Boundary conditions based upon a modified Maxwellian velocity distribution for flows of identical, smooth, nearly elastic spheres

Abstract

We focus attention on the rapid flows of identical, smooth, nearly elastic spheres and introduce a statistical description of the spheres' velocities. Based upon a velocity distribution function that contains improvements to the Maxwellian, we calculate the rate at which momentum and energy are transferred across bumpy boundaries and obtain conditions that ensure the balance of momentum and energy at such boundaries. Using these conditions we carry out an approximate analysis of a granular shear flow driven by bumpy boundaries to obtain an explicit dependence of the slip velocity and resulting stresses on boundary roughness. Finally, we compare these results to those obtained by employing a theory based on a simple Maxwellian velocity distribution.