Droplets on an elastic membrane: Configurational energy balance and modified Young equation. (May 2020) - Liu, Tianshu; Liu, Zezhou; Jagota, Anand; Hui, Chung-Yuen
Abstract: We study wetting of an elastic membrane whose surface can resist stretch by surface stress. Through energy minimization, we obtain the general equilibrium equations and a configurational energy balance equation at the contact line, i.e., the Young equation, modified for an elastic membrane. We use a 3D large deformation formulation with general elastic constitutive behavior for the membrane and its surfaces. Our results allow for non-flat reference membrane shape, non-uniform and anisotropic tension and dependence of surface stress on surface strain – the generalized Shuttleworth effects. We use two examples to demonstrate the application of our theory: plane strain and axisymmetric wetting of an initially flat elastic membrane. A large deformation solution for an axisymmetric droplet on a deformable membrane is obtained numerically. We show that when surface elastic moduli for solid–vapor and solid–liquid interfaces are different, continuity of membrane strain, a key assumption used in many previous studies, no longer holds at the contact line.