Inverted Cheerios effect: Liquid drops attract or repel by elasto-capillarity

Solid particles floating at a liquid interface exhibit a long-ranged attraction mediated by surface tension. In the absence of bulk elasticity, this is the dominant lateral interaction of mechanical origin. Here we show that an analogous long-range interaction occurs between adjacent droplets on solid substrates, which crucially relies on a combination of capillarity and bulk elasticity. We experimentally observe the interaction between droplets on soft gels and provide a theoretical framework that quantitatively predicts the migration velocity of the droplets. Remarkably, we find that while on thick substrates the interaction is purely attractive and leads to drop-drop coalescence, for relatively thin substrates a short-range repulsion occurs which prevents the two drops from coming into direct contact. This versatile, new interaction is the liquid-on-solid analogue of the "Cheerios effect". The effect will strongly influence the condensation and coarsening of drop soft polymer films, and has potential implications for colloidal assembly and in mechanobiology.