On a generalized free-interface model of solid combustion

Abstract

In solid combustion, a chemical reaction converts a solid fuel directly into solid products without intermediate gas-phase formation. For example, in self-propagating high-temperature synthesis, a flame wave advances through powdered ingredients, leaving high-quality ceramic materials or metallic alloys in its wake. Simple conceptual descriptions of such combustion, as well as of explosive solidification and other exothermic phenomena such as frontal polymerization, can be given by considering reaction–diffusion equations with concentrated kinetics. Our model generalizes a specialized case from the literature in which diffusivities in the reactant and product are assumed equal. Our generalized model pinpoints the dynamics in a range of settings, as long as the diffusivity ratio does not approach zero or infinity too closely. Our numerical study quantitatively predicts the behavior of exothermic reaction fronts in this spectrum of material contexts. We also compare with the case of negligible heat diffusion behind the front. The dynamics involve an interplay of competing effects as the diffusivity ratio is tuned to capture different physical systems.