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Young's law fails on soft solid and liquid substrates where there aresubstantial deformations near the contact line. On liquid substrates, this iscaptured by Neumann's classic analysis, which provides a geometricalconstruction for minimising the interfacial free energy. On soft solids, thetotal free energy includes an additional contribution from elasticity. Alinear-elastic model incorporating an out-of-plane restoring force due to solidsurface tension was recently shown to accurately predict the equilibrium shapeof a thin elastic film due to a large sessile droplet. Here, we extend thismodel to find substrate deformations due to droplets of arbitrary size. Whilethe macroscopic contact angle matches Young's law for large droplets, itmatches Neumann's prediction for small droplets. The cross-over droplet size isroughly given by the ratio of the solid's surface tension and elastic modulus.At this cross-over, the macroscopic contact angle increases, indicating thatthe substrate is effectively less wetting. For droplets of all sizes, themicroscopic behaviour near the contact line follows the Neumann constructiongiving local force balance.

Static wetting on deformable substrates, from liquids to soft solids