Abstract In this paper, a ternary phase-field based LBM, capable of handling high density ratios [O(1000)] and total spreading situations is presented. In order to improve the density ratio between three components, stable discretization incorporating mixed differentiating scheme (average of the biased and central schemes) is adopted, which instead of 8, involves 16 neighboring points to approximate the derivative terms. The multi-component Cahn-Hilliard equations are employed to track phasic evolution of the system. The bulk free energy in these equations is chosen in such a way that it enables the model to cope with total spreading problems, where one of the components is totally wetted by one, or both of the other fluids. Two LB equations are used to capture the interface between three incompressible-immiscible fluids, and another one for simulation of the hydrodynamic flow field. To demonstrate versatility and accuracy of the proposed model, a wide range of benchmark problems and numerical tests, including static and dynamic interaction of a bubble at liquid-liquid interface, ternary phase separation, binary and ternary Rayleigh-Taylor instability (RTI), and finally collision and coalescence between an oil droplet and a gas bubble that are rising in water due to the buoyancy force, are investigated. A good agreement is found between simulation results and available data/theoretical predictions. The simulation results of the bubble-droplet interaction reveals that the film drainage and coalescence times of the off-center collisions are higher compared to the head-on impacts, and these times increase with the horizontal distance separating the bubble and the droplet.

中文翻译：

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具有高密度比和模拟总扩散状态能力的三分量相场格子玻尔兹曼方法

摘要 在本文中，提出了一种基于三元相场的 LBM，能够处理高密度比 [O(1000)] 和总传播情况。为了提高三个分量之间的密度比，采用了包含混合微分方案（偏置和中心方案的平均值）的稳定离散化，它不是 8 个，而是涉及 16 个相邻点来近似导数项。采用多分量 Cahn-Hilliard 方程来跟踪系统的阶段演化。这些方程中的体积自由能的选择方式使模型能够处理总扩散问题，其中一个组件被一种或两种其他流体完全润湿。两个 LB 方程用于捕获三种不可压缩-不混溶流体之间的界面，另一个用于流体动力流场的模拟。为了证明所提出模型的多功能性和准确性，广泛的基准问题和数值测试，包括液-液界面气泡的静态和动态相互作用、三元相分离、二元和三元瑞利-泰勒不稳定性 (RTI)，以及最后，研究了由于浮力而在水中上升的油滴和气泡之间的碰撞和聚结。在模拟结果和可用数据/理论预测之间找到了很好的一致性。气泡-液滴相互作用的模拟结果表明，与正面碰撞相比，偏心碰撞的薄膜排水和聚结时间更高，