Hydrodynamics and transport coefficients for Granular Gases

TL;DR

This paper develops a hydrodynamic theory for granular gases of viscoelastic particles with impact-velocity dependent restitution, deriving transport coefficients that differ qualitatively from previous models with constant restitution.

Contribution

It introduces a modified Chapman-Enskog approach to derive hydrodynamic equations and transport coefficients for viscoelastic granular gases with impact-velocity dependent restitution.

Findings

Transport coefficients depend qualitatively on temperature unlike constant restitution models.

The adiabatic approximation for the velocity distribution is valid up to intermediate dissipation.

The derived coefficients relate to material and gas parameters.

Abstract

The hydrodynamics of granular gases of viscoelastic particles, whose collision is described by an impact-velocity dependent coefficient of restitution, is developed using a modified Chapman-Enskog approach. We derive the hydrodynamic equations and the according transport coefficients with the assumption that the shape of the velocity distribution function follows adiabatically the decaying temperature. We show numerically that this approximation is justified up to intermediate dissipation. The transport coefficients and the coefficient of cooling are expressed in terms of the elastic and dissipative parameters of the particle material and by the gas parameters. The dependence of these coefficients on temperature differs qualitatively from that obtained with the simplifying assumption of a constant coefficient of restitution which was used in previous studies. The approach formulated for gases of viscoelastic particles may be applied also for other impact-velocity dependencies of the restitution coefficient.