Fingering Instability in Combustion

Abstract

A thin solid (e.g., paper), burning against an oxidizing wind, develops a fingering instability with two decoupled length scales. The spacing between fingers is determined by the Péclet number (ratio between advection and diffusion). The finger width is determined by the degree two dimensionality. Dense fingers develop by recurrent tip splitting. The effect is observed when vertical mass transport (due to gravity) is suppressed. The experimental results quantitatively verify a model based on diffusion limited transport.