A continuum theory for first-order phase transitions based on the balance of structure order

✍ Scribed by M. Fabrizio; C. Giorgi; A. Morro

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 188 KB
• Volume: 31
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.930

✦ Synopsis

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.