Effects of surface tension on the adhesive contact of a rigid sphere to a compliant substrate

In problems of indentation of an elastic half-space by a rigid sphere, the effects of surface tension outside the contact zone are not accounted for by classical theories of contact mechanics. However surface tension plays a dominant role in determining the mechanics of this adhesive contact when the half-space becomes very compliant and the sphere is very small. Using a finite element method (FEM), we present a numerical solution of such a problem, showing the transition between the classical Johnson-Kendall-Roberts (JKR) deformation and a liquid-like deformation in the absence of external load and gravity. The numerical model is in good agreement with previous experiments [R. W. Style et al., Nat. Commun., 2013, 4, 2728].