Elastic wetting: Substrate-supported droplets confined by soft elastic membranes

While classical wetting is well captured by the famous Young's equation and classical bulge and blister models are readily available, there is limited understanding of a micro- or nano-scale droplet being covered by an ultrasoft elastic membrane. We call this phenomenon elastic wetting to feature the interplay between the liquid's surface tension and the membrane's elastic deformation. Examples of elastic wetting include cell blebs and 2D material bubbles, where the membrane thickness ranges from microns to sub-nanometers. In this work, we study the equilibrium of elastic wetting and solve for the profiles and the pressure-volume relations of the membrane-confined droplets. We show that in elastic wetting, the pressure across the membrane/droplet interface can be described by a simple superposition of the Young-Laplace equation and the nonlinear membrane equation. Furthermore, nonlinear elasticity, geometric nonlinearity, and surface tension, together with membrane-substrate adhesion, interweave at the contact line, leading to rich membrane-confined droplet configurations. Finally, we examine the effect of substrate compliance on elastic wetting and find that the rigid substrate assumption approximates well for most of the existing experiments in the literature. Our results provide fundamental mechanistic insights into the various phenomena of elastic wetting as well as viable means to extract physical parameters including the bubble pressure and the interface energies.