Hot-spot combustion of heterogeneous condensed mixtures. Thermal percolation

A model of combustion of heterogeneous condensed mixtures composed of reactive particles separated by an inert heat-conducting substance is considered. Propagation of the reaction in a one-dimensional periodic system of point reaction cells connected by inert thermal bridges is examined. The burning rate is determined as a function of the basic parameters of the system, and stability of the steady combustion mode is studied. It is shown that there exists a range of parameters in which the reaction propagates in an unstable manner. Combustion of the system in the instability domain is examined. It is shown that the reaction propagation loses its stability many times as the adiabatic temperature of the system decreases; in this case, the existing unsteady mode is replaced by another, more complicated mode, and the alteration of the regimes in the examined systems always proceeds as a period-doubling bifurcation. Beginning from a certain value of adiabatic temperature, the reaction-propagation process becomes stochastic. In the systems examined, there exists an ultimate adiabatic temperature, below which self-sustained propagation of the reaction in the system becomes impossible.