MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Criteria for Floating I

Robert Finn


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.

MSC Codes:
76B45, 49Q10, 53A10
capillarity, surface tension, surface energy, floating bodies

Related publications

2011 Journal Open Access
Robert Finn

Criteria for floating I

In: Journal of mathematical fluid mechanics, 13 (2011) 1, pp. 103-115