Flame propagation in random media

We introduce a phase-field model to describe the dynamics of a self-sustaining propagating combustion front within a medium of randomly distributed reactants. Numerical simulations of this model show that a flame front exists for reactant concentration c>${\mathit{c}}^{\mathrm{*}}$>0, while its vanishing at ${\mathit{c}}^{\mathrm{*}}$ is consistent with mean-field percolation theory. For c>${\mathit{c}}^{\mathrm{*}}$, we find that the interface associated with the diffuse combustion zone exhibits kinetic roughening characteristic of the Kardar-Parisi-Zhang equation.