Transport coefficients for driven granular mixtures at low-density

TL;DR

This paper derives the transport coefficients for a driven low-density granular binary mixture using kinetic theory, providing explicit formulas and comparing with previous models to enhance understanding of granular flow behavior.

Contribution

It extends previous monocomponent gas results to binary mixtures, deriving explicit transport coefficients under external driving conditions.

Findings

Explicit forms for diffusion coefficients and shear viscosity are obtained.

Comparison with previous models shows consistency and differences.

Transport coefficients depend on steady state conditions and external driving.

Abstract

The transport coefficients of a granular binary mixture driven by a stochastic bath with friction are determined from the inelastic Boltzmann kinetic equation. A normal solution is obtained via the Chapman-Enskog method for states near homogeneous steady states. The mass, momentum, and heat fluxes are determined to first order in the spatial gradients of the hydrodynamic fields, and the associated transport coefficients are identified. They are given in terms of the solutions of a set of coupled linear integral equations. As in the monocomponent case, since the collisional cooling cannot be compensated locally for by the heat produced by the external driving, the reference distributions (zeroth-order approximations) $f_i^{(0)}$ ($i=1,2$) for each species depend on time through their dependence on the pressure and the temperature. Explicit forms for the diffusion transport coefficients and the shear viscosity coefficient are obtained by assuming the steady state conditions and by considering the leading terms in a Sonine polynomial expansion. A comparison with previous results obtained for granular Brownian motion and by using a (local) stochastic thermostat is also carried out. The present work extends previous theoretical results derived for monocomponent dense gases [V. Garz\'o, M. G. Chamorro, and F. Vega Reyes, Phys. Rev. E \textbf{87}, 032201 (2013)] to granular mixtures at low density.