Download Mariotte`s Floating Object Legacy

WICHITA STATE UNIVERSITY
Department of Mathematics, Statistics & Physics
The Twenty First Midwest Geometry Conference and
Lecture Series in the Mathematical Sciences
Presents Our Guest:
Prof. Robert Finn
Stanford University
“Mariotte’s Floating Object Legacy”
Abstract:
During the 17th Century, Edme Mariotte observed that objects floating on a liquid surface could either attract or
repel each other, and he attempted (without success) to find general laws describing the phenomenon. A century later P.S.
Laplace took an initial step toward clarification of Mariotte’s observations via the then newly introduced concept of surface
tension. He considered two parallel vertical plates, partially immersed in a liquid in a vertical gravity field, and examined the
horizontal force between them. He found results confirming attracting forces in expected orders of magnitude, in the
restricted case of a single contact angle on all surfaces. He also found that when the contact angles differ, the plates might
repel each other, and he provided explicit examples.
In the present work (joint with R. Bhatnagar) we permit arbitrary contact angles on all four exposed surfaces; it turns
out that only two of the four surfaces have direct relevance to the occurring forces, but for varying choices of those angles
and of plate separation, we distinguish ten geometrically differing kinds of interface behavior, with correspondingly differing
force ranges. Of special note is a remarkable singular behavior, which occurs when the contact angles on the two plate
surfaces facing each other are close to being supplementary.
Related results from a different point of view were established in recent work of Aspley. He and McCuan, who
displayed three criteria on prescribed data that cover all eventualities in a mutually exclusive (if somewhat less complete)
way.
Friday, March 11, 2016
3:00 PM in 127 Jabara Hall