Scaling, Propagation, and Kinetic Roughening of Flame Fronts in Random Media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density, below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with mean field theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time dependent width and equal time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.