B. Nowakowski, SOLUTION OF THE FOKKER-PLANCK EQUATION FOR REACTIVE RAYLEIGH GAS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 53(3), 1996, pp. 2964-2967
A Rayleigh model of heavy molecules diluted in a thermal bath of light
molecules is extended to include a chemical reaction between both spe
cies. The solution of the appropriate Fokker-Planck equation for the d
istribution function is obtained from the corresponding solution for t
he nonreactive mixture. In the hydrodynamic regime the shape of the ve
locity distribution of heavy molecules is Maxwellian, but with a tempe
rature different from that of the carrier gas. Exact results are deriv
ed for the reaction rate constant and diffusion coefficient.