Diatomic gas diffusing in a background medium: kinetic approach and reaction-diffusion equations

The problem of a diatomic gas made up by atoms and molecules undergoing reactions of dissociation and recombination through a transition state is addressed. The gas is diffusing in a scattering and dissociating background medium. Extended Boltzmann-like kinetic equations for the relevant distribution functions and exact balance equations for mass, momentum, and energy are derived and discussed. It is shown that, in the asymptotic limit of small Knudsen numbers, a suitable scaling leads to a consistent formal derivation of hydrodynamic equations of reaction-diffusion type for number densities of atoms and molecules.