The Gibbs-Thompson relation within the gradient theory of phase transitions |
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Authors: | Stephan Luckhaus Luciano Modica |
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Institution: | (1) Institut füt Angewandte Mathematik, Universität Bonn, Germany;(2) Dipartimento di Matematica, Università di Pisa, Italy |
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Abstract: | This paper discusses the asymptotic behavior as 0+ of the chemical potentials associated with solutions of variational problems within the Van der Waals-Cahn-Hilliard theory of phase transitions in a fluid with free energy, per unit volume, given by 2¦¦2+ W(), where is the density. The main result is that is asymptotically equal to E/d+o(), with E the interfacial energy, per unit surface area, of the interface between phases, the (constant) sum of principal curvatures of the interface, and d the density jump across the interface. This result is in agreement with a formula conjectured by M. Gurtin and corresponds to the Gibbs-Thompson relation for surface tension, proved by G. Caginalp within the context of the phase field model of free boundaries arising from phase transitions. |
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