  An example of capillary phenomena commonly seen and often studied is a
droplet of water hanging in air from a horizontal surface. A thin capillary
surface interface between the liquid and gas develops tangential surface
tension, which provides a balance of the internal and external pressures. The
Young-Laplace equation has been historically used to establish the equilibrium
geometry of the droplet, relating the pressure difference across the surface to
the mean curvature of the surface and the surface tension, which is presumed
constant and isotropic. The surface energy per unit area is often referred to
as simply surface energy and is commonly considered equal to the surface
tension. The relation between the surface energy and the surface tension can be
established for axisymmetric droplets in a gravitational field by the
application of the calculus of variations, minimizing the total potential
energy. Here it is shown analytically and experimentally that, for conditions
of constant volume of the droplet, equilibrium states exist with surface
tensions less than the surface energy of the water-air interface. The surface
tensions of the interface membrane vary with position and are anisotropic.
