Criteria for Floating I

Criteria for Floating I,10.1007/s00021-009-0009-y,Journal of Mathematical Fluid Mechanics,Robert Finn

Criteria for Floating I   (Citations: 4)
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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 for an infinitely deep liquid in a downward gravity field there is no absolute energy minimum. Of notable interest are the results (a) that if a smooth 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) a formal proof that there can be a free-floating locally energy minimizing configuration that does not globally minimize, even if the density of the body exceeds that of the liquid. 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 details of behavior can change significantly. That work will appear in an independent study written jointly with T. I. Vogel.
Journal: Journal of Mathematical Fluid Mechanics - J MATH FLUID MECH , vol. 13, no. 1, pp. 103-115, 2011
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    • ...Finn [Fin08] has recently given the first rigorous proof of this fact, at least in an idealized situation which we describe in §4 below...

    John McCuanet al. Capillarity and Archimedes' Principle of Floatation

    • ...We mention specifically [Fin08 ,K el98 ]a nd [VM05]...
    • ...It has recently been shown in a mathematically rigorous way by Finn [Fin08], working under some special assumptions that fit into this basic framework, that it is sometimes possible for a heavier object to float on the surface of a lighter liquid...

    John McCuan. Archimedes Revisited

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