Kinetic Theory of a Dilute Gas System under Steady Heat Conduction

The velocity distribution function of the steady-state Boltzmann equation for hard-core molecules in the presence of a temperature gradient has been obtained explicitly to second order in density and the temperature gradient. Some thermodynamical quantities are calculated from the velocity distribution function for hard-core molecules and compared with those for Maxwell molecules and the steady-state Bhatnagar-Gross-Krook(BGK) equation. We have found qualitative differences between hard-core molecules and Maxwell molecules in the thermodynamical quantities, and also confirmed that the steady-state BGK equation belongs to the same universality class as Maxwell molecules.Comment: 36 pages, 4 figures, 5 table

Nonequilibrium Effects in a Bimolecular Chemical Reaction in a Dilute Gas

Perturbation solution of the Boltzmann equation for a dilute gas with a chemical reaction A + A → B + B is presented. Analytical results for the nonequilibrium effects on the rate of chemical reaction are obtained for the line-of-centers model. It is shown that taking into account the energy transfer from reagents A to products B permits to get new results. The nonequilibrium corrections obtained from these results are much larger than those obtained with neglecting this energy transfer. These results are verified by a comparison with the numerical results obtained from the modified Nanbu-Babovsky Monte Carlo computer simulations

Theory of Translational Energy Relaxation in Binary Mixtures of Dilute Gases with Chemical Reaction

A simple approach to the process of translational energy relaxation in dilute gases due to Dahler, Malkin, Shizgal and others is extended to the case of systems with chemical reaction. Fundamental quantities characterizing the relaxation processes such as the relaxation time and collision numbers during this time are computed for a number of molecular models of the chemical reaction (the Prigogine-Xhrouet model, the line-of-centers model, a modified line-of-centers model, and reverse versions of these models). Results of this analytical theory are compared with the results of numerical simulations of solutions of the appropriate Boltzmann equation with the use of the modified Nanbu-Babovsky method. This comparison leads to very good agreement between the analytical theory and numerical calculations. A marked influence of the chemical reaction on the translational relaxation in a dilute gas is another important conclusion of this paper