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SIAM J. Appl. Math. 68, pp. 619-628 (10 pages)
Homogeneous Branched-Chain Explosions
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Add to FacebookA 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.
© 2007 Society for Industrial and Applied Mathematics
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Received May 24, 2007
Accepted September 05, 2007
Published online December 07, 2007
Accepted September 05, 2007
Published online December 07, 2007
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