SIAM Journal on Applied Mathematics, Volume 80, Issue 1, Page 572-598, January 2020.
In this paper, we study a phase-field model for the dynamics of a solid particle in two-phase flow. The governing system in our model is a coupled system of Navier--Stokes equations, Cahn--Hillard equations for the multiphase flow, and Newton's law for the motion of the particle. The effect of the wettability of the particle and the motion of the contact line are modeled by the generalized Navier boundary condition. To show that our model is physically consistent, we show that the model can be derived from the principle of minimum energy dissipation (entropy production) and has the energy decaying property. Using the method of matched asymptotic expansions, we also derive the sharp interface limit for our model.

中文翻译：

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两相流中流体-颗粒相互作用的能量衰减相场模型

SIAM应用数学杂志，第80卷，第1期，第572-598页，2020
年1月。在本文中，我们研究了两相流中固体颗粒动力学的相场模型。我们模型中的控制系统是Navier-Stokes方程，用于多相流的Cahn-Hillard方程和用于粒子运动的牛顿定律的耦合系统。粒子的可湿性和接触线的运动的影响通过广义的Navier边界条件进行建模。为了表明我们的模型在物理上是一致的，我们表明该模型可以从最小能量耗散（熵产生）原理推导而来，并且具有能量衰减特性。使用匹配渐近展开法，我们还为模型得出了尖锐的界面极限。