Deformation of a Solid Film with Surface Tension by a Liquid Drop

A drop placed under a solid thin film causes it to bulge due to the action of liquid surface tension, Laplace pressure, difference in surface tension on two sides of the film, and gravity. Deformation is resisted by solid surface tension, bending, and in-plane stretching. For sufficiently thin films and small drops, the film mainly carries tension and the deformed configuration can be obtained simply by force balance of tensions at the contact line. In this work, we examine more closely the conditions under which this simplified situation exists. We show that generally the effect of surface tension asymmetry on two sides of the film is negligible, as is the effect of gravity on the local deformed shape. Further, we show that for sufficiently thin films, bending affects the solution only in a boundary layer near the contact region and that tensions in the films can still be estimated from force balance.