Thermal explosion: Escape times in the uniform temperature approximation. Part 1. - Effects of parameter perturbations

We consider the classical self-heating single reaction in a well stirred medium (the Semenov model) in a condition just beyond critical, i.e. in a condition where it will just exhibit thermal runaway. We calculate, by means of singular perturbation techniques, the time for the system to 'escape' from the critical temperature region when each of three control parameters is varied so as to exceed criticality. We demonstrate the need for careful re-scaling of the problem depending on which control parameter is varied (we consider ambient temperature, initial reactant concentration or pressure and vessel surface/volume ratio). Classical results for this problem are shown to be quantitatively in error, although correct in order of magnitude. Some mathematical obscurities in the latter are also clarified.