Universal Phase Diagram for Wetting on Mesoscale Roughness

Abstract

The wetting properties of solid substrates with mesoscale (between van der Waals tails and the capillary length) random roughness are considered as a function of the microscopic contact angle of the wetting liquid and its partial pressure in the surrounding gas phase. It is shown that the well-known transition occurring at Wenzel's angle is accompanied by a transition line at which a jump in the adsorbed liquid volume occurs. This should be present generally on surfaces bearing homogeneous, isotropic random roughness. While a similar abrupt filling transition has been reported before for certain idealized groove or trough geometries, it is identified here as a universal phenomenon. Its location can be analytically calculated under certain mild conditions.