Model for the propagation of a stationary reaction front in a viscoelastic medium

Abstract

A coupled thermomechanical model for the propagation of a stationary chemical-reaction wave in a condensed medium is developed. Stresses and strains that arise during the reaction as a result of thermal and “concentration” expansion of the material are related by Maxwell’s equations for a viscoelastic medium. The expression for the heat flux is written as a generalized Fourier law with finite relaxation time for the heat flux. It is shown that deformation of the material in the reaction zone can lead to an apparent change in the activation energy, heat effect, and other characteristics of the system. This model allows for the existence of two different — subsonic and supersonic — regimes of propagation of the front, as well as the model in which the stress- and strain-tensor components are related by a generalized Hooke’s law.