Abstract
Our aim is to describe phase transitions in a system of an arbitrary number of components and phases. Based on a gradient flow for the entropy (including surface anisotropy) we propose a phase field model that can be regarded as an extension of the Penrose-Fife model and that is thermodynamically consistent. By formal asymptotic expansions we see that the considered domain splits into several phases. We define the surface entropies on the phase boundaries and then we can show that in the limit the model satisfies the Gibbs—Thomson relation and other conditions known from classical sharp interface models. Finally, some possibilities to linearize the equations are outlined.
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Garcke, H., Nestler, B., Stinner, B. (2003). A Phase-field Model for the Solidification Process in Multicomponent Alloys. In: Emmerich, H., Nestler, B., Schreckenberg, M. (eds) Interface and Transport Dynamics. Lecture Notes in Computational Science and Engineering, vol 32. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07969-0_12
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DOI: https://doi.org/10.1007/978-3-662-07969-0_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07320-5
Online ISBN: 978-3-662-07969-0
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