Dynamics of inelastically colliding rough spheres: Relaxation of translational and rotational energy

TL;DR

This paper investigates how translational and rotational energies in inelastically colliding rough spheres evolve over time, revealing a universal algebraic decay and persistent temperature differences after initial energy redistribution.

Contribution

It introduces a generalized homogeneous cooling state with separate translational and rotational temperatures and characterizes their algebraic decay dynamics.

Findings

Equipartition is immediately broken by collisions.

Both energies decay as t^{-2} after a crossover time.

The ratio of translational to rotational energy remains constant during decay.

Abstract

We study the exchange of kinetic energy between translational and rotational degrees of freedom for inelastic collisions of rough spheres. Even if equipartition holds in the initial state it is immediately destroyed by collisions. The simplest generalisation of the homogeneous cooling state allows for two temperatures, characterizing translational and rotational degrees of freedom separately. For times larger than a crossover frequency, which is determined by the Enskog frequency and the initial temperature, both energies decay algebraically like $t^{-2}$ with a fixed ratio of amplitudes, different from one.