Influence of nonconservative external forces on self-diffusion in dilute gases

Abstract

The influence of a nonconservative force proportional to the velocity acting on a system described by the Boltzmann equation is analyzed. When this force is the only external action on the system, an H-theorem is proved, showing that the distribution function tends towards a Maxwellian with a time-dependent temperature. Self-diffusion in such a state is analyzed in the case of Maxwell molecules. It is shown that the external force can even prevent the system to reach a hydrodynamic stage. Next, self-diffusion in a system under uniform shear flow is considered. For Maxwell molecules, the conditions under which a hydrodynamic regime is reached are discussed. In the hydrodynamic regime, a self-diffusion tensor is obtained to first order in the concentration gradient. This tensor is a highly nonlinear function of both the shear rate and the strength of the external force. Comparison with previous work is carried out.