Liquid bridges between a sphere and a plane - Classification of meniscus profiles for unknown capillary pressure

The motivation for this study results from the following practical observation: for the experimenter, the value of the capillary pressure is a priori an unknown of the problem, it corresponds to a spontaneous value resulting a posteriori from a static equilibrium. A general classification of axisymmetric capillary bridge profiles for unknown capillary pressure between a sphere and a plane is addressed in this article. The meridian of the liquid bridge is classified into convex or concave profiles as portions of nodoid or unduloid surfaces based on measured geometrical data with special limit cases as catenoid, cylinder, or sphere. The theoretical work is then validated by an image-processing technique applied to images of real capillary bridges from experiments for small water volumes and small sphere–plate separation distances. The laboratory tests show very good agreement between the theoretical calculations and the associated classification proposed. Even the transition case of a catenoid can be observed.