Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-13T01:41:52.875Z Has data issue: false hasContentIssue false
  • English
  • Français

Exotic containers for capillary surfaces

Published online by Cambridge University Press:  26 April 2006

Paul Concus  and
Robert Finn
Paul Concus
Affiliation:
Lawrence Berkeley Laboratory and Department of Mathematics, University of California, Berkeley, CA 94720, USA
Robert Finn
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we discuss ‘exotic’ rotationally symmetric containers that admit an entire continuum of distinct equilibrium capillary free surfaces. The paper extends earlier work to a larger class of parameters and clarifies and simplifies the governing differential equations, while expressing them in a parametric form appropriate for numerical integration. A unified presentation suitable for both zero and non-zero gravity is given. Solutions for the container shapes are depicted graphically along with members of the free-surface continuum, and comments are given concerning possible physical experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 224 , March 1991 , pp. 383 - 394
Copyright
© 1991 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Concus, P.: 1968 Static menisci in a vertical right circular cylinder. J. Fluid Mech. 34, 481–495.Google Scholar
Concus, P. & Finn, R., 1989 Instability of certain capillary surfaces. Manuscr. Math. 63, 209–213.Google Scholar
Finn, R.: 1986 Equilibrium Capillary Surfaces. Springer.
Finn, R.: 1988 Nonuniqueness and uniqueness of capillary surfaces. Manuscr. Math. 61, 347–372.Google Scholar
Gulliver, R. & Hildebrandt, S., 1986 Boundary configurations spanning continua of minimal surfaces. Manuscr. Math. 54, 323–347.Google Scholar
Vogel, T. I.: 1988 Uniqueness for certain surfaces of prescribed mean curvature. Pacific J. Maths 134, 197–207.Google Scholar