A ternary phase‐field model for wetting of soft elastic structures

Abstract

AbstractSoft wetting, that is, the interaction of liquid–fluid interfaces with deformable elastic structures, provides a rich variety of physical phenomena (stick‐slip motion, durotaxis, Shuttleworth effect, etc.) which are not yet understood. We propose a novel phase‐field approach to study such problems. The method uses two phase‐fields to describe the three domains (solid, liquid, ambient fluid) by the ternary Navier–Stokes Cahn–Hilliard equations. We use a recent phase‐field approach for fluid‐structure interaction to equip one phase with elastic properties. The resulting method is significantly simpler than all previous approaches for soft wetting, since no grids are used to represent the geometries. Accordingly, the method avoids grid‐based computation of interface curvature, mappings between different grids, complicated mesh generation, and retriangulation, while the elastic object can move freely through the computational domain. As a special feature, the elastic structure is for the first time represented as a neo‐Hookean Kelvin–Voigt–Maxwell material which makes it very versatile. The accuracy of the method is shown in a benchmark simulation of a droplet on an elastic substrate. The geometrical flexibility is illustrated by simulating a rotating solid object within a fluidic interface. Finally, we provide the first 3D simulations of soft wetting including solid surface tensions.