Dynamic Aspects of Spontaneous Ignition: Thermal Runaway Induced by Increasing Ambient Temperature

In this paper we consider an exothermic reaction obeying simple kinetics, with rate propto (concentration)^n and rate coefficient propto exp (-E/RT), effected under conditions of linearly increasing ambient temperature T_a. The treatment uses 'large activation energy asymptotics'. Critical conditions for the zero-order case constitute the natural reference point for asymptotic expansions, and the group ɛ = RT_ao/E is adopted here as the suitable small parameter. Three factors are involved; (i) the rate of change of ambient temperature, (ii) the rate of increase of reactant temperature that could occur under adiabatic conditions and (iii) the order of reaction, n. Normally one of these factors is dominant and the conditions for dominance are expressed in terms of a single exponent, k. When all three factors can participate on equal terms k takes the special value 2. Under these circumstances there is a particular rate of increase of ambient temperature that just compensates for the effects of reactant consumption and yields the same critical ignition temperature and other parameters as would be found for a zero-order reaction.