Abstract
The singularly perturbed system of differential equations describing metal particle ignition is analyzed. Two general types of combustion reactions are recognized, namely subcritical and supercritical. It is shown that there exists a so-called critical regime, which separates domains of subcritical and supercritical regimes. The critical regime is modelled by the special phase trajectory of the system, which includes the repulsive part with slow variation of the temperature of a metal particle and the thickness of the oxide film. The asymptotic formulae for the calculation of critical values of the modified Semenov number are obtained in the cases of parabolic and cubic laws of oxidation kinetics.
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