A continuum theory for first‐order phase transitions based on the balance of structure order |
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Authors: | M Fabrizio C Giorgi A Morro |
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Institution: | 1. Department of Mathematics, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy;2. Department of Mathematics, Via Valotti 9, 25133 Brescia, Italy;3. University of Genova, DIBE, Via Opera Pia, 11a, 16145 Genova, Italy |
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Abstract: | First‐order phase transitions are modelled by a non‐homogeneous, time‐dependent scalar‐valued order parameter or phase field. The time dependence of the order parameter is viewed as arising from a balance law of the structure order. The gross motion is disregarded and hence the body is regarded merely as a heat conductor. Compatibility of the constitutive functions with thermodynamics is exploited by expressing the second law through the classical Clausius–Duhem inequality. First, a model for conductors without memory is set up and the order parameter is shown to satisfy a maximum theorem. Next, heat conductors with memory are considered. Different evolution problems are established through a system of differential equations whose form is related to the manner in which the memory property is represented. Copyright © 2007 John Wiley & Sons, Ltd. |
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Keywords: | phase changes evolution equation structure order heat conductor |
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