Mass transport of an impurity in a strongly sheared granular gas

Abstract

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