Fingering Instability in Combustion

A thin solid, burning against an oxidizing wind, develops a fingering instability. The effect is observed in a narrow gap geometry, where free convection is suppressed. Focusing on the developed nonlinear state, we find that two length scales coexist. The spacing between fingers is determined by the P\'eclet number, and the finger width is determined by heat losses. Dense fingers develop by tip splitting. A phenomenological model accurately predicts the fingers' spacing, and is generally applicable to diffusion limited systems. We suggest that the effect is a new, accurately controllable, version of the thermal-diffusive instability.