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Abstract
The critical conditions for vigorous burning of spherical carbon particles are derived using asymptotic techniques for large Zel'dovich numbers. The particle lifetime and the temperature history are obtained for both supercritical and subcritical regimes, when a carbon particle is suddenly exposed to a stagnant high temperature oxidizing atmosphere. For Damkohler numbers below a critical number, that is, the subcritical regime, slow burning occurs in the carbon particle. That means that throughout the life of the particle, the chemical reaction is controlled by kinetics. In this regime, the lifetime is extremely long. On the other hand, for Damkohler numbers above the critical one, the process ends with a rapid increase of temperature finally reaching a reaction controlled by diffusion. In this supercritical regime, the life is relatively short. For values of the reduced Damkohler number very close to the critical one, a Ricatti equation is derived for the non-dimensional temperature of the particle, the solution of which defines whether the particle undergoes subcritical or supercritical behavior.
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