STOICHIOMETRIC FLAMES AND THEIR STABILITY

We consider a flame in a stoichiometric combustible mixture of two rea ctants, A and B, having different diffusivities. We employ a thin reac tion zone approximation and assume that the reaction ceases when the c oncentrations and temperature approach their thermodynamic equilibrium values. Thus, our analysis accounts for the possibility of a reversib le stage in the combustion reactions. We find uniform flames and analy ze both their cellular and pulsating instabilities. We compare our res ults with those for a one reactant flame as well as with previously ob tained 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 clo se to 1. They showed that the cellular stability boundary for bimolecu lar 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 consideri ng the limiting case of a negligibly small equilibrium constant, so th at the final concentrations of the reactants approach zero, we show th at for general Lewis numbers, not limited to being close to 1, the cel lular stability boundary is determined by an effective Lewis number wh ich, for equimolecular, e.g., bimolecular reactions, is the harmonic m ean 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 sim ple arithmetic mean, previously obtained. For significantly different Lewis numbers, a case not covered by previous results, our solution sh ows that stability is determined by diffusion of the lighter reactant, in accord with experimental observations. Thus, we provide a theoreti cal basis for the effect of preferential diffusion. We also find that dissociation of the product is stabilizing.