Macroscopic models for melting derived from averaging microscopic Stefan problems I: Simple geometries with kinetic undercooling or surface tension

A. A. LACEY; L. A. HERRAIZ

doi:10.1017/S0956792599004027

Abstract

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A mushy region is assumed to consist of a fine mixture of two distinct phases separated by free boundaries. For simplicity, the fine structure is here taken to be periodic, first in one dimension, and then a lattice of squares in two dimensions. A method of multiple scales is employed, with a classical free-boundary problem being used to model the evolution of the two-phase microstructure. Then a macroscopic model for the mush is obtained by an averaging procedure. The free-boundary temperature is taken to vary according to Gibbs–Thomson and/or kinetic-undercooling effects.

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Macroscopic models for melting derived from averaging microscopic Stefan problems I: Simple geometries with kinetic undercooling or surface tension

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