Enskog kinetic theory for $d$-dimensional dense granular gases

TL;DR

This paper derives explicit expressions for transport coefficients and cooling rate in dense granular gases using an advanced Chapman-Enskog method with a new Sonine approach, applicable in any number of dimensions.

Contribution

It introduces a novel Sonine approximation replacing local equilibrium with the homogeneous cooling state in the Chapman-Enskog solution for the Enskog equation.

Findings

Explicit transport coefficients in terms of restitution and volume fraction

Cooling rate expressions derived for arbitrary dimensions

Method applicable to dense granular gases in various dimensions

Abstract

The goal of this note is to provide most of the technical details involved in the application of the Chapman-Enskog method to solve the revised Enskog equation to Navier-Stokes order. Explicit expressions for the transport coefficients and the cooling rate are obtained in terms of the coefficient of restitution and the solid volume fraction by using a new Sonine approach. This new approach consists of replacing, where appropriate in the Chapman-Enskog procedure, the local equilibrium distribution (used in the standard first Sonine approximation) by the homogeneous cooling state distribution. The calculations are performed in an arbitrary number of dimensions.