In this paper, a hybrid lattice-Boltzmann finite-difference method is developed for the simulation of ternary fluids near immersed solid objects of general shapes. The flow equations are solved by the lattice-Boltzmann method and the coupled Cahn–Hilliard equations for interface evolutions are solved by the finite-difference method. A special implementation of the wetting boundary condition on a surface of general shapes immersed inside the domain was extended for ternary fluids within the phase-field framework with no need to use complicated interpolations. Several two and three dimensional problems with three immiscible fluids were studied by using the proposed method and the results agree well with analytical predictions and/or previous numerical and experimental studies. In particular, the inclusion of properly chosen free energy to handle total spreading enabled us to numerically reproduce the encapsulation of a small droplet by another bigger one of different component on a round fiber. The proposed method is expected to be useful to investigate a variety of multiphase problems involving ternary fluids and surfaces with different configurations, including the challenging total spreading regime.

中文翻译：

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一般形状浸没固体附近三元流体的混合晶格-玻尔兹曼有限差分模拟

在本文中，开发了一种混合格子-玻尔兹曼有限差分方法，用于模拟一般形状的浸入固体附近的三元流体。流动方程通过格子-玻尔兹曼方法求解，界面演化的耦合 Cahn-Hilliard 方程通过有限差分方法求解。浸入域内的一般形状表面上的润湿边界条件的特殊实现被扩展到相场框架内的三元流体，无需使用复杂的插值。使用所提出的方法研究了具有三种不混溶流体的几个二维和三维问题，结果与分析预测和/或先前的数值和实验研究非常吻合。特别是，the inclusion of properly chosen free energy to handle total spreading enabled us to numerically reproduce the encapsulation of a small droplet by another bigger one of different component on a round fiber. 所提出的方法有望用于研究涉及具有不同配置的三元流体和表面的各种多相问题，包括具有挑战性的总扩散机制。