First-order kinetic approximation for a chemically reactive gas mixture.

A multicomponent reacting gas with an arbitrary number of chemical species and one reversible reaction is studied at a kinetic level in the frame of discrete velocity models of the Boltzmann equation, with the main objective of deriving the “reactive” Navier Stokes equations of the model, and characterizing the dissipative terms related to shear viscosity, thermal conductivity and thermal diffusion. The closure of the system formed by conservation and chemical rate equations is based on a first-order Chapman-Enskog method, to be applied in the strong reaction regime, and on a convenient representation of the density vector space in terms of the macroscopic variables. A mathematical procedure is proposed which leads to identification of the transport coefficients, and may be applied to a quite large variety of reactive gas flows. Moreover, it allows characterization of the functional form of the transport coefficients in dependence on the local gas concentrations, once the model is specified.