A kinetic model for chemical reactions without barriers: transport coefficients andeigenmodes

Abstract

The kinetic model of the Boltzmann equation proposed in the work of Kremer and Soares2009 for a binary mixture undergoing chemical reactions of symmetric type which occurwithout activation energy is revisited here, with the aim of investigating in detail thetransport properties of the reactive mixture and the influence of the reaction process on thetransport coefficients. Accordingly, the non-equilibrium solutions of the Boltzmannequations are determined through an expansion in Sonine polynomials up to the first order,using the Chapman–Enskog method, in a chemical regime for which the reactionprocess is close to its final equilibrium state. The non-equilibrium deviations areexplicitly calculated for what concerns the thermal–diffusion ratio and coefficients ofshear viscosity, diffusion and thermal conductivity. The theoretical and formalanalysis developed in the present paper is complemented with some numericalsimulations performed for different concentrations of reactants and products ofthe reaction as well as for both exothermic and endothermic chemical processes.The results reveal that chemical reactions without energy barrier can induce anappreciable influence on the transport properties of the mixture. Oppositely tothe case of reactions with activation energy, the coefficients of shear viscosityand thermal conductivity become larger than those of an inert mixture whenthe reactions are exothermic. An application of the non-barrier model and itsdetailed transport picture are included in this paper, in order to investigate thedynamics of the local perturbations on the constituent number densities, andvelocity and temperature of the whole mixture, induced by spontaneous internalfluctuations. It is shown that for the longitudinal disturbances there exist twohydrodynamic sound modes, one purely diffusive hydrodynamic mode and one kineticmode.