Strongly Nonlinear Asymptotic Model of Cellular Instabilities in Premixed Flames with Stepwise Ignition-Temperature Kinetics

In this paper we consider an ignition-temperature, first-order reaction model of thermo-diffusive combustion that describes dynamics of thick flames arising, for example, in a theory of combustion of hydrogen-oxygen and ethylene-oxygen mixtures. These flames often assume the shape of propagating curved interfaces that can be identified with level sets corresponding to a prescribed ignition temperature. The present paper is concerned with the analysis of such interfaces in two spatial dimensions under a single assumption of their small curvature. We derive a strongly nonlinear evolution equation that governs the dynamics of an interface. This equation relates the normal velocity of the interface to its curvature, the derivatives of the curvature with respect to the arc-length of the interface, and physical parameters of the problem. We study solutions of the evolution equation for various parameter regimes and discuss the ranges of validity of the corresponding simplified models. Our theoretical findings a...