Diffusion in Granular Gases of Viscoelastic Particles

TL;DR

This paper investigates how the impact velocity dependence of the restitution coefficient affects diffusion in granular gases, revealing that realistic particles exhibit power-law spreading rather than logarithmic.

Contribution

It introduces a model accounting for impact velocity dependence of the restitution coefficient, demonstrating its significant effect on particle diffusion in granular gases.

Findings

Impact velocity dependence alters diffusion behavior drastically.

Realistic particles spread with a power-law, not logarithmically.

Constant restitution coefficient models underestimate particle spread.

Abstract

In most of the literature on granular gases it is assumed that the restitution coefficient \epsilon, which quantifies the loss of kinetic energy upon a collision is independent on the impact velocity. Experiments as well as theoretical investigations show, however, that for real materials the restitution coefficient depends significantly on the impact velocity. We consider the diffusion process in a homogeneous granular gas, i.e. in a system of dissipatively colliding particles. We show that the mean square displacement of the particles changes drastically if we take the impact velocity dependence of \epsilon into account. Under the oversimplifying assumption of a constant coefficient one finds that the particles spread in space logarithmically slow with time, whereas realistic particles spread due to a power law.