Criteria for Floating I

Robert Finn

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Submission date: 26. Nov. 2007
published in: Journal of mathematical fluid mechanics, 13 (2011) 1, p. 103-115 
DOI number (of the published article): 10.1007/s00021-009-0009-y
Bibtex
MSC-Numbers: 76B45, 49Q10, 53A10
Keywords and phrases: capillarity, surface tension, surface energy, floating bodies

Abstract:
Conditions are determined under which solid bodies will float on a liquid surface in stable equilibrium, under the influence of gravity and of surface tension. These include configurations in which the density of the body exceeds the density of the ambient liquid, so that in a downward gravity field there is no absolute energy minimum. Of notable interest are the results a) that if a body is held rigidly and translated downward into an infinite fluid bath through a family of fluid equilibrium configurations in a downward gravity field, the transition is necessarily discontinuous, and b) if the density of the body exceeds that of the liquid and if the contact angle exceeds π/2, then there can be a locally minimizing (free floating) configuration that does not globally minimize. The present work is limited to the two dimensional case corresponding to a long cylinder that is floating horizontally. The more physical three-dimensional case can be studied in a similar way, although behavior changes in some details. That work is now in preparation.