Abstract
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.
Original language | English |
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Pages (from-to) | 153-169 |
Number of pages | 17 |
Journal | European Journal of Applied Mathematics |
Volume | 11 |
Issue number | 2 |
Publication status | Published - 2000 |