Forces between a stiff and a soft surface

The contact between a sphere and a planar half space, one being rigid and the other elastic (or between two elastic spheres), can be described by the JKR theory of Johnson, Kendall and Roberts (Proc. R. Soc. Lond. A 1971, 324, 301). One assumption of JKR theory is that the characteristic length scale L ≈ w/E is much smaller than the radius R of the sphere; where w is the work of adhesion and E is the Young's modulus of the soft, elastic body. Relative deformations for a mechanical contact increase with increasing L and decreasing particle size R. Experiments show that up to at least L/R = 0.2, JKR theory predicts the correct dependencies between the contact radius, the indentation and the load. However, when R ≫ L is no longer satisfied, the change in total free surface area due to deformation needs to be considered. Then, elastocapillary effects start playing a significant role. In addition to discussing theory and experiments of pure solid contacts, the effect of elastic deformation on capillary and hydrodynamic forces is discussed. Finally, we consider the interaction of hollow capsules as one example of a deformable body that is still formed from a stiff material.