The description of homogeneous branched-chain explosions with slow radicalrecombination by self-adjusting time scales

A nonlinear multiscale technique is used to describe the time history of a spatially homogeneous chain-branching/chain-breaking explosion when chain b ranching is much faster than chain breaking. We select a two-step chemistry model that closely reproduces the ignition characteristics of hydrogen-oxy gen systems above the second explosion limit. The resulting combustion hist ory exhibits an induction period with small radical concentrations, followe d by a short period of rapid radical growth and a long period of slow radic al recombination. The solution can be described by using the ratio of the r ate of chain breaking to that of chain branching as an asymptotically small parameter. The problem is formulated by identifying a linear combination o f the original variables that evolves with the slow time of radical recombi nation, and by allowing the fast time to depend on this slowly varying unkn own. The associated solution procedure is nonstandard in that it exhibits d ifferent solvability conditions for the slow time evolution in the inductio n and recombination periods. The method proposed emerges as a natural alter native to activation-energy asymptotics for the analysis of branched-chain explosions at high temperatures.