Capillary forces between soft, elastic spheres

Abstract

The adhesive capillary force between two elastic spheres or a sphere and a plane is usually described by F_adh = 4πR*, where γ is the surface tension of the liquid and R* is the effective radius of the sphere(s). With approximate analytical calculations we show that for soft materials and radii larger than 5r³E²/γ² (r: radius of curvature of the liquid and E: Young's modulus) the capillary force increases more steeply and scales with R*² . This result is confirmed by finite element simulations. It may be relevant for an understanding of bioadhesion of insects and tree frogs and for an understanding of film formation from dispersions of soft particles.