Fingering in slow combustion

We report numerical simulations of the structure of advancing burning fronts under conditions where the dominating transport mechanisms is the diffusion of oxygen and heat. The model we study describes the interplay between two diffusive fields: one which accounts for the destabilizing mechanism leading to the production of a large surface area and the other for a stabilizing mechanism. The typical length scale associated with the observed fingering instability turns out to be a combination of the diffusion lengths associated with the two competing processes.