Floating criteria in three dimensions

Robert Finn and Thomas Vogel

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Submission date: 09. Dec. 2009
published in: Analysis, 29 (2009) 4, p. 387-402 
DOI number (of the published article): 10.1524/anly.2009.0931
Bibtex
MSC-Numbers: 76B45, 49Q10, 53A10
Keywords and phrases: capillarity, surface tension, floating bodies

Abstract:
We extend to objects of general convex form an earlier criterion given by Finn for ensuring a local energy minimum corresponding to floating of a heavy horizontal cylinder on a liquid surface. We obtain a formal analogue of Finn’s criterion, and additionally a condition on interfacial surface energies under which an object of given shape with density exceeding that of the liquid must float if it is scaled to be sufficiently small. In analogy with Finn’s earlier work, we show also in the more physical case presently considered that if a body is lowered rigidly from a position above the undisturbed liquid surface to a position below the surface, the liquid configuration must change during the motion in a discontinuous way.