Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-03T02:21:26.596Z Has data issue: false hasContentIssue false
  • English
  • Français

The unsteady motion of a drop moving vertically under gravity

Published online by Cambridge University Press:  21 April 2006

R. F. Chisnell
R. F. Chisnell
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The unsteady flow field pertaining to a drop moving vertically under gravity is obtained from the Stokes equations applicable to low-Reynolds-number flow. A proof is given that there is no variation in the normal stress over the drop surface. In consequence unsteadily moving drops remain spherical, subject only to the criterion of low Reynolds number. Numerical results are presented for a water drop moving through air. A small-time analysis of the motion provides a comparison between the motion of any drop, or bubble, with that of the presented water-drop solution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 176 , March 1987 , pp. 443 - 464
Copyright
© 1987 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

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops, and Particles. Academic.
Harper, J. F. 1972 Adv. Appl. Mech. 12, 59.
Ockendon, J. R. 1968 J. Fluid Mech. 34, 229.
Sy, F. & Lightfoot, E. N. 1971 AIChE J. 17, 177.
Sy, F., Taunton, J. W. & Lightfoot, E. N. 1970 AIChE J. 16, 386.
Taylor, T. D. & Acrivos, A. 1964 J. Fluid. Mech. 18, 466.
Villat, H. 1943 LecLons sur les Fluides Visqueux. Paris: Gauthier-Villars.