The interaction between fluids and solids is of great importance in different fields of science and engineering. Such interactions have become of great interest not only at the macroscale, but also at the micro and sub-millimetric scales dominated by capillary forces. At the microscale, the effect of surface tension at the interfacial boundaries plays an important role in defining flow patterns and regimes for a system of immiscible multiphase fluids. Such dynamic forces bring about the deformation of surrounding solid structures. In this paper, we present a multiphase fluid solver, with preferential-wetting boundary conditions at the fluid–solid interface, coupled together with a hyperelastic solid solver via a partitioned approach. The multiphase fluid-solid interaction (FSI) problem is solved by employing the Volume of Fluid (VOF) method for transporting a scalar function which acts as a phase indicator in the multiphase problem. The scalar transport equation is solved on the same mesh as the Navier-Stokes equation to avoid errors from projection. Sharpening of the fluid-fluid interface is achieved algebraically using artificial compression, enforced by Multidimensional Universal Limiter with Explicit Solution (MULES). The surface tension forces are obtained using Filtered Surface Force (FSF) model which filters out unphysical fluxes. The formulation of the multiphase FSI problem is based on the use of Arbitrary Lagrangian Eulerian (ALE). FSI interface displacements are relaxed using the Interface Quasi-Newton with Inverse Least Square root-finding relaxation technique (IQN-ILS). We then validate the model by comparing the present numerical results to experimental data for a static droplet on a soft substrate. The model shows good agreement with experimental data and captures the resulting deformation due to excess Laplace pressure. The model is also tested for a dynamic droplet case, and deformation in a microchannel with obstacles.

流体与固体之间的相互作用在科学和工程的不同领域中非常重要。这种相互作用不仅在宏观上，而且在由毛细作用力主导的微观和亚毫米尺度上都引起了极大的兴趣。在微观尺度上，界面张力在界面边界的影响在为不混溶的多相流体系统定义流型和状态方面起着重要作用。这种动力导致周围实体结构的变形。在本文中，我们提出了一种多相流体求解器，它在流固界面处具有优先润湿边界条件，并通过分区方法与超弹性固体求解器耦合在一起。多相流固耦合（FSI）问题是通过采用体积体积（VOF）方法传输标量函数来解决的，该标量函数充当多相问题中的相指示符。在与Navier-Stokes方程相同的网格上求解标量输运方程，以避免投影误差。流体-流体界面的锐化通过使用人工压缩进行代数实现，该压缩由具有显式解决方案（MULES）的多维通用限制器实施。使用过滤表面力（FSF）模型获得表面张力，该模型可以滤除非物理通量。多相FSI问题的表述基于任意拉格朗日欧拉（ALE）的使用。FSI界面位移是使用带有反最小二乘方根查找松弛技术（IQN-ILS）的界面拟牛顿松弛的。然后，我们通过将当前数值结果与在软性基材上的静态液滴的实验数据进行比较来验证模型。该模型与实验数据显示出良好的一致性，并捕获了由于拉普拉斯压力过大而导致的变形。还针对动态液滴情况以及在带有障碍物的微通道中变形对模型进行了测试。