In this study, two schemes to treat fluid-solid interaction on complex boundaries are proposed and solved in the framework of lattice Boltzmann method. The schemes are applied on the phase-field-based wettability implementation methods for binary and ternary fluids to simulate static contact angle on a circular surface generated by the staircase approximation. For the binary system, surface-energy and geometric wetting conditions are adopted, while for the ternary system, surface-energy model with two discretization schemes resulting in explicit and implicit wetting conditions are developed and examined. It is proven that the implicit wetting condition approximating the value of order parameters on the boundary node, as the average of their value between the neighboring fluid node and solid node, enhances the accuracy of predicted contact angles. For modeling of contact angle on the circular surface and identifying the direction of normal vectors required for incorporating wetting condition, the gradient of fluid-solid field is calculated. Two methods namely, round-off and interpolation describing how the information of neighboring nodes given the direction of normal vector on the boundary nodes should be used, are discussed. It is illustrated that results of the interpolation method exhibit a good agreement with the analytical solution as opposed to the round-off when tested in the case of static contact angle on a circular surface for both binary and ternary systems. Finally, it is shown incorporating different wetting conditions with the appropriate way of handling normal vectors and in combination with the conservative phase-field model can model static contact angle at high-density ratios for both binary and ternary fluids with good accuracy.

在这项研究中，在格子玻尔兹曼方法的框架内提出并解决了两种处理复杂边界上流固相互作用的方案。该方案应用于二元和三元流体的基于相场的润湿性实现方法，以模拟阶梯近似生成的圆形表面上的静态接触角。对于二元系统，采用表面能和几何润湿条件，而对于三元系统，开发和检验具有两种离散化方案的表面能模型，导致显式和隐式润湿条件。事实证明，近似边界节点上阶参数值的隐式润湿条件，作为相邻流体节点和固体节点之间的值的平均值，提高了预测接触角的准确性。为了模拟圆形表面上的接触角并确定结合润湿条件所需的法向矢量的方向，计算了流体-固体场的梯度。讨论了两种方法，即舍入和插值，描述了如何使用给定边界节点上的法向量方向的相邻节点的信息。这表明，在二元和三元系统的圆形表面上的静态接触角的情况下测试时，插值方法的结果与解析解表现出良好的一致性，而不是四舍五入。最后，