Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation

TL;DR

This paper derives explicit Navier-Stokes transport coefficients for polydisperse granular mixtures using Sonine polynomial approximation, applicable to arbitrary inelasticity levels and mixture parameters.

Contribution

It provides a comprehensive analytical solution for transport coefficients in polydisperse granular mixtures using a Sonine polynomial expansion, extending previous theories.

Findings

Explicit expressions for all NS transport coefficients.

Transport coefficients valid for arbitrary inelasticity.

Comparison with previous theories highlights methodological differences.

Abstract

The linear integral equations defining the Navier-Stokes (NS) transport coefficients for polydisperse granular mixtures of smooth inelastic hard disks or spheres are solved by using the leading terms in a Sonine polynomial expansion. Explicit expressions for all the NS transport coefficients are given in terms of the sizes, masses, compositions, density and restitution coefficients. In addition, the cooling rate is also evaluated to first order in the gradients. The results hold for arbitrary degree of inelasticity and are not limited to specific values of the parameters of the mixture. Finally, a detailed comparison between the derivation of the current theory and previous theories for mixtures is made, with attention paid to the implication of the various treatments employed to date.