  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.
