Homogeneous Branched-Chain Explosions

A model of homogeneous explosions with competing branching and recombination processes due to Kapila is analyzed by singular perturbation methods. In this model, the concentration of radicals is very low during a long induction period that ends with a rapid radical-growth stage in which all the reactants are consumed as the radicals reach their peak concentrations. The sudden jump in radical concentration is then followed by a long period of chain termination. Based on an exact relation between the fuel concentration and a slowly varying combination of fuel and radicals, we find a composite of two matched asymptotic expansions providing very good agreement with the numerical solution. This approximation is compared to another composite obtained by the method of multiple self-adjusting scales. Both approximations seem to be similarly accurate provided the induction time is calculated beyond leading order.