Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-06T10:07:53.395Z Has data issue: false hasContentIssue false
  • English
  • Français

Spherical cap bubbles

Published online by Cambridge University Press:  26 April 2006

Yumin Yang  and
Herbert Levine
Yumin Yang
Affiliation:
Department of Physics and Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093-0075, USA Present address: Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY 11794-3600, USA.
Herbert Levine
Affiliation:
Department of Physics and Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093-0075, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the rise of a spherical cap bubble in both two- and three-dimensional unbounded regions. In particular we focus on the problem of finding steady state-solutions. We assume that the fluid is incompressible, inviscid and irrotational, and use two different models to approximate the turbulent wake behind the bubble. We demonstrate numerically that in the case of zero surface tension we have a continuous spectrum of rise velocities. When we add small surface tension to the problem, the degeneracy is broken via a solvability mechanism, and we obtain velocity selection. Our results are in good agreement with the existing experimental studies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 235 , February 1992 , pp. 73 - 87
Copyright
© 1992 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

Collins, R. 1965 A simple model of the plane gas bubble in a finite liquid. J. Fluid Mech. 22, 763–771.Google Scholar
Collins, R. 1967a The effect of a containing cylindrical boundary on the velocity of a large gas bubble in a liquid. J. Fluid Mech. 28, 97–112.Google Scholar
Collins, R. 1967b The cycloidal bubble: A neglected solution in the theory of large plane gas bubbles in liquids. Chem. Engng Sci. 22, 89–97.Google Scholar
CoueUt, B. & Strumolo, G. S. 1987 The effects of surface tension and tube inclination on a two-dimensional rising bubble. J. Fluid Mech. 184, 1–14.Google Scholar
Davies, R. M. & Taylor, G. I. 1950 The mechanics of large bubbles rising through extended liquids and through liquids in tubes. Proc. R. Soc. Lond. A 200, 375–390.Google Scholar
Grace, J. R. & Harrison, D. 1967 The influence of bubble shape on the rising velocities of large bubbles. Chem. Engng Sci. 22, 1337–1347.Google Scholar
Gurevich, M. I. 1965 Theory of Jets in Ideal Fluids. Academic.
Haberman, W. L. & Morton, R. K. 1956 An experimental study of bubbles moving in liquids. Trans. ASCE 121, 227–252.Google Scholar
Hnat, J. G. & Buckmaster, J. D. 1976 Spherical cap bubbles and skirt formation. Phys. Fluids 19, 182–194.Google Scholar
Kessler, D. A. & Levine, H. 1989a Velocity selection for Taylor bubbles. Phys. Rev. A 39, 39–5462.Google Scholar
Kessler, D. A. & Levine, H. 1989b Steady-state cellular growth during directional solidification. Phys. Rev. A 39, 39–3041.Google Scholar
Lamb, H. 1932 Hydrodynamics. Dover.
Levine, H. & Yang, Y. 1990 A rising bubble in a tube. Phys. Fluids A 2, 542–546.Google Scholar
Levinson, N. 1946 On the asymptotic shape of the cavity behind an axially symmetric nose moving through an ideal fluid. Annals Maths 47, 704–730.Google Scholar
Maneri, C. C. & Zuber, N. 1974 An experimental study of plane bubbles rising at inclination. Intl J. Multiphase Flow 1, 623–644.Google Scholar
Maxworthy, T. 1967 A note on the existence of wakes behind large rising bubbles. J. Fluid Mech. 27, 367–368.Google Scholar
Rippin, D. W. T. & Davidson, J. F. 1967 Free streamline theory for a large gas bubble in a liquid. Chem. Engng Sci. 22, 217–228.Google Scholar
Vanden-Broeck, J. M. 1984a Bubbles rising in a tube and jets falling from a nozzle. Phys. Fluids 27, 1090–1093.Google Scholar
Vanden-Broeck, J. M. 1984b Rising bubbles in a two-dimensional tube with surface tension. Phys. Fluids 27, 2604–2607.Google Scholar
Vanden-Broeck, J. M. 1986 Free streamline model for a rising bubble. Phys. Fluids 29, 2798–2801.Google Scholar
Vanden-Broeck, J. M. 1988 Joukovskii's model for a rising bubble. Phys. Fluids 31, 974–977.Google Scholar
Van Dyke, M. D. 1982 An Album of Fluid Motion. Parabolic.
Wegener, P. & Parlange, Y. 1973 Spherical-cap bubbles. Ann. Rev. Fluid Mech. 5, 79–100.Google Scholar