Transition from thermal runaway to propagating flames

In analysing thermal runaway in reactive-diffusive systems, it can be seen that diffusion and conduction become significantly reduced in importance towards the final stages. As a result, these diffusive effects play a negligible role in the early structure of the reaction waves that finally emerge from an ignition kernel. These flames simply travel too fast to be genuinely self-propagating and move by virtue of the fact that the induction process causes some points to ignite before other points. It is convenient, therefore, to refer to these waves of chemical activity as 'induction flames'. As they slow down, however, diffusion becomes important again until, after an appropriate transition, self-propagating reaction waves are able to emerge. A simple unit Lewis number model is used to represent the final stage of thermal runaway via a temperature sensitive one-step exothermic reaction. With this, the progress of the transition from reaction runaway to self-propagating flames is described using a large activation energy asymptotic analysis.