Theory of chemical fluctuations in thermal explosions

Abstract

Autoignition phenomena in combustion problems exhibit a remarkable random behavior. We show on a simple model of an exothermic reaction that the phenomena has strong analogies with the transient behavior of a chemical explosion (Malthus model). These analogies lead to the construction of a simple theory of fluctuations. This theory is a natural extension of the theory already developed for the transient behavior associated with the Malthus-Verhulst problem and laser instability. Although we study only a very simple model, the approach that we propose is expected to be valid also in more complicated and realistic cases.