Edges of flames that don’t exist

A counterflow diffusion flame model is studied revealing that, at least as a part of the quenching boundary is approached in parameter space at low enough Lewis numbers, an edge of a diffusion flame, or triple flame, has a propagation speed that still advances the burning solution into regions that are not burning. In crossing the quenching boundary, the advancing flame edge remains a robust part of the solution but the flame behind the edge is found to break up into periodic regions, resembling “tubes” of burning and non-burning, accompanied by the appearance of an oscillatory component in the speed of propagation of the edge. In crossing a second boundary the propagation speed of the flame edge disappears altogether. The only unbounded, non-periodic stationary solution then consists of an isolated flame tube although stationary periodic flame tubes can also exist under the same conditions. In passing back through parameter space, starting with a single flame tube already present, there is no sign of hysteresis and the oscillatory edge propagation reappears at the same point where it disappears. On the other hand, in continuing forwards across a third, final boundary the flame tube is extinguished leaving no combustion whatever. Boundaries in parameter space where different solutions arise are mapped out.