Capillary Surfaces pp 67-88 | Cite as
Stability Criteria
Chapter
First Online:
Abstract
The capillary equation is the Euler—Lagrange equation resulting from minimizing the energy of the liquid under the constraints of constant liquid volume, constant angular momentum, constant frequency of rotation, etc. A solution of the capillary equation, however, is not automatically stable. One may have reached a saddle point or even a maximum of the energy instead. Around an extremum, the energy of the liquid can be represented by a quadratic form in the coordinates, which may be transformed to its principal axes. If all eigenvalues of this transformation are positive, the surface is stable.
Keywords
Contact Angle Contact Line Circular Tube Viscous Friction Recede Contact Angle
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Carruthers JR, Gibson EG, Klett MG, Facemire BR: Studies of rotating liquid floating zones on Skylab IV. AIAA Paper 75-692, Denver, CO (1975)Google Scholar
- 2.Carruthers J, Gibson EG: Liquid floating zone. NASA TM-78234 (1979) pp. 6–9 to 6–15Google Scholar
- 3.Vreeburg JPB: Summary review of microgravity fluid science experiments. ESA, Amsterdam (1986)Google Scholar
- 4.DaRiva I, Martinez I: Floating liquid zones. Naturwissenschaften 73 (1986) 345–347CrossRefGoogle Scholar
- 5.Erle MA, Gilette RD, Dyson DC: Stability of interfaces of revolution with constant surface tension. The case of the catenoid. Chem. Eng. J. 1 (1970) 97CrossRefGoogle Scholar
- 6.Gilette RD, Dyson DC: Smallest volume. Chem. Eng. 2 (1971) 44CrossRefGoogle Scholar
- 7.Gillis J: Stability of a column of rotating viscous liquid. Proc. Camb. Phil. Soc. 57 (1961) 152CrossRefGoogle Scholar
- 8.Heywang W: 1956 Zur Stabilität senkrechter Schmelzzonen. Z. Naturforsch. 11a (1956) 238–243Google Scholar
- 9.Langbein D, Rischbieter F: Form, Schwingungen und Stabilität von Flüssigkeitsgrenzflächen. Forschungsbericht W 86-29 des BMFT (1986) 1–130Google Scholar
- 10.Martinez I: Stability of long liquid columns in Spacelab-D1. ESA-SP 256 (1987) 235–240Google Scholar
- 11.Martinez I, Meseguer J: Floating liquid zones in microgravity. In: Scientific Results of the German Spacelab Mission D1. P.R. Sahm, R. Jansen, M. Keller (eds.) (1986) 105–112Google Scholar
- 12.Sprenger HJ, Pötschke J, Potard C, Rogge V: Composites. In: Fluid Sciences and Materials Science in Space. H.U. Walter (ed.) Springer Berlin Heidelberg (1987), Chap. 16, 567–597Google Scholar
- 13.Rayleigh, Lord (J.W. Strutt): On the capillary phenomena of jets. Proc. Roy. Soc. London 29 (1879) 71–97CrossRefGoogle Scholar
- 14.Rayleigh, Lord (J.W. Strutt): The Theory of Sound. Dover, New York (1945) Sect. 364Google Scholar
- 15.Vega JM, Perales JM: Almost cylindrical isorotating liquid bridges for small Bond numbers. In: Materials Sciences in Space. ESA SP-191 (1983) 247–252Google Scholar
- 16.Weber C: Zum Zerfall eines Flüssigkeitsstrahles. Z. angew. Math. Mech. 11 (1931) 136–155CrossRefGoogle Scholar
- 17.Vreeburg JPB: Summary review of microgravity fluid science experiments. ESA, Amsterdam (1986)Google Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2002