A note on a kinetic relaxation model for a reactive gas mixture

A reactive BGK-type model is proposed for a binary mixture of rarefied gases, by resorting to a simple Boltzmann collision operator for a slow irreversible deexcitation reaction, in a process driven by mechanical encounters. The hydrodynamic limit is worked out by a Chapman-Enskog asymptotic procedure up to the Navier-Stokes equations, and can fit exactly Fick's law for diffusion velocities and Newton's law for the viscous stress, which is traceless in the present scaling. Transport coefficients are not affected by the chemical reaction, whereas reactive effects are described by additional source terms (integrals involving the chemical cross sections), vanishing at chemical equilibrium, which in turn are not affected by mechanical relaxation parameters.