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Comments on radially symmetric liquid bridges with inflected profiles
For a liquid bridge between parallel planes
which makes equal contact angles with those planes, it is already
known that a pitchfork bifurcation occurs when there is an
inflection in the profile curve. A geometrical argument is
outlined to give an alternate and more elementary proof of this
fact. In contrast to the behavior of liquid bridges between
parallel planes, it is shown that a liquid bridge between spheres
exists which is stable and has two inflections. Along the way, a
result relating stability and \(dH/dV\) for a family of capillary
surfaces is established.