Abstract
An existence theorem for floating drops due to Elcrat, Neel, and Siegel is generalized. The theorem applies to all radially symmetric domains, and to both light and heavy floating drops, and utilizes new results in annular capillary theory.
Similar content being viewed by others
References
Concus P., Finn R.: On capillary free-surfaces in a gravitational field. Acta Math. 132, 207–223 (1974)
P. Concus and R. Finn, The shape of a pendent liquid drop, Philos. Trans. Roy. Soc. London Ser. A 292 (1978), no. 1391, 307–340.
Elcrat A., Kim T.-E., Treinen R.: Annular capillary surfaces. Arch. Math. (Basel) 82, 449–467 (2004)
Elcrat A., Neel R., Siegel D.: Equilibrium configurations for a floating drop. J. Math. Fluid Mech. 6, 405–429 (2004)
A. Elcrat and R. Treinen, Numerical results for floating drops, Discrete Contin. Dyn. Syst. (2005), suppl., 241–249.
A. Elcrat and R. Treinen, Floating drops and functions of bounded variation, CAOT (2009).
R. Finn, Equilibrium capillary surfaces, Grundlehren der Mathematischen Wissenschaften 284, Springer-Verlag, New York, 1986.
S. T. Gibbs, Ph.D. Thesis Research Proposal, University of Waterloo (1989).
Marquis de La Place, Celestial mechanics. Vols. I–IV, Translated from the French, with a commentary, by N. Bowditch, Chelsea Publishing Co., Bronx, N.Y., 1966.
U. Massari, The parametric problem of capillarity: the case of two and three fluids, Astérisque 118 (1984), 197–203 (English, with French summary).
Siegel D.: Height estimates for capillary surfaces. Pacific J. Math. 88, 471–515 (1980)
Siegel D.: Approximating symmetric capillary surfaces. Pacific J. Math. 224, 355–365 (2006)
Slobozhanin L.A.: Equilibrium and stability of three capillary surfaces with a common line of contact, Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza 176, 170–173 (1986)
R. Treinen, Extended annular capillary surfaces, To appear.
R. Treinen, On the symmetry of solutions to some floating drop problems, To appear.
R. Treinen, A study of floating drops, Wichita State Univ., 2004.
Turkington B.: Height estimates for exterior problems of capillarity type. Pacific J. Math. 88, 517–540 (1980)
Vogel T.I.: Symmetric unbounded liquid bridges. Pacific J. Math. 103, 205–241 (1982)
Wente H.C.: The stability of the axially symmetric pendent drop. Pacific J. Math. 88, 421–470 (1980)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Treinen, R. A general existence theorem for symmetric floating drops. Arch. Math. 94, 477–488 (2010). https://doi.org/10.1007/s00013-010-0123-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-010-0123-3