Intersurface Adhesion in the Presence of Capillary Condensation

Abstract

An elastic sphere adheres to a rigid substrate in the presence of moisture. The adhesion–detachment trajectory is derived based on the Hertz contact theory that governs the contact mechanics and Laplace–Kelvin equation that governs the water meniscus at the interface. The intersurface attraction is solely provided by the Laplace pressure within the meniscus. Interrelation between the applied load, contact radius, and approach distance is derived based on a force balance. The resulting “pulloff” force to detach the sphere exceeds the critical load in the Derjaguin–Muller–Toporov (DMT) limit which only holds at saturated moisture. The new model accounts for the finite size of water molecules that is missing in virtually all classical models.