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Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext. 32700
Fax: 5197464319
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M3 4206
Hanzhe(Tom) Chen  Applied Math, University of Waterloo
Two and Three Dimensional Floating Objects with Surface Tension
The study of floating objects can be traced back to Archimedes’ time. With the consideration of surface tension, the ability and stability of flotation gets complicated but more interesting. We propose two basic problems: the infinity long horizontal floating cylinder and the floating ball on an unbounded reservoir. For the floating cylinder problem (twodimensional), circular and strictly convex crosssections are both considered. The circular floating cylinder has a symmetric configuration. As the solution of onedimensional capillary equation can be translated horizontally, there is a possibility that the fluid interfaces intersect. We apply both the force and the energy approaches, at most two equilibrium configurations can be obtained, one is stable, the other is not, in consideration of the possible of intersection of interfaces. Unlike the circular cylinder, the configuration of strictly convex body usually admits asymmetric configurations. Conditions are imposed to guarantee a unique configuration for a fixed position. An example of an ellipse with rotation will be given. For the floating ball problem (threedimensional), we assume the floating configuration is radially symmetric. The fluid interface has to be solved numerically. An example with two force balanced points will be given, we will show both of them are stable. More examples and applications are anticipated.
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Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext. 32700
Fax: 5197464319
PDF files require Adobe Acrobat Reader