Flames with Chain-Branching/Chain-Breaking Kinetics

Source abstract

A steady plane flame subject to the chain-branching/chain-breaking kinetics $$A + X \to 2X,\quad 2X + M \to 2P + M$$ is considered for a certain distinguished limit of parameter values corresponding to fast recombination. Here A is the reactant, X the radical, P the product, and M a third body. The activation energy of the production step is very large, while that of the recombination step is small and taken to be zero. These kinetics are the most attractive of the two-step schemes that have been proposed for explaining interesting phenomena not covered by one-step kinetics, and the purpose is to provide a firm foundation for exploitation of the scheme. The object is to find the “laminar-flame eigenvalue” $\Delta$, representing the burning rate, as a function of r, which is essentially the ratio of the two reaction rates. The response function $\Delta ( r )$ is described by numerical integration and by asymptotic analysis for $r \to 0,\infty$.