Composite states of wetting

The analytical expressions of liquid–vapor equilibrium contact angles are analyzed in the thermodynamic limit for various simple geometries and arrangements of the substrate, in particular when the latter exhibits two or more scales. It concerns the Wenzel state of wetting when the substrate is completely wet, the Cassie–Baxter state when the liquid hangs over the substrate, but also intermediate states of wetting which are shown to be relevant and in competition with the two other ones. Under a separation of scales hypothesis, a composition rule of contact angles is developed whose interest is illustrated in a close packing setup of raspberry-like particles.