation and temperature evolution in a binary granular fluid of inelastic rough spheres, revealing how even minimal roughness significantly affects long-term temperature ratios.

Contribution

It explicitly decomposes collisional energy production rates into equipartition and cooling components and examines the impact of roughness on the free cooling state, especially near the smooth limit.

Findings

Roughness influences long-time temperature ratios even when very small.

The effect of roughness appears rapidly, within transient timescales.

Singular behavior occurs in the asymptotic state as roughness approaches zero.

Abstract

In a recent paper [A. Santos, G. M. Kremer, and V. Garz\'o, \emph{Prog. Theor. Phys. Suppl.} \textbf{184}, 31-48 (2010)] the collisional energy production rates associated with the translational and rotational granular temperatures in a granular fluid mixture of inelastic rough hard spheres have been derived. In the present paper the energy production rates are explicitly decomposed into equipartition rates (tending to make all the temperatures equal) plus genuine cooling rates (reflecting the collisional dissipation of energy). Next the homogeneous free cooling state of a binary mixture is analyzed, with special emphasis on the quasi-smooth limit. A previously reported singular behavior (according to which a vanishingly small amount of roughness has a finite effect, with respect to the perfectly smooth case, on the asymptotic long-time translational/translational temperature ratio) is further elaborated. Moreover, the study of the time evolution of the temperature ratios shows that this dramatic influence of roughness already appears in the transient regime for times comparable to the relaxation time of perfectly smooth spheres.