Travelling waves in a mixture of gases with bimolecular reversible reactions

TL;DR

This paper derives and analyzes the equations governing travelling waves in a reacting gas mixture, providing explicit dispersion relations and numerical solutions for various interaction laws.

Contribution

It presents a kinetic-based derivation of fluid dynamics equations for reacting gases and explicitly derives the dispersion relation for travelling waves in such mixtures.

Findings

Explicit dispersion relation for reacting gas mixture

Numerical solutions for Maxwellian and hard spheres interactions

Macroscopic observables like velocity, temperature, and composition analyzed

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.