Interplay of dry and capillary adhesion in elastic solids and structures

Abstract Dry adhesion between solids relies on direct surface–surface interactions (such as van der Waals forces) that require intimate contact. In contrast, capillary adhesion occurs when a liquid bridge forms between surfaces and generates attractive forces through line force and negative Laplace pressure. At first glance, these two adhesion mechanisms appear mutually exclusive or at least fundamentally different in origins, raising the question: When a liquid bridge brings two solid surfaces into contact, does the system exhibit dry or capillary adhesion as the bridge size becomes small? We show that the answer depends on whether the liquid energetically spreads at the solid–solid interface and, in either case, the system adopts the maximum adhesion possible. Specifically, when the liquid spreads, the system asymptotically exhibits capillary adhesion; otherwise, dry adhesion eventually prevails. Naturally, the term “small” for the liquid bridge should be defined relative to the characteristic size of the specific system. We then elucidate the capillary and dry adhesion interplay by examining two representative systems: the adhesion of a folded elastica loop and the adhesion of a rigid sphere on a linearly elastic half space. The corresponding small parameters are defined by a combination of geometry and elasticity.