Stoichiometric flames and their stability

We consider a flame in a stoichiometric combustible mixture of two reactants, A and B, having different diffusivities. We employ a thin reaction zone approximation and assume that the reaction ceases when the concentrations and temperature approach their thermodynamic equilibrium values. Thus, our analysis accounts for the possibility of a reversible stage in the combustion reactions. We find uniform flames and analyze both their cellular and pulsating instabilities. We compare our results with those for a one reactant flame as well as with previously obtained results for a stoichiometric mixture of two reactants. Studies of the latter assumed complete consumption of one of the reactants in the reaction front and that both Lewis numbers, L_A and L_B, are close to 1. They showed that the cellular stability boundary for bimolecular reactions is determined by an effective Lewis number which is the arithmetic mean of L_A and L_B, i.e., 1 2(L_A + L_B). By considering the limiting case of a negligibly small equilibrium constant, so that the final concentrations of the reactants approach zero, we show that for general Lewis numbers, not limited to being close to 1, the cellular stability boundary is determined by an effective Lewis number which, for equimolecular, e.g., bimolecular reactions, is the harmonic mean of the Lewis numbers of the two reactants, i.e., L_eff = 2(L_A^-1 + L_B^-1)^-1 The leading term of an asymptotic expansion of our effective Lewis number, for both L_A and L_B close to 1, is the simple arithmetic mean, previously obtained. For significantly different Lewis numbers, a case not covered by previous results, our solution shows that stability is determined by diffusion of the lighter reactant, in accord with experimental observations. Thus, we provide a theoretical basis for the effect of preferential diffusion. We also find that dissociation of the product is stabilizing.