

Preprint 104/2007
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.