Capillary condensation between disks in two dimensions

Capillary condensation between two two-dimensional wetted circular substrates (disks) is studied by an effective free energy description of the wetting interface. The interfacial free-energy potential is developed on the basis of the theory for the wetting of a single disk, where interfacial capillary fluctuations play a dominant role. A simple approximative analytical expression of the interfacial free energy is developed and is validated numerically. The capillary condensation is characterized by the analysis of the coverage of the condensed phase, its stability, and asymptotic behaviors. The theory can be applied to the description of flocculations in two-dimensional systems of colloids.