Elastocapillarity modeling of multiphase flow-induced solid deformation using volume of fluid method

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.