Flame propagation in random media

TL;DR

This paper presents a phase-field model for flame propagation in random media, revealing a critical concentration threshold for flame existence and demonstrating kinetic roughening of the combustion interface consistent with KPZ universality.

Contribution

The study introduces a novel phase-field model linking combustion dynamics with percolation theory and interface roughening phenomena.

Findings

Flame front exists for reactant concentration c > c*

Flame vanishes at the critical concentration c*

Interface exhibits kinetic roughening consistent with KPZ equation

Abstract

We introduce a phase-field model to describe the dynamics of a self-sustaining propagating combustion front within a medium of randomly distributed reactants. Numerical simulations of this model show that a flame front exists for reactant concentration $c > c^* > 0$, while its vanishing at $c^*$ is consistent with mean-field percolation theory. For $c > c^*$, we find that the interface associated with the diffuse combustion zone exhibits kinetic roughening characteristic of the Kardar-Parisi-Zhang equation.