Solution of the Boltzmann Equation for Uniform Shear Flow

Abstract

In many textbooks (Reif, 1965), the derivation of the shear viscosity of a gas by using elementary kinetic theory assumes the existence of a simple shear flow characterized by a linear velocity profile of a component of the flow velocity, say u _x , along a normal direction, say the y-direction, while the density and the temperature remain spatially uniform (See Fig. 2.1). Implicit in those arguments and conditions is the assumption that the shear rate ∂u _x /∂y is very small, and so the xy-element of the pressure tensor is just proportional to this shear rate.