Capillary bridging and long-range attractive forces in a mean-field   approach
  When a mixture is confined, one of the phases can condense out. This condensate, which is otherwise metastable in the bulk, is stabilized by the presence of surfaces. In a sphere-plane geometry, routinely used in atomic force microscope (AFM) and surface force apparatus (SFA), it can form a bridge connecting the surfaces. The pressure drop in the bridge gives rise to additional long-range attractive forces between them.   Minimizing the free energy of a binary mixture we obtain the force-distance curves as well as the structural phase diagram of the configuration with the bridge. Numerical results predict a discontinuous transition between the states with and without the bridge and linear force-distance curves with hysteresis.   We also show that similar phenomenon can be observed in a number of different systems, e.g. liquid crystals and polymer mixtures. 
D. Andrienko, P. Patricio, O. I. Vinogradova