text: Water meniscus forces are highly interesting for AFM measurements in air. Due to the ambient humidity, a thin layer of water is formed between the tip and the sample during air measurements. The resulting capillary force gives rise to a strong attractive force that pulls the tip onto the surface. In fact, the adhesion force measured between tip and sample in ambient air of finite humidity is usually dominated by capillary forces. As a consequence, it is difficult to pull the tip away from the surface. For soft samples including many polymers and in particular biological materials, the strong adhesive capillary force gives rise to sample degradation and destruction upon imaging in contact mode. Historically, these problems were an important motivation for the development of dynamic imaging in air (e.g. "tapping mode"). During tapping mode imaging in air, capillary bridges still form. Yet, for suitable imaging conditions, the capillary bridges are formed and broken in every oscillation cycle of the cantilever normal to the surface, as can be inferred from an analysis of cantilever amplitude and phase vs. distance curves. As a consequence, destructive shear forces are largely reduced and soft samples can be investigated.
  In order to quantify the equilibrium capillary force, it is necessary to start from the Laplace equation for pressure:
  where γ, is the surface energy and r and r are defined in the figure.
  The pressure is applied on an area of
  where θ is the angle between the tips surface and the liquids surface while  h is the height difference between the surrounding liquid and the top of the miniscus.
  The force that pulls together the two surfaces is
  The same formula could also be calculated as a function of relative humidity.
  Gao calculated formulas for different tip geometries. As an example, the force decreases by 20% for a conical tip with respect to a spherical tip.
  When these forces are calculated, a difference must be made between the wet on dry situation and the wet on wet situation.
  For a spherical tip, the force is:
  : for dry on wet,
  :for wet on wet,
  where θ is the contact angle of the dry sphere and φ is the immersed angle, as shown in the figure
  For a conical tip, the formula becomes:
  : for dry on wet
  : for wet on wet
  where δ is the half cone angle and r and h are parameters of the meniscus profile.