Mass transport of an impurity in a strongly sheared granular gas

TL;DR

This paper derives tensorial transport coefficients for impurity mass flux in a sheared granular gas using an inelastic Boltzmann framework, highlighting significant deviations from elastic behavior due to dissipation.

Contribution

It introduces a tensorial description of mass transport in sheared granular gases and provides approximate solutions for the associated transport coefficients.

Findings

Transport coefficients are tensorial due to anisotropy.

Deviations from elastic forms are significant even at moderate dissipation.

Transport coefficients are obtained from coupled integral equations solved via Sonine expansion.

Abstract

Transport coefficients associated with the mass flux of an impurity immersed in a granular gas under simple shear flow are determined from the inelastic Boltzmann equation. A normal solution is obtained via a Chapman-Enskog-like expansion around a local shear flow distribution that retains all the hydrodynamic orders in the shear rate. Due to the anisotropy induced by the shear flow, tensorial quantities are required to describe the diffusion process instead of the conventional scalar coefficients. The mass flux is determined to first order in the deviations of the hydrodynamic fields from their values in the reference state. The corresponding transport coefficients are given in terms of the solutions of a set of coupled linear integral equations, which are approximately solved by considering the leading terms in a Sonine polynomial expansion. The results show that the deviation of these generalized coefficients from their elastic forms is in general quite important, even for moderate dissipation.