Theory of deflagration in disordered media

TL;DR

This paper develops a new theory of deflagration in disordered media, highlighting the role of hot spots and phase transitions, which differ significantly from conventional uniform media models.

Contribution

It introduces a novel theoretical framework for burning in disordered media, revealing a phase transition akin to percolation and identifying conditions for first or second order transitions.

Findings

Disordered media exhibit a phase transition similar to percolation.

Hot spots can dominate heat propagation in disordered systems.

The transition can be first or second order, separated by a tricritical point.

Abstract

The conventional theory of burning works well in the case of uniform media where all system parameters are spatially independent. We develop a theory of burning in disordered media. In this case, rare regions (hot spots) where the burning process is more effective than on average may control the heat propagation in an explosive sample. We show that most predictions of the theory of burning are quite different from the conventional case. In particular, we show that a system of randomly distributed hot spots exhibits a dynamic phase transition, which is similar to the percolation transition. Depending on parameters of the system the phase transition can be either first or second order. These two regimes are separated by a tricritical point. The above results may be applicable to dynamics of any over-heated disordered system with a first order phase transition.