Condensed phase combustion with a merged sequential reaction mechanism

A model is presented for the propagation of an exothermic chemical reaction through a condensed combustible mixture where the reaction is characterized by the sequential production and depletion of a significant intermediate species. The effects of melting of the initial deficient component and intermediate species are also included. Under the assumptions of large activation energies and both steps of the reaction occurring at nearly the same temperature, together with other constraints on the effective heat released during each stage of the combustion process, an asymptotic approximation for the speed of a uniformly propagating planar merged reaction front is given. A time-dependent asymptotic model is also derived under the same assumptions. This is used to determine conditions for the loss of stability of the uniformly propagating planar-front solution via Hopf bifurcation to a pulsating propagating-front solution in which the velocity of propagation varies periodically.