Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-19T03:01:09.993Z Has data issue: false hasContentIssue false

Static menisci in a vertical right circular cylinder

Published online by Cambridge University Press:  28 March 2006

Paul Concus
Affiliation:
Lawrence Radiation Laboratory, University of California, Berkeley, California 94720

Abstract

The solution of the differential equation describing the equilibrium meniscus in a vertical right circular cylinder is obtained over the entire range of contact angles and Bond numbers (dimensionless ratios of gravitational to capillary forces) for which a stable meniscus exists. The first few terms of the asymptotic series valid for Bond numbers of small and large magnitude are given, and the numerical solution for intermediate values is computed. The behaviour of the solution as a function of contact angle and Bond number is depicted graphically.

Type
Research Article
Copyright
© 1968 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

Bashforth, F. & Adams, J. C. 1883 An Attempt to Test the Theories of Capillary Action by Comparing the Theoretical and Measured Forms of Drops of Fluid. Cambridge University Press.
Concus, P. 1963 Capillary stability in an inverted rectangular tank. Adv. Astronautical Sci. (Western Periodicals Co., No. Hollywood, Calif.) 14, 2137.Google Scholar
Concus, P. 1964 Capillary stability in an inverted rectangular channel for free surfaces with curvature of changing sign AIAA J. 2, 222830.Google Scholar
Fox, L. 1962 Numerical Solution of Ordinary and Partial Differential Equations. Oxford: Pergamon.
Habip, L. M. 1965 On the mechanics of liquids in subgravity Astronautica Acta, 11, 4019.Google Scholar
Laplace, P. S. 1805 Mécanique Céleste, no. 4, Supplément au X Livre.
Lockheed, MISSILES AND SPACE CO. 1967 The literature of low-g propellant behaviour. LMSC-A 874730 code Y-87-67-1.Google Scholar
Rayleigh, LORD 1916 On the theory of the capillary tube. Proc. Roy. Soc. Lond A 92, 18495.Google Scholar
Reynolds, W. C. & Satterlee, H. M. 1966 Liquid propellant behavior at low and zero g. In The Dynamic Behavior of Liquids in Moving Containers. Ed. by H. N. Abramson. NASA SP-106, 387439.
Runge, C. 1895 Über die numerische Auflösung von Differentialgleichungen Math. Ann. 46, 16778.Google Scholar
White, D. A. & Tallmadge, J. A. 1965 Static menisci on the outside of cylinders J. Fluid Mech. 23, 32535.Google Scholar