On the velocity relaxation of a Rayleigh gas

Leonardo Ferrari

Physica A: Statistical Mechanics and its Applications, 1989, vol. 154, issue 2, 271-288

Abstract: Two methods of solution of the usual (Fokker-Planck) kinetic equation for a Rayleigh gas are discussed. One is that based on the so-called, and well-known, “fundamental solution” of the same equation, while the other profits by the expansion of the heavy-particle velocity distribution in eigenfunctions of the Fokker-Planck collision operator. The particular case is considered in which the initial heavy-particle velocity distribution is Maxwellian (around a given flow velocity) at a temperature generally different from that of equilibrium. Moreover, the inadequacies of the usual Fokker-Planck equation in describing the relaxation processes are individuated and discussed devoting particular attention to situations in which the initial heavy-particle velocity distribution is anisotropic. In this regard, exploiting the circumstance that the eigenfunctions of the Fokker-Planck collision operator are also eigenfunctions of the Boltzmann collision operator in the Maxwell model, an enlightening comparison between our results and those of the exact Boltzmann theory is presented.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:154:y:1989:i:2:p:271-288

DOI: 10.1016/0378-4371(89)90013-7

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