Fokker-Planck and Langevin equations for arbitrary slip velocities.

Abstract

An expression for the Fokker-Planck equation governing the velocity distribution function of particles or heavy molecules immersed in a host light gas valid for arbitrary mean velocities of the heavy component is given. This expression generalizes previous results which were limited to small differences between the mean velocities of the heavy and light components compared with the thermal velocity of the light gas. The derivation assumes a Maxwellian velocity distribution function for the light gas, elastic heavy-light collisions, and makes use of integrals computed by Riesco-Chueca, Fern\'andez-Feria, and Fern\'andez de la Mora in Ref. 1. The stochastic Langevin equation associated with this Fokker-Planck collision operator is also obtained. More in general, we derive the Langevin equation corresponding to the general form of the Fokker-Planck collision operator, and particularize it to the present case.