Hostname: page-component-7dd5485656-c8zdz Total loading time: 0 Render date: 2025-10-29T10:08:04.221Z Has data issue: false hasContentIssue false
  • English
  • Français

A long bubble rising in still liquid in a vertical channel: a plane inviscid solution

Published online by Cambridge University Press:  25 May 2016

Jean Fabre
Jean Fabre*
Affiliation:
Institut de Mécanique des Fluides, Institut National Polytechnique de Toulouse, Allée du Professeur Camille Soula, 31400 Toulouse, France
*
†Email address for correspondence: Jean.Fabre@imft.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

An analytical model is proposed for flow around a plane bubble rising steadily in a channel. The fluid surrounding the bubble is assumed to be inviscid, and the flow is assumed to be irrotational. The resulting potential flow is sought as the sum of a uniform stream and a source in the unit strip. Explicit expressions for the bubble shape and rise velocity, and for the streamlines, are given as functions of the dimensionless surface tension. The predictions are in good agreement with existing experimental and numerical results.

JFM classification

Drops and Bubbles: Bubble dynamics Drops and Bubbles: Drops and Bubbles Multiphase and Particle-laden Flows: Gas/liquid flow

Information

Type
Rapids
Information
Journal of Fluid Mechanics , Volume 797 , 25 June 2016 , R4
Copyright
© 2016 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.)

Article purchase

Temporarily unavailable

References

Birkhoff, G. & Carter, D. 1957 Rising plane bubbles. J. Math. Mech. 6, 769–779.Google Scholar
Birkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes and Cavities. Academic.Google Scholar
Collins, R. 1965 A simple model of the plane gas bubble in a finite liquid. J. Fluid Mech. 22, 763–771.CrossRefGoogle Scholar
Couët, 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
Couët, B., Strumolo, G. S. & Dukler, A. E. 1986 Modelling two-dimensional large bubbles in a rectangular channel of finite width. Phys. Fluids 29, 2367.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 A200, 375–390.Google Scholar
Dumitrescu, D. T. 1943 Strömung an einer Luftblase im senkrechten Rohr. Z. Angew. Math. Mech. 23, 139–149.Google Scholar
Fabre, J. & Figueroa-Espinoza, B. 2014 Taylor bubble rising in a vertical pipe against laminar or turbulent downward flow: symmetric to asymmetric shape transition. J. Fluid Mech. 755, 485–502.CrossRefGoogle Scholar
Figueroa-Espinoza, B. & Fabre, J. 2011 Taylor bubble moving in a flowing liquid in vertical channel: transition from symmetric to asymmetric shape. J. Fluid Mech. 679, 432–454.CrossRefGoogle Scholar
Garabedian, P. R. 1957 On steady-state bubbles generated by Taylor instability. Proc. R. Soc. Lond. A 241, 423–431.Google Scholar
Ha Ngoc, H. & Fabre, J. 2004 The velocity and shape of 2D long bubbles in inclined channels or in vertical tubes. Part I: in a stagnant liquid. Multiphase Sci. Technol. 16 (1–3), 175–188.Google Scholar
Ha Ngoc, H. & Fabre, J. 2006 A boundary element method for calculating the shape and velocity of two-dimensional long bubble in stagnant and flowing liquid. Engng Anal. Bound. Elem. 30, 539–552.Google Scholar
Lamb, H. 1945 Hydrodynamics, 6th edn. Dover.Google Scholar
Layzer, D. 1955 On the instability of superposed fluids in a gravitational field. Astrophys. J. 122, 1–12.Google Scholar
Maneri, C. & Zuber, N. 1974 An experimental study of plane bubbles rising at inclination. Intl J. Multiphase Flow 1, 623–645.Google Scholar
Mao, Z. S. & Dukler, A. E. 1990 The motion of Taylor bubbles in vertical tubes I. A numerical simulation for the shape and rise velocity of Taylor bubbles in stagnant and flowing liquids. J. Comput. Phys. 91, 132–160.Google Scholar
Vanden-Broëck, J.-M. 1984a Bubble rising in a tube and jets falling from a nose. Phys. Fluids 27, 1090–1093.Google Scholar
Vanden-Broëck, J.-M. 1984b Rising bubble in two-dimensional tube with surface tension. Phys. Fluids 27, 2604–2607.Google Scholar
Zudin, Y. B. 2013 Analytical solution of the problem of the rise of a Taylor bubble. Phys. Fluids 25, 1–16.CrossRefGoogle Scholar