多相材料的扩散界面方法：能量变分法
Diffuse Interface Methods for Multiple Phase Materials: An Energetic Variational Approach
摘要：
在本文中，我们介绍了一个扩散界面模型，用于描述涉及多个（两个或多个）相的混合物的动力学。通过能量变分法导出耦合流体动力学系统。系统的总能量包括动能和混合（界面）能。应用最小作用量原理（或虚功原理）推导动力学的保守部分，重点是混合能产生的应力张量的可逆部分。动态的耗散部分，然后通过一个耗散函数的能量法，在最小能量耗散的Onsager原则。最后的系统，由一组耦合的时间相关的偏微分方程，反映了各种保守力和耗散力之间的平衡，并支配速度和相场的演变。为了证明所提出的模型的适用性，已经进行了一些二维模拟，包括（1）在平衡的三相接触线处的力平衡，（2）上升的气泡穿透流体-流体界面，和（3）固体颗粒落入二元流体。在固体表面的滑移的影响已被检查与接触线运动和夹断现象。
英文摘要：
In this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy of the system includes the kinetic energy and the mixing (interfacial) energies. The least action principle (or the principle of virtual work) is applied to derive the conservative part of the dynamics, with a focus on the reversible part of the stress tensor arising from the mixing energies. The dissipative part of the dynamics is then introduced through a dissipation function in the energy law, in line with the Onsager principle of least energy dissipation. The final system, formed by a set of coupled time-dependent partial differential equations, reflects a balance among various conservative and dissipative forces and governs the evolution of velocity and phase fields. To demonstrate the applicability of the proposed model, a few two-dimensional simulations have been carried out, including (1) the force balance at the three-phase contact line in equilibrium, (2) a rising bubble penetrating a fluid-fluid interface, and (3) a solid particle falling in a binary fluid. The effects of slip at solid surface have been examined in connection with contact line motion and a pinch-off phenomenon.
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