Liquid drops on soft solids

A sessile drop can elastically deform a substrate by the action of capillary forces. The typical size of the deformation is given by the ratio of surface tension and the elastic modulus, !/E, which can reach up to 10-100 microns for soft elastomers. In this report we theoretically show that the contact angles of drops on such a surface exhibit two transitions when increasing !/E: (i) the microsocopic geometry of the contact line first develops a Neumann-like cusp when !/E is of the order of few nanometers, (ii) the macroscopic angle of the drop is altered only when !/E reaches the size of the drop. Using the same framework we then show that two neighboring drops exhibit an e↵ective interaction, mediated by the deformation of the elastic medium. This is in analogy to the well-known Cheerios e↵ect, where small particles at a liquid interface attract eachother due to the meniscus deformations. We find that drop-drop interactions have both an attractive and repulsive regime depending on their separation distance, with the typical cross-over from attractive to repulsive taking place at a separation of a few drop diameters.