Fingering Instability in Combustion

TL;DR

This paper investigates the fingering instability in combustion of thin solids like paper, revealing how finger spacing and width are influenced by transport mechanisms and dimensionality, supported by experimental validation of a diffusion-limited model.

Contribution

It introduces a quantitative model for fingering instability in combustion, linking finger spacing to Péclet number and width to two-dimensional effects, with experimental verification.

Findings

Finger spacing depends on Péclet number.

Finger width is influenced by two-dimensionality.

Recurrent tip splitting leads to dense fingers.

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 P\'eclet 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.