Percolation phase transition in combustion of heterogeneous mixtures

Combustion of heterogeneous mixtures with a stepwise dependence of the reaction rate on temperature is considered. A two-dimensional model of the process is proposed, which takes into account, in addition to other factors, the random distribution of fuel particles in the mixture and nonisothermality of the latter. The flammability limits are compared by methods of numerical simulation for two types of heterogeneous systems with an identical mean density of the fuel: with a uniform distribution of the fuel for all particles of the mixture and with its distribution based on random sampling of particles. It is shown that, as the degree of heterogeneity increases (dimensionless coefficient of heat transfer between the particles, Bi, decreases), the flammability limit for systems of both types becomes significantly higher than its “thermodynamic” value, and the upper boundary of the limit is twice as high. Differences in flammability limits and burning rates for heterogeneous systems of these types are found. A relationship between the flammability limit of a random system and a percolation phase transition, which occurs in a heterogeneous condensed mixture with scarce inclusions of the fuel, is demonstrated. An analytical approach for evaluation of the threshold concentration of the fuel in such systems, based on the problem of percolation on random nodes, is proposed.