Combustion of heterogeneous systems with a stochastic spatial structure near the propagation limits

Abstract

Extinction of a heterogeneous reactant mixture in the vicinity of thermal and concentration limits of propagation is considered. The consideration is based on an analysis of analytical solutions of combustion-theory problems and on their comparison with both the results of mathematical modeling and a number of experimental works on self-propagating high-temperature synthesis. It is shown that solid-phase-combustion models based on the approximation of a continuous medium are only applicable away from the extinction limits. It is demonstrated that it is fluctuations of the spatial reactant distribution that play a decisive role on the limit of propagation of a combustion wave; these fluctuations must be allowed for, among other factors, when self-sustaining combustion waves are investigated. A percolation model that enables one to explain a number of distinctive features found in the behavior of a combustion wave near the propagation limit is presented.