A kinetic model for chemical reactions without barriers : transport coefficients and eigenmodes

Abstract

The kinetic model of the Boltzmann equation proposed in the work of Kremer and Soares 2009 for a binary mixture undergoing chemical reactions of symmetric type which occur without activation energy is revisited here, with the aim of investigating in detail the transport properties of the reactive mixture and the influence of the reaction process on the transport coefficients. Accordingly, the non-equilibrium solution of the Boltzmann equation is determined through an expansion in Sonine polynomials up to the first order, using the Chapman-Enskog method, in a chemical regime for which the reaction process is close to its final equilibrium state. The non-equilibrium deviations are explicitly calculated for what concerns the thermal-diffusion ratio and coefficients of shear viscosity, diffusion and thermal conductivity. The theoretical and formal analysis developed in the present paper is complemented with some numerical simulations performed for different concentrations of reactants and products of the reaction as well as for both exothermic and endothermic chemical processes. The results reveal that chemical reactions without energy barrier can induce an appreciable influence on the transport properties of the mixture. Oppositely to the case of reactions with activation energy, the coefficients of shear viscosity and thermal conductivity become larger than those of an inert mixture when the reactions are exothermic. An application of the non-barrier model and its detailed transport picture is included in this paper, in order to investigate the dynamics of the local perturbations on the constituent number densities, and velocity and temperature of the whole mixture, induced by spontaneous internal fluctuations. It is shown that for the longitudinal disturbances there exist two hydrodynamic sound modes, one purely diffusive hydrodynamic mode and one kinetic mode.