Nonequilibrium contributions to the rate of chemical reaction in the Lorentz gas: A comparison of perturbation and numerical solutions of the Boltzmann equation

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Abstract
The corrections to the equilibrium rate of the chemical reaction A+B→products are analyzed for the Lorentz gas composed of light particles A reacting with heavy particles B in the presence of heavy particles of a carrier gas C. Particles B and C are treated as a heat bath. The reaction is analyzed under conditions in which the products can be neglected. The model of reacting hard spheres (line‐of‐centers model) introduced by Present is used. Analysis is performed in two ways: (1) By obtaining analytical expressions following from the Chapman–Enskog perturbation solution of the Boltzmann equation generalized for gases reacting chemically. (2) By obtaining numerical results which follow from a numerical solution of a partial differential equation which can be derived from the Boltzmann equation for the reactive Lorentz gas. It is shown that for a specified region of system parameters both types of solution of the Boltzmann equation coincide. The comparison of both methods permits us to find out under which conditions the perturbation method of solution may be used.