Homogeneous cooling of rough, dissipative particles: Theory and simulations

TL;DR

This paper studies the cooling behavior of rough, dissipative particles through simulations and kinetic theory, revealing energy decay patterns and the influence of particle properties on system dynamics.

Contribution

It introduces an approximate kinetic theory for rough particles and validates it with simulations, highlighting the decay laws and parameter effects in cooling systems.

Findings

Translational and rotational energies decay as t^{-2} at large times.

Good agreement between theory and simulations when no clustering occurs.

Energy decay depends primarily on restitution and surface roughness.

Abstract

We investigate freely cooling systems of rough spheres in two and three dimensions. Simulations using an event driven algorithm are compared with results of an approximate kinetic theory, based on the assumption of a generalized homogeneous cooling state. For short times $t$, translational and rotational energy are found to change linearly with $t$. For large times both energies decay like $t^{-2}$ with a ratio independent of time, but not corresponding to equipartition. Good agreement is found between theory and simulations, as long as no clustering instability is observed. System parameters, i.e. density, particle size, and particle mass can be absorbed in a rescaled time, so that the decay of translational and rotational energy is solely determined by normal restitution and surface roughness.