Abstract
The stability of the flat crystallization front of a dilute binary melt is investigated within the two-dimensional model of solidification taking into account the latent heat of fusion and the difference between thermal conductivities of the solid and liquid phases by the method of integral functionals with an unknown region of integration. The stationary problem of impurity diffusion in a crystallizing melt and heat propagation in a limited region Ω is solved within the second-order approximation in the amplitude of deviation from a flat crystallization front. An expression for the functional is obtained whose value is proportional to the energy dissipated in the region Ω owing to heat and mass transfer processes. The results obtained are compared with the literature data on the stability of the flat crystallization front of a binary melt.
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