American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 862-867. doi: 10.3934/proc.2005.2005.862

Comments on radially symmetric liquid bridges with inflected profiles

Thomas I. Vogel 1,

1. 

Department of Mathematics, Texas A&M University, College Station, TX 77843, United States

Received  September 2004 Revised  February 2005 Published  September 2005

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: stability, inflections., capillarity.
Mathematics Subject Classification: Primary: 53A10, 49Q1.
Citation: Thomas I. Vogel. Comments on radially symmetric liquid bridges with inflected profiles. Conference Publications, 2005, 2005 (Special) : 862-867. doi: 10.3934/proc.2005.2005.862
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