Transport coefficients for inelastic Maxwell mixtures

TL;DR

This paper derives exact expressions for the transport coefficients of inelastic Maxwell mixtures using the Boltzmann equation, providing insights into granular gas dynamics and comparing results with inelastic hard sphere models.

Contribution

It provides the first exact analytical expressions for all Navier-Stokes transport coefficients of inelastic Maxwell mixtures, extending understanding of granular gas behavior.

Findings

Transport coefficients are exactly expressed in terms of restitution coefficients and particle ratios.

Good agreement with inelastic hard sphere models for moderate dissipation.

Results enhance theoretical modeling of granular mixtures.

Abstract

The Boltzmann equation for inelastic Maxwell models is used to determine the Navier-Stokes transport coefficients of a granular binary mixture in $d$ dimensions. The Chapman-Enskog method is applied to solve the Boltzmann equation for states near the (local) homogeneous cooling state. The mass, heat, and momentum fluxes are obtained to first order in the spatial gradients of the hydrodynamic fields, and the corresponding transport coefficients are identified. There are seven relevant transport coefficients: the mutual diffusion, the pressure diffusion, the thermal diffusion, the shear viscosity, the Dufour coefficient, the pressure energy coefficient, and the thermal conductivity. All these coefficients are {\em exactly} obtained in terms of the coefficients of restitution and the ratios of mass, concentration, and particle sizes. The results are compared with known transport coefficients of inelastic hard spheres obtained analytically in the leading Sonine approximation and by means of Monte Carlo simulations. The comparison shows a reasonably good agreement between both interaction models for not too strong dissipation, especially in the case of the transport coefficients associated with the mass flux.