The Floating Ball Paradox

Henry C. Wente

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Submission date: 14. Dec. 2006
Pages: 22
published in: Journal of mathematical fluid mechanics, 10 (2008) 4, p. 569-582 
DOI number (of the published article): 10.1007/s00021-007-0251-0
Bibtex
MSC-Numbers: 76B45, 76D45, 74G65
Keywords and phrases: capillarity, surface tension

Abstract:
In capillary theory there are two kinds of surface tension. There is the surface tension at the interface between two immiscible fluids. Thomas Young (T. Young, An essay on the cohesion of fluids, Phil. Transactions Royal Society, London, 95, (1805) 65-87) also allowed for there to be a surface tension associated with a liquid-solid interface. He proceeded to use a balance of forces argument to derive the well-known contact angle condition along a liquid-liquid-solid intersection. The validity of this argument has recently been called into question by R. Finn (R. Finn, The contact angle in capillarity, Physics of Fluids 18, 047102, (2006)). A floating ball experiment discussed in that paper leads to an apparent paradox. We address this issue.

Please see also the MPI MIS preprint 154/2006 by Robert Finn.