Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T12:44:54.831Z Has data issue: false hasContentIssue false
  • English
  • Français

The stability of pendent liquid drops. Part 1. Drops formed in a narrow gap

Published online by Cambridge University Press:  29 March 2006

E. Pitts
E. Pitts
Affiliation:
Research Division, Kodak Limited, Headstone Drive, Harrow, Middlesex HA 1 4TY
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a drop of liquid hanging from a horizontal support and sandwiched between two vertical plates separated by a very narrow gap. Equilibrium profiles of such ‘two-dimensional’ drops were calculated by Neumann (1894) for the case when the angle of contact between the liquid and the horizontal support is zero. This paper gives the equilibrium profiles for other contact angles and the criterion for their stability. Neumann showed that, as the drop height increases, its cross-sectional area increases until a maximum is reached. Thereafter, as the height increases, the equilibrium area decreases. This behaviour is shown to be typical of all contact angles. When the maximum area is reached, the total energy is a minimum. It is shown that the drops are stable as long as the height and the area increase together.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 4 , 7 August 1973 , pp. 753 - 767
Copyright
© 1973 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

Bakker, G. 1928 Kapillarität. Handbuch der Experimental-physik (ed. W. Wien & F. Harms), vol. 6. Leipzig: Akademische Verlagsgesellschaft.
Neumann, F. 1894 Die Theorie der Capillarität. Vorlesungen über Mathematische Physik, vol. 7, chap. 5. Leipzig: B. G. Teubner.
Padday, J. F. 1971 Phil. Trans. Roy. Soc. 269, 265–293.
Padday, J. F. & Pitt, A. R. 1973 To be published.