Nonequilibrium effects for reactions with activation energy: Convergence of the expansions of solutions of the Boltzmann and Lorentz Fokker Planck equations with Sonine and Maxwell polynomials as basis functions

In this paper, we consider the kinetic theory of a reactive species of mass m dilutely dispersed in a second reactive component of mass M, at equilibrium with a Boltzmann distribution. The primary objective of these studies is the correction, η, to the equilibrium rate coefficient, keq, where the nonequilibrium rate coefficient is expressed as k=keq(1−η). The Chapman–Enskog method of solution together with the Sonine (Laguerre) polynomials as basis functions for the solution of the Boltzmann equation with reaction is the method of choice of most researchers. The main objective of this paper is the study of the convergence of the Sonine polynomials in the solution of the reactive Boltzmann equation, for m/M→0, that is for the Lorentz limit. We report the solution of the Lorentz Fokker–Planck equation for m/M→0 with the expansion of the distribution function in the Maxwell polynomials as basis functions orthogonal on x∈[0,∞] with weight function x2exp(−x2). The variable x=mv2/2kBTB is the reduced speed of the particle of mass m with TB the background gas temperature and kB the Boltzmann constant. We demonstrate that the nonclassical Maxwell polynomials provide a rapidly convergent solution of the chemical kinetic Fokker–Planck equation in the Lorentz limit. The reactive line-of-centers cross section is employed as representative of reactions with activation energy.