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Bubbles in viscous liquids: shapes, wakes and velocities

Published online by Cambridge University Press:  20 April 2006

D. Bhaga
Department of Chemical Engineering, McGill University, Montreal, P.Q., Canada Present address: Chemetics International, Toronto, Ontario.
M. E. Weber
Department of Chemical Engineering, McGill University, Montreal, P.Q., Canada


The shapes and terminal velocities of bubbles rising in viscous liquids have been determined. For Morton numbers (M) greater than 4 × 10−3 the drag coefficient and dimensionless bubble shape are functions only of Reynolds number (R). Shape regimes and terminal rise velocities have been correlated. The flow field around a rising bubble was visualized through the hydrogen bubble tracer technique. For M > 4 × 10−3 and R < 110 the bubbles trailed closed, laminar toroidal wakes. For R > 110 the wake was open and unsteady. Streamlines for the flow were obtained by raising a ciné camera at the same speed as the bubble and filming the H2 tracer bubbles. Results are presented for R < 150 and 7·4 × 10−4 < M < 850.

Research Article
© 1981 Cambridge University Press

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Angelino, H. 1966 Hydrodynamique des grosses bulles dans les liquides visqueux. Chem. Eng. Sci. 21, 541550.Google Scholar
Bhaga, D. 1976 Bubbles in viscous liquids: shapes, wakes and velocities. Ph.D. thesis, McGill University, Montreal.
Clift, R. C., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles. Academic.
Collins, R. 1966 A second approximation for the velocity of a large bubble rising in an infinite liquid. J. Fluid Mech. 25, 469480.Google Scholar
Coppus, J. H. C., Rietema, K. & Ottengraf, S. P. P. 1977 Wake phenomena behind sphericalcap bubbles and solid spherical-cap bodies. Trans. Inst. Chem. Eng. 55, 122129.Google Scholar
Davies, R. M. & Taylor, G. I. 1950 The mechanics of large bubbles rising through extended liquids and through liquids in tubes. Proc. Roy. Soc. A 200, 375590.Google Scholar
Grace, J. R. 1973 Shapes and velocities of bubbles rising in infinite liquids. Trans. Inst. Chem. Eng. 51, 116120.Google Scholar
Guthrie, R. I. L. & Bradshaw, A. V. 1969 The stability of gas envelopes trailed behind large spherical cap bubbles rising through viscous liquids. Chem. Eng. Sci. 24, 913917.Google Scholar
Harper, J. F. 1972 The motion of bubbles and drops through liquids. Adv. Appl. Mech. 12, 59129.Google Scholar
Harper, J. F. & Moore, D. W. 1968 The motion of a spherical liquid drop at high Reynolds number. J. Fluid Mech. 32, 367391.Google Scholar
Hnat, J. G. & Buckmaster, J. D. 1976 Spherical cap bubbles and skirt formation. Phys. Fluids 19, 182194. Erratum. Ibid. 19, 611.Google Scholar
Jones, D. R. M. 1965 The steady rise of air bubbles in viscous liquids. Ph.D. thesis, University of Cambridge.
Kalra, T. R. 1971 Bluff body wakes - geometry and mass transfer. Ph.D. thesis, Monash University, Melbourne.
Kalra, T. R. & Uhlerr, P. H. T. 1971 Properties of bluff-body wakes. 4th Australian Conf. Hydraulics and Fluid Mech., Melbourne.Google Scholar
Masliyah, J. B. 1972 Steady wakes behind oblate spheroids: flow visualization. Phys. Fluids 15, 11441146.Google Scholar
Masliyah, J. B. & Epstein, N. 1970 Numerical study of flow past spheroids. J. Fluid Mech. 44, 493512.Google Scholar
Moore, D. W. 1963 The boundary layer on a spherical bubble. J. Fluid Mech. 16, 161176.Google Scholar
Parlange, J.-Y. 1969 Spherical-cap bubbles with laminar wakes. J. Fluid Mech. 37, 257263.Google Scholar
Parlange, J.-Y. 1970 Motion of spherical drops at large Reynolds numbers. Acta Mech. 9, 323328.Google Scholar
Schraub, F. A., Kline, S. J., Henry, J., Runstadler, P. W. & Littell, A. 1965 Use of hydrogen bubbles for quantitative determination of time-dependent velocity fields in low-speed water flows. Trans. A.S.M.E. D, J. Basic Engng 87, 429444.Google Scholar
Seeley, L. E., Hummel, R. L. & Smith, J. W. 1975 Experimental velocity profiles in laminar flow around spheres at intermediate Reynolds numbers. J. Fluid Mech. 68, 591608.Google Scholar
Slaughter, I. 1967 The motion of gas bubbles rising singly and in streams through liquids. Ph.D. thesis, University of Newcastle upon Tyne.
Slaughter, I. & Wraith, A. E. 1968 The wake of a large gas bubble. Chem. Eng. Sci. 23, 932.Google Scholar
Tadaki, T. & Maeda, S. 1961 On the shape and velocity of single air bubbles rising in various liquids. Kagaku-Kogaku 25, 254264.Google Scholar
Taylor, T. D. & Acrivos, A. 1964 On the deformation and drag of a falling viscous drop at low Reynolds number. J. Fluid Mech. 18, 466477.Google Scholar
Wairegi, T. 1974 The mechanics of large drops and bubbles moving through extended liquid media. Ph.D. thesis, McGill University, Montreal.
Wairegi, T. & Grace, J. R. 1976 The behaviour of large drops in immiscible liquids. Int. J. Multiphase Flow 3, 6777.Google Scholar