Comments on radially symmetric liquid bridges with inflected profiles

Pages: 862 - 867, Issue Special, August 2005

 Abstract        Full Text (172.9K)              

Thomas I. Vogel - Department of Mathematics, Texas A&M University, College Station, TX 77843, United States (email)

Abstract: 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.

Keywords:  capillarity, stability, inflections.
Mathematics Subject Classification:  Primary: 53A10, 49Q10.

Received: September 2004;      Revised: February 2005;      Published: September 2005.