Solid surface tension measured by a liquid drop under a solid film

We show that a drop of liquid a few hundred microns in diameter placed under a solid, elastic, thin film (∼10 μm thick) causes it to bulge by tens of microns. The deformed shape is governed by equilibrium of tensions exerted by the various interfaces and the solid film, a form of Neumann's triangle. Unlike Young's equation, which specifies the contact angles at the junction of two fluids and a (rigid) solid, and is fundamentally underdetermined, both tensions in the solid film can be determined here if the liquid-vapor surface tension is known independently. Tensions in the solid film have a contribution from elastic stretch and a constant residual component. The residual component, extracted by extrapolation to films of vanishing thickness and supported by analysis of the elastic deformation, is interpreted as the solid-fluid surface tension, demonstrating that compliant thin-film structures can be used to measure solid surface tensions.