Geometry-dominated fluid adsorption on sculpted solid substrates

The shape(1,2) and chemical composition(3) of solid surfaces can be controlled at a mesoscopic scale. Exposing such structured substrates to a gas that is close to coexistence with its liquid phase can produce quite distinct adsorption characteristics compared to those of planar systems(4), which may be important for technologies such as super-repellent surfaces(5,6) or micro-fluidics(7,8). Recent studies have concentrated on the adsorption of liquids on rough(9-11) and heterogeneous(12) substrates, and the characterization of nanoscopic liquid films(13). But the fundamental effect of geometry on the adsorption of a fluid from the gas phase has hardly been addressed. Here we present a simple theoretical model which shows that varying the shape of the substrate can exert a profound influence on the adsorption isotherms of liquids. The model smoothly connects wetting and capillary condensation through a number of examples of fluid interfacial phenomena, and opens the possibility of tailoring the adsorption properties of solid substrates by sculpting their surface shape.