Kinetic theory for identical, frictional, nearly elastic spheres

Abstract

We derive a simple kinetic theory for collisional flows of identical, slightly frictional, nearly elastic spheres that is based on a physically realistic model for a frictional collision between two spheres. When the coefficient of friction is small, the equations of balance for rotational momentum and energy can be solved in approximation. This permits the rotational temperature to be related to the translation temperature and the introduction of an effective coefficient of restitution in the rate of dissipation of translation fluctuation energy. With this incorporation of the additional loss of translational energy to friction and the rotational degrees of freedom, the structure of the resulting theory is the same as for frictionless spheres.