Travelling waves in a mixture of gases with bimolecular reversible reactions

Abstract

Starting from the kinetic approach for a mixture of reacting gases whose particles interact through elastic scattering and a bimolecular reversible chemical reaction, the equations that govern the dynamics of the system are obtained by means of the relevant Boltzmann-like equation. Conservation laws are considered. Fluid dynamic approximations are used at the Euler level to obtain a close set of PDEs for six unknown macroscopic fields. The dispersion relation of the mixture of reacting gases is explicitly derived in the homogeneous equilibrium state. A set of ODE that governs the propagation of a plane travelling wave is obtained using the Galilei invariance. After numerical integration some solutions, including the well-known Maxwellian and the hard spheres cases, are found for various meaningful interaction laws. The main macroscopic observables for the gas mixture such as the drift velocity, temperature, total density, pressure and its chemical composition are shown.