Criticality and Induction Time of Hot Spots in Detonating Heterogeneous Explosives

Detonation reaction in physically heterogeneous explosives is--to an extent that depends on multiple material attributes--likewise heterogeneous. Like all heterogeneous reaction, detonation heterogeneous reaction begins at nucleation sites, which, in this case, comprise localized regions of higher-than-average temperature--so-called hot spots. Burning grows at, and then spreads from these nucleation sites, via reactive-thermal (R-T) waves, to consume the interstitial material. Not all hot spots are consequential, but only those that are 1) supercritical, and 2) sufficiently so as to form R-T waves before being consumed by those already emanating from neighboring sites. I explore aspects of these two effects by deriving simple formulae for hot spot criticality and the induction time of supercritical hot spots. These results serve to illustrate the non-intuitive, yet mathematically simplifying, effects of extreme dependence of reaction rate upon temperature. They can play a role in the development of better reactive burn models, for which we seek to homogenize the essentials of heterogeneous detonation reaction without introducing spurious complexity.