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The motion of a large gas bubble rising through liquid flowing in a tube

Published online by Cambridge University Press:  19 April 2006

R. Collins ,
F. F. De Moraes ,
J. F. Davidson  and
D. Harrison
R. Collins
Affiliation:
Department of Mechanical Engineering, University College London
F. F. De Moraes
Affiliation:
Department of Chemical Engineering, University of Cambridge Present address: Department of Chemical Engineering, University of Maringá, Caixa postal 331, 87.100 Maringá, Brazil.
J. F. Davidson
Affiliation:
Department of Chemical Engineering, University of Cambridge
D. Harrison
Affiliation:
Department of Chemical Engineering, University of Cambridge
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Abstract

The theory presented here describes the motion of a large gas bubble rising through upward-flowing liquid in a tube. The basis of the theory is that the liquid motion round the bubble is inviscid, with an initial distribution of vorticity which depends on the velocity profile in the liquid above the bubble. Approximate solutions are given for both laminar and turbulent velocity profiles and have the form \begin{equation} U_s = U_c+(gD)^{\frac{1}{2}}\phi(U_c/(gD)^{\frac{1}{2}}), \end{equation}Us being the bubble velocity, Uc the liquid velocity at the tube axis, g the acceleration due to gravity, and D the tube diameter; ϕ indicates a functional relationship the form of which depends upon the shape of the velocity profile. With a turbulent velocity profile, a good approximation to (1) which is suitable for many practical purposes is \begin{equation} U_s = U_s + U_{s0}, \end{equation}Us0 being the bubble velocity in stagnant liquid. Published data for turbulent flow are known to agree with (2), so that in this case the theory supports a well-known empirical result. Our laminar flow experiments confirm the validity of (1) for low liquid velocities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 89 , Issue 3 , 13 December 1978 , pp. 497 - 514
Copyright
© 1978 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics, pp. 507–593, 475. Cambridge University Press.
Behringer, P. 1936 Z. Geo. Kalte. Ind. 43 (3), 55–58.
Collins, R. 1966 J. Fluid Mech. 25, 469–480.
Collins, R. 1967 J. Fluid Mech. 28, 97–112.
Collins, R. 1968 Gas bubbles in liquids and in fluidized beds. Ph.D. thesis, University of London.
Collins, R. & Hoath, M. T. 1973 J. Fluid Mech. 57, 515–527.
Davies, R. M. & Taylor, G. I. 1950 Proc. Roy. Soc. A 200, 375.
Dumitrescu, D. T. 1943 Z. angew. Math. Mech. 23, 139–149 (English trans. obtainable from Library (translations), Bldg 465, AERE, Harwell).
Govier, G. W. & Aziz, K. 1972 The Flow of Complex Mixtures in Pipes, pp. 388–414, 142. Van Nostrand.
Griffith, P. & Wallis, G. B. 1961 J. Heat Transfer 83, 307–320.
Hawthorne, W. R. 1967 In Fluid Mechanics of Internal Flow (ed. G. Sovran), pp. 239–269. Elsevier.
Hinze, J. O. 1976 Turbulence, p. 733. McGraw-Hill.
Lai, W. 1964 J. Fluid Mech. 18, 587–594.
Lamb, H. 1932 Hydrodynamics, p. 245. Cambridge University Press.
Layzer, D. 1955 Astrophys. J. 122, 1–12.
Moraes, F. F. De 1977 Gas slugs in liquids and three-phase fluidisation. Ph.D. dissertation, University of Cambridge.
Nicklin, D. J., Wilkes, J. O. & Davidson, J. F. 1962 Trans. Inst. Chem. Engrs Lond. 40, 61–68.
Nicolitsas, A. J. & Murgatroyd, W. 1968 Chem. Engng Sci. 23, 934–936.
Nobel, L. 1972 The Slug Flow Equation. Commission of the European Communities, Joint Nuclear Research Centre–Ispra Establishment (Italy), Technology, Luxembourg, EUR. 4811 e.
Pai, S. I. 1957 Viscous Flow Theory, vol. 2, p. 43. Van Nostrand.
Reichardt, H. 1951 Z. angew. Math. Mech. 31, 208–219.
Stewart, P. S. B. & Davidson, J. F. 1967 Powder Tech. 1, 61–80.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn, p. 150. Cambridge University Press.
Wallis, G. B. 1969 One Dimensional Two-Phase Flow, pp. 282–314. McGraw-Hill.
White, E. T. & Beardmore, R. H. 1962 Chem. Engng Sci. 17, 351–361.
White, F. M. 1974 Viscous Fluid Flow, p. 338. McGraw-Hill.
Zuber, N. & Findlay, J. A. 1965 J. Heat Transfer 87, 453–468.