A numerical method for simulating three-phase flows with moving contact lines on arbitrarily complex surfaces is developed in the framework of the lattice Boltzmann method. In this method, the immiscible three-phase flow is modeled through a multiple-relaxation-time color-gradient model, which not only allows for a full range of interfacial tensions but also produces stable outcomes for a wide range of viscosity ratios. A characteristic line model is introduced to implement the wetting boundary condition, which is not only easy to implement but is also able to handle arbitrarily complex boundaries with prescribed contact angles. The developed method is first validated by the simulation of a Janus droplet resting on a flat surface, a perfect Janus droplet deposited on a cylinder, and the capillary intrusion of ternary fluids for various viscosity ratios. It is then used to study a compound droplet subject to a uniform incoming flow passing through a multipillar structure, where three different values of surface wettability are considered. The simulated results show that the surface wettability has significant impact on the droplet dynamic behavior and final fluid distribution.

中文翻译：

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曲面上具有移动接触线的三相流的格子 Boltzmann 模拟

在格子 Boltzmann 方法的框架内，开发了一种模拟任意复杂表面上具有移动接触线的三相流的数值方法。在这种方法中，不混溶的三相流通过多松弛时间颜色梯度模型进行建模，该模型不仅允许全范围的界面张力，而且在广泛的粘度比下产生稳定的结果。引入特征线模型来实现润湿边界条件，不仅易于实现，而且能够处理具有规定接触角的任意复杂边界。所开发的方法首先通过模拟停留在平坦表面上的 Janus 液滴进行验证，完美的 Janus 液滴沉积在圆柱体上，以及不同粘度比的三元流体的毛细侵入。然后，它用于研究受均匀流入流通过多柱结构的复合液滴，其中考虑了三种不同的表面润湿性值。模拟结果表明，表面润湿性对液滴动力学行为和最终流体分布有显着影响。