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Two-scale model of phase transitions

✍ Scribed by Augusto Visintin

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
880 KB
Volume
106
Category
Article
ISSN
0167-2789

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✦ Synopsis

Phase transition in solid-liquid systems is described, combining the Gibbs-Thomson law with the classical Stefan model. Here solid nucleation is the main concern. A model is proposed, which accounts for the smallness of the capillarity length with respect to the macroscopic scale. Transition from the finer to the coarser length scale is provided by convolution with a Gaussian kernel. This accounts for fast diffusion of latent heat of fusion, and allows one to represent solid nucleation at low undercooling. A new description of so-called mushy regions is thus achieved.

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## Abstract We study a model for liquid‐phase epitaxy that is based on a continuum description of the transport processes in the liquid and a Burton–Cabrera–Frank (BCF) model for the growth of the solid by epitaxy. In order to develop a model that is capable to incorporate structures of a very smal