Tug-of-war between liquids and membranes

Predicting the deformation behavior of an initially stressed membrane subjected to liquid self-weight is nontrivial. Experimental observation indicates that in the tug-of-war competition between liquids and membranes, which side will prevail does not depend on the liquid volume. However, the existing models cannot explain this counterintuitive phenomenon. With the aim of understanding the underlying mechanics behind those unexpected features, we propose a theoretical model for deriving the configuration of membrane–liquid interactions. The analytical solutions for one-dimensional and two-dimensional axisymmetric membrane deflections are derived by combining the linear membrane theory and configuration-dependent loading. These solutions yield quantitative predictions for the three types of configuration that are in excellent agreement with the experiments. Remarkably, we find that a dimensionless parameter concerning the liquid density, the size of the system, and the membrane tension controls the intensity of the membrane–liquid competition. Our model opens up a new perspective for studying fluid–structure interaction systems.