Transport Around Steady Simple Shear Flow in Dilute Granular Gases

Abstract

This chapter deals with the study of linear transport around the uniform or simple shear flow state. The analysis is made from a perturbation solution of the Boltzmann kinetic equation through first-order in the deviations of the hydrodynamic fields with respect to their values in the (unperturbed) non-Newtonian shear flow state. Given that the reference state (zeroth-order approximation in the Chapman–Enskog-like expansion) applies to arbitrary shear rates, the successive approximations in perturbation expansion retain all the hydrodynamic orders in the shear rate. As expected, due to the anisotropy in velocity space induced in the system by the shear flow, mass, momentum, and heat fluxes are given in terms of tensorial transport coefficients instead of the conventional scalar Navier–Stokes transport coefficients. The study is carried out for monocomponent granular gases and binary granular mixtures in the tracer limit.