Mass and heat fluxes for a binary granular mixture at low-density

TL;DR

This paper derives and analyzes the transport coefficients for a low-density binary granular mixture using hydrodynamic equations, exploring their dependence on physical parameters and implications for Onsager relations and stability.

Contribution

It provides explicit expressions for mass and heat flux transport coefficients in a binary granular mixture, including their variation with system parameters and the violation of Onsager relations.

Findings

Transport coefficients depend on mass ratio, size ratio, and restitution.

Quantitative variation of coefficients demonstrated via Sonine polynomial approximations.

Violation of Onsager reciprocal relations quantified.

Abstract

The Navier--Stokes order hydrodynamic equations for a low density granular mixture obtained previously from the Chapman--Enskog solution to the Boltzmann equation are considered further. The six transport coefficients associated with mass and heat flux in a binary mixture are given as functions of the mass ratio, size ratio, composition, and coefficients of restitution. Their quantitative variation across this parameter set is demonstrated using low order Sonine polynomial approximations to solve the exact integral equations. The results are also used to quantify the violation of the Onsager reciprocal relations for a granular mixture. Finally, the stability of the homogeneous cooling state is discussed.