Droplets sitting on thin elastic sheets: a study with the boundary element method

Abstract Elasto-capillarity of a droplet wetting an elastic sheet provides an interesting system, both for fundamental and applied research. The droplet sinks into the sheet and assumes the shape of a lens. To determine the equilibrium shape in simulations, we formulate a boundary element method (BEM) extending our earlier approaches, and apply the BEM to three specific protocols for the boundary conditions of the sheet. For a clamped elastic sheet, we use various morphological metrics to demonstrate that the lens shape crucially depends on the sheet thickness. Stretching the sheet isotropically allows for an additional control parameter to influence the droplet shape and the tension in the sheet, which we quantify by radial profiles of the azimuthal and radial elastic stresses. We further demonstrate how the focal length of a liquid lens can be tuned by varying the applied tension. Finally, stretching the sheet along one direction elongates the droplet, and the sheet shows folds and dimples. Graphical abstract A droplet wetting a clamped elastic sheet assumes a lens shape (bottom); stretching the sheet along one direction, the droplet also elongates and the sheet shows folds and dimples (top)