In this study, we propose an immersed boundary-phase field fluid-surfactant model that incorporates moving contact lines on complex geometries. To accurately capture the interface, we introduce an additional phase field variable to represent the solid phase, which remains fixed throughout the process. The modified Cahn–Hilliard equations are utilized to describe the interface. In order to address stiffness issues, a stabilization technique is incorporated into the calculations. To prevent streamlines from penetrating into solid obstacles, a boundary condition-enforced immersed boundary method is applied at the solid boundaries. The desired contact angle is ensured using the characteristic moving contact line method. All variables are treated independently in the computations, and the numerical results demonstrate the accuracy and excellent performance of our model on curved substrates with surfactants.

中文翻译：

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弯曲基底上具有移动接触线的浸没边界相场流体表面活性剂模型

在这项研究中，我们提出了一种浸没边界相场流体表面活性剂模型，该模型结合了复杂几何形状上的移动接触线。为了准确捕获界面，我们引入了一个额外的相场变量来表示固相，该变量在整个过程中保持固定。修正后的 Cahn-Hilliard 方程用于描述界面。为了解决刚度问题，计算中纳入了稳定技术。为了防止流线穿透固体障碍物，在固体边界处应用边界条件强制浸入边界方法。使用特有的移动接触线方法确保所需的接触角。所有变量在计算中都是独立处理的，数值结果证明了我们的模型在含有表面活性剂的弯曲基材上的准确性和优异的性能。