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The rate at which a long bubble rises in a vertical tube

  • D. A. Reinelt (a1)

As a viscous fluid in a vertical tube drains under the effect of gravity, a finger of air rises in the tube. The shape of the interface and the rate at which the finger rises is determined numerically for different values of the dimensionless parameter G = ρgb2/T, where ρ is the density difference between the viscous fluid and the air, b is the radius of the tube, and T is the interfacial tension. A relationship between the Bond number G and the capillary number Ca = μU/T is found and compared with the perturbation result of Bretherton (1961), where μ is the viscosity of the fluid and U is the constant velocity at which the finger rises. The numerical results support Bretherton's conclusions for very small values of Ca and extend the relationship between G and Ca to a region where the perturbation expansion is no longer valid. The results are also valid for long bubbles rising in a tube.

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Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166188.
Cox, B. G. 1962 On driving a viscous fluid out of a tube. J. Fluid Mech. 14, 8196.
Kreiss, B. 1983 Construction of a curvilinear grid. SIAM J. Sci. Stat. Comput. 4, 270279.
Park, C. W. & Homsy, G. M. 1984 Two-phase displacement in Hele-Shaw cells: theory. J. Fluid Mech. 139, 291308.
Reinelt, D. A. & Saffman, P. G. 1985 The penetration of a finger into a viscous fluid in a channel and tube. SIAM J. Sci. Stat. Comput. 6, 542561.
Silliman, W. J. & Scriven, L. E. 1980 Separating flow near a static contact line: slip at a wall and shape of a free surface. J. Comp. Phy. 34, 287313.
Youngren, G. K. & Acrivos, A. 1976 On the shape of a gas bubble in a viscous extensional flow. J. Fluid Mech. 76, 433442.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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