On the mechanism of triggering the transition from smoldering to flaming

We consider the transition from smoldering to flaming. Though there have been numerous experimental studies of this topic, it has been virtually untouched theoretically. Rather than investigating the details of either the transition process or the subsequent flaming, we focus on determining the mechanism and the conditions that trigger the transition. We consider a planar, forward smolder wave driven by a constant forced flow of gas containing oxidizer. The kinetic scheme consists of three reactions: pyrolysis, fuel oxidation and char oxidation. There have been a number of speculations about the nature of the triggering mechanism, including the gaseous reactions, the char oxidation reaction, destruction of the porous matrix through which the smolder wave propagates, and others. However, no mechanism has, as yet, been shown to be capable of acting as the triggering mechanism. We show that the char oxidation reaction hardly affects the characteristics of smolder wave propagation due to its small reaction rate, though under appropriate conditions, it can act as the trigger for the transition to flaming due to its ability to self-accelerate. Specifically, we introduce the concept of, and then compute, a quantity which we term the flaming distance L_F. This is the distance that a propagating smolder wave initiated at the gas flux inlet, travels before the char oxidation reaction spontaneously self-accelerates, resulting in an eruption of the temperature in the smolder front, i.e., the smolder wave propagates for a long time until it reaches L_F. A transition to flaming then occurs. L_F depends on the physicochemical parameters of the fuel and the products and external parameters, e.g., the velocity and composition of the incoming gas, heat loss. We show that smolder waves propagating in samples of length L do (do not) exhibit a transition to flaming if L_F < L (L_F > L).