On the Dynamics of Nearly-Extinguished Non-Adiabatic Cellular Flames

We study the dynamics of a nearly-extinguished and weakly unstable non-adiabalic flame For simplicity sake, the analysis is conducted in the framework of a thermal-diffusional flame model Using high activation energy techniques and bifurcation methods, we derive a non-linear partial differential evolution equation for the changes of front shape and velocity By solving it approximately in a particular case, we show that the spontaneously growing front corrugations, due to diffusive instability, are sufficient to prevent flame quenching: a diffusively unstable flame front can still propagate with heat-loss intensities that would quench a planar one.