Particles dispersed in a dilute gas. II. from the Langevin equation to a more general kinetic approach

Abstract In the attempt to solve the age-old problem of unifying Langevin, Fokker-Planck and Boltzmann theories for test particles in a dilute gas, the Uhlenbeck and Ornstein's theory relating Langevin and Fokker-Planck equations is critically analyzed. Agreement and discrepancies between such theory and the results following from the Boltzmann one are also examined. It is concluded that the currently assumed form of the fluctuating-force autocorrelation function, which is extremely successful for Brownian particles in dense fluids, cannot generally guarantee an accurate (or acceptable) relaxation law for the mean square velocity components of generic test particles in dilute gases. This difficulty can be overcome in the framework of a more general kinetic approach which is shown to consistently include Langevin, Fokker-Planck, and Boltzmann theories. The advantages of such approach in interpreting experimental results are particularly evident when the test particles move in a (homogeneous) gas in non-equilibrium conditions and when correlations exist between test- and gas-particle velocities. © 2013 The Authors. Published by Elsevier B.V. All rights reserved.