Drops on soft solids: free energy and double transition of contact angles

The equilibrium shape of liquid drops on elastic substrates is determined by minimizing elastic and capillary free energies, focusing on thick incompressible substrates. The problem is governed by three length scales: the size of the drop R, the molecular size a and the ratio of surface tension to elastic modulus gamma/E. We show that the contact angles undergo two transitions upon changing the substrate from rigid to soft. The microscopic wetting angles deviate from Young's law when gamma/(Ea) >> 1, while the apparent macroscopic angle only changes in the very soft limit gamma/(ER) >> 1. The elastic deformations are worked out for the simplifying case where the solid surface energy is assumed to be constant. The total free energy turns out to be lower on softer substrates, consistent with recent experiments.