Stochastic theory of ignition processes

We consider a closed gaseous system immersed in a heat bath undergoing a thermal explosion. The effects of instantaneous fluctuations in the temperature on the heat removal mechanism and on the reaction rate are considered. The intensity of the fluctuations in situations far from equilibrium is determined by calculating the temperature self-correlation. This quantity scales with the inverse of an effective volume Ω obtained from generalized fluctuation-dissipation theory. This determines a virtual system corresponding to the localized ignition process, possibly leading to a global runaway. The induction period is identified with the Kramers mean passage time for diffusion across a kinetic barrier. The induction period is thus shown to be dependent on the fluctuation volume Ω. The diffusion process is hastened by the critical fluctuations. The explosive decomposition of ethyl azide was selected to test the theory and the results exhibit very good agreement with experimental data. Our treatment resolves the previous discrepancy between the predictions rooted in the classical Frank-Kamenetsky treatment and the premature ignition observed experimentally.