The Scaling of Nonequilibrium Fluctuations in Gaseous Thermal Explosions

Closed gaseous systems are considered in contact with a heat bath, undergoing a thermal explosion in the rarified gas regime (0.02–0.06 atm.) where the effect of turbulent fluctuations in temperature and acoustic fields on the reaction rate is negligible. This situation is chosen to elucidate the stochastic nature of the ignition processes. An ensemble of combustion experiments is treated where in some replicas, the explosion is accelerated while in others, it is retarded. The influence of spatially localized temperature inhomogeneities on the stochastic ignition process is examined. The induction period is calculated making use of the time‐dependence of the probability distribution of temperatures over the ensemble. This induction period is identified with the Kramers mean passage time corresponding to a critical fluctuation‐induced diffusion across a barrier in an unsymmetric bistable potential. The potential is determined from the competition between the heat production given by the exothermic reaction and the heat removal process. One of the potential wells corresponds to the stationary combustion regime and the other well, to the explosive regime. The critical fluctuations are confined to a virtual volume corresponding to a hot spot whose size is determined from generalized fluctuation‐dissipation theory. As an example, the experimentally measured induction periods for the explosive decomposition of ethyl azide are found to be in very good agreement with our predictions. This treatment successfully explains the discrepancies which arise for the size‐dependence of the induction period and the Frank‐Kamenetsky constant when comparing results from classical Semenov theory and experimental evidence of premature explosions.