The influence of line tension on the formation of liquid bridges in atomic force microscope-like geometry
We investigate thermodynamic and geometrical conditions for the formation of a liquid bridge between a planar and conical walls modeling atomic force microscope (AFM). Our macroscopic analysis is based on the grand canonical functional of the shape of the liquid-vapor interface which contains the relevant bulk, surface and line free energies. The phase diagram of such a confined fluid displays the existence of two phases: one with a liquid bridge connecting the walls, and the other without a bridge. The structure of the corresponding coexistence line is determined and its dependence on the value of the line tension coefficient is discussed.