Kinetic description of Brownian movement of heated particles in rarefied gas

Abstract

Translational and rotational Brownian movement of a spherical particle in a rarefied gas is considered. It is assumed that the particle radius is much less than the free path of the molecules in the gas. The collision integral of the considered particles and the gas molecules is generalized to the case of an arbitrary law of interaction between the molecules and the particle surface, this making it possible to consider the situation when there is no thermodynamic equilibrium between the particles and the gas, in particular, the particle temperature differs from the gas temperature. By expansion with respect to the small parameter — the ratio of the molecule and particle masses — the kinetic equation of the Boltzmann type reduces to the Fokker-Planck equation for the particle distribution function. The coefficients of the equation are calculated in an explicit form for the case of diffuse interaction between the molecules and the particle surface. A dependence of the diffusion coefficients on the ratio of the particle and gas temperatures is obtained.