Microscopic kinetic theory of the mean collision force of a particle moving in rarefied gases.

Abstract

The friction of an incident particle interacting with the background molecules is a cornerstone in the nonequilibrium dynamics and statistics. It is reported that the Stokes force may fail while the Brown particle's size is small enough. In this work, the mean collision force of a small classical particle moving through the rarefied gases is analyzed by the direct calculation of the mean decrease of particle's velocity by elastic collisions. As an example, a whole velocity space applicable mean collision force in Maxwell gas is obtained. A self-consistent solution is further provided based on the numerical simulations. Within the low speed limit, comparison of the friction and the Stokes force has been demonstrated. Although the two forces are both proportional to the speed of the particle, their coefficients are different. Unlike the linear speed dependence of Stokes force, the linear behavior in rarefied gases is broken with increasing the speed of incident particle, and a quadratic speed dependence is resulted in high speed. This work clarifies the nonequilibrium dynamics of microscopic particles moving in rarefied gases, and can improve our microscopic understanding of the collision force.