Tuesday, March 13, 2012 - 3:05pm
1 hour (actually 50 minutes)
The stability of a liquid drop of prescribed volume hanging from a circular cylindrical tube in a gravity field has been a problem of continuing interest. This problem was treated variationally in the late '70s by Henry Wente who showed there was a continuous family indexed by increasing volume which terminated in a final unstable equilibrium due to one or the other of two specific geometric mechanisms. I will describe a similar problem arising in mathematical biology for drops at the bottom of a rectangular tube and explain, among other things, how the associated instability occurs through exactly three physical mechanisms.