Archiv der Mathematik

, Volume 94, Issue 5, pp 477–488 | Cite as

A general existence theorem for symmetric floating drops



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.

Mathematics Subject Classification (2000)

76B45 35A15 35R35 49J05 


Floating drops Capillarity Floatation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Concus P., Finn R.: On capillary free-surfaces in a gravitational field. Acta Math. 132, 207–223 (1974)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    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.Google Scholar
  3. 3.
    Elcrat A., Kim T.-E., Treinen R.: Annular capillary surfaces. Arch. Math. (Basel) 82, 449–467 (2004)MATHMathSciNetGoogle Scholar
  4. 4.
    Elcrat A., Neel R., Siegel D.: Equilibrium configurations for a floating drop. J. Math. Fluid Mech. 6, 405–429 (2004)MATHMathSciNetGoogle Scholar
  5. 5.
    A. Elcrat and R. Treinen, Numerical results for floating drops, Discrete Contin. Dyn. Syst. (2005), suppl., 241–249.Google Scholar
  6. 6.
    A. Elcrat and R. Treinen, Floating drops and functions of bounded variation, CAOT (2009).Google Scholar
  7. 7.
    R. Finn, Equilibrium capillary surfaces, Grundlehren der Mathematischen Wissenschaften 284, Springer-Verlag, New York, 1986.Google Scholar
  8. 8.
    S. T. Gibbs, Ph.D. Thesis Research Proposal, University of Waterloo (1989).Google Scholar
  9. 9.
    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.Google Scholar
  10. 10.
    U. Massari, The parametric problem of capillarity: the case of two and three fluids, Astérisque 118 (1984), 197–203 (English, with French summary).Google Scholar
  11. 11.
    Siegel D.: Height estimates for capillary surfaces. Pacific J. Math. 88, 471–515 (1980)MATHMathSciNetGoogle Scholar
  12. 12.
    Siegel D.: Approximating symmetric capillary surfaces. Pacific J. Math. 224, 355–365 (2006)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    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)Google Scholar
  14. 14.
    R. Treinen, Extended annular capillary surfaces, To appear.Google Scholar
  15. 15.
    R. Treinen, On the symmetry of solutions to some floating drop problems, To appear.Google Scholar
  16. 16.
    R. Treinen, A study of floating drops, Wichita State Univ., 2004.Google Scholar
  17. 17.
    Turkington B.: Height estimates for exterior problems of capillarity type. Pacific J. Math. 88, 517–540 (1980)MATHMathSciNetGoogle Scholar
  18. 18.
    Vogel T.I.: Symmetric unbounded liquid bridges. Pacific J. Math. 103, 205–241 (1982)MATHMathSciNetGoogle Scholar
  19. 19.
    Wente H.C.: The stability of the axially symmetric pendent drop. Pacific J. Math. 88, 421–470 (1980)MATHMathSciNetGoogle Scholar

Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.138 Cardwell HallKansas State UniversityManhattanUSA

Personalised recommendations