The role of radiative losses in self-extinguishing and self-wrinkling flames

We have developed a general theory of non-adiabatic premixed flames that is valid for flames of arbitrary shape that fully accounts for the hydrodynamic and diffusive-thermal processes, and incorporates the effects of volumetric heat losses. The model is used to describe aspects of experimentally observed phenomena of self-extinguishing (SEFs) and self-wrinkling flames (SWFs), in which radiative heat losses play an important role. SEFs are spherical flames that propagate considerable distances in sub-limit conditions before suddenly extinguishing. Our results capture many aspects of this phenomenon including an explicit determination of flame size and propagation speed at quenching. SWFs are hydrodynamically unstable flames in which cells spontaneously appear on the flame surface once the flame reaches a critical size. Our results yield expressions of the critical flame size at the onset of wrinkling and expected cell size beyond the stability threshold. The various possible burning regimes are mapped out in parameter space.