Because of the high activation energy involved in the Arrhenius laws, non-linear kinetic effects cannot be neglected even in first approximation in the dynamics of some flame fronts as for example in solid combustion. This is true even for small variations of the flame temperature. The situation is quite different in crystal growth where, the temperature of the interface Tf being always very close to the equilibrium temperature Te, kinetic effects are assumed to be negligible in a first approximation. By using singular methods originally developed in flame theory, this problem is revisited by solving a particular model for the diffuse interface. The results point out the limits of validity of the Gibbs-Thomson boundary condition. New phenomena that can be produced by non-linear kinetic effects even for (Tf-Te)/Te≪l are predicted, as for example the appearance of intermediate phases of a purely kinetic nature.
KeywordsFlame Front Flame Temperature Lewis Number Kinetic Effect Flame Speed
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