Statistical mechanics of fluids adsorbed in wedges and at edges

Abstract

Some of the history and modern significance of wetting phenomena involving wedge and edge geometries is discussed. The adsorption of fluids onto structured surfaces or colloidal objects yields rich behaviour, including new classes of interfacial phase transitions and alternative ways to consider classical capillarity. I describe how the equilibrium properties of these systems can be described with exact virial theorems obtained from statistical mechanics, that are of immediate relevance to computer simulation procedures, density functional theories and experiments capable of measuring inhomogeneous fluid density profiles. In wedge geometry the physics behind these sum rules can be illustrated with the use of the Derjaguin approximation, familiar to colloidal science. Three specific examples of the utility of statistical mechanics to this field are described: (i) a sum rule analysis is provided of capillarity phenomena involving two-phase coexistence within a linear triangular wedge, whose walls could be chemically distinct, (ii) an example emphasizing that experimental systems will typically involve both wedge and edge geometries that cannot be readily separated and (iii) an example concerning adsorption within an annular wedge, taken from colloidal science.