Brownian Motion of Rotating Particles

Abstract

A kinetic theory for the Brownian motion of spherical rotating particles is given starting from a generalized Fokker-Planck equation. The generalized Fokker-Planck collision operator is a sum of two ordinary Fokker-Planck differential operators in velocity and angular velocity space respectively plus a third term which provides a coupling of translational and rotational motions. This term stems from a transverse force proportional to the cross product of velocity and angular velocity of a Brownian particle. Collision brackets pertaining to the generalized Fokker-Planck operator are defined and their general properties are discussed. Application of WALDMANN'S moment method to the Fokker-Planck equation yields a set of coupled linear differential equations (transport-relaxation equations) for certain local mean values. The constitutive laws for diffusion, heat conduction by Brownian particles and spin diffusion are deduced from the transport-relaxation equations. The transport-relaxations coefficients appearing in them are given in terms of the two friction coefficients for the damping of translational and rotational motions and a third coefficient which is a measure of the transverse force. By the coupling of translational and rotational motions a diffusion flow gives rise to a correlation of linear and angular velocities.