text: The Kelvin equation indicates that as P/P increases inside a capillary, the radius of curvature will also increase, creating a flatter interface.  (Note: This is not to say that larger radii of curvature result in more vapor condensation.  See the discussion on contact angle below.)  Figure 2 above demonstrates this dependence in a simple situation whereby the capillary radius is expanding toward the opening of the capillary and thus vapor condensation occurs smoothly over a range of vapor pressures.  In a parallel situation, where the capillary radius is constant throughout its height, vapor condensation would occur much more rapidly, reaching the equilibrium radius of curvature (Kelvin radius) as quickly as possible.  This dependence on pore geometry and curvature can result in hysteresis and vastly different liquid/vapor equilibria over very small ranges in pressure.
  It is also worthy to mention that different pore geometries result in different types of curvature.  In scientific studies of capillary condensation, the hemispherical meniscus situation (that resulting from a perfectly cylindrical pore) is most often investigated due to its simplicity.  Cylindrical menisci are also useful systems because they typically result from scratches, cuts, and slit-type capillaries in surfaces.  Many other types of curvature are possible and equations for the curvature of menisci are readily available at numerous sources.  Those for the hemispherical and cylindrical menisci are shown below.
  General Curvature Equation:
  Cylinder:  
  Hemisphere: