General dynamical sharp-interface conditions for phase transformations in viscous heat-conducting fluids
General dynamical sharp-interface conditions for phase transformations in viscous heat-conducting fluids
复制标题
DOI：
10.1017/s0022112007005587
复制
发表时间：
2007-05
影响因子：
3.7
通讯作者：
Daniel M. Anderson;P. Cermelli;E. Fried;M. Gurtin;G. McFadden
中科院分区：
文献类型：
--
作者：
Daniel M. Anderson;P. Cermelli;E. Fried;M. Gurtin;G. McFadden
我们开发了一套完整的方程组的演变的一个尖锐的界面分离两个流体相进行改造。除了质量、线性动量和能量的常规平衡之外，这些方程还包括从晶体生长理论中熟悉的吉布斯-汤姆森方程的对应物。这个附加的方程是在一个几何框架内考虑构形力而产生的。尽管构型力的概念对于描述具有自然参考构型的材料（例如结晶固体）而言是良好发展和理解的，但是关于它们在不具有优选参考状态的材料（例如粘性流体）中的作用几乎没有做。因此，我们提供了一个全面的讨论组态的力量，平衡的组态动量，和组态热力学，不需要选择的参考配置。从我们的理论所产生的一般演化方程帐户的体相和界面的热力学结构和体相的粘性和热耗散和界面上的粘性耗散。由于这些方程的复杂性，我们提供了一个简化的本构假设和近似的基础上，在文献中常见的相变方程系统。使用这些简化的方程，我们应用的理论的径向对称问题的冷凝液滴到汽相。
We develop a complete set of equations governing the evolution of a sharp interface separating two fluid phases undergoing transformation. In addition to the conventional balances for mass, linear momentum and energy these equations include also a counterpart of the Gibbs–Thomson equation familiar from theories for crystal growth. This additional equation arises from a consideration of configurational forces within a thermodynamical framework. Although the notion of configurational forces is well-developed and understood for the description of materials, such as crystalline solids, that possess natural reference configurations, little has been done regarding their role in materials, such as viscous fluids, that do not possess preferred reference states. We therefore provide a comprehensive discussion of configurational forces, the balance of configurational momentum, and configurational thermodynamics that does not require a choice of reference configuration. The general evolution equations arising from our theory account for the thermodynamic structure of the bulk phases and the interface and for viscous and thermal dissipation in the bulk phases and for viscous dissipation on the interface. Because of the complexity of these equations, we provide a reduced system of equations based on simplified constitutive assumptions and approximations common in the literature on phase transformations. Using these reduced equations, we apply the theory to the radially symmetric problem for the condensation of a liquid drop into the vapour phase.