Competing reactions in condensed phase combustion: wave structure and stability

We consider the use of step functions to model Arrhenius reaction terms for traveling wave solutions to combustion problems involving condensed-phase competing reactions such as those occurring in combustion synthesis via the self-propagating high-temperature synthesis process. For each reaction, the Arrhenius temperature dependence of the reaction rate is replaced by a step function. The resulting model introduces interior interfaces and allows the transport equations for energy and species to be solved explicitly within the subdomains bounded by these interfaces. The problem can then be reduced to a small number of algebraic equations describing appropriate interface conditions. We apply this methodology to study steady traveling waves with competing reactions, finding regions where multiple solutions are possible, and comparing our results with numerical calculations employing Arrhenius kinetics. We then analyze and determine regions of stability and instability for the traveling wave solutions.