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Experimental studies of wakes behind circularly capped bubbles

Published online by Cambridge University Press:  21 April 2006

W. F. Bessler  and
H. Littman
W. F. Bessler
Affiliation:
Department of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180–3590, USA
H. Littman
Affiliation:
Department of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180–3590, USA
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Abstract

The wake behind a circularly capped bubble rising in fluids of different viscosity has been experimentally investigated using aspirin powder for flow visualization and high-speed photography synchronized with pressure-time measurements to measure the pressure field. The bubble plus its primary wake with a cusped tail is observed to contain symmetric pressure minima within the primary wake. Adjacent to the boundary wake is a free shear layer which contains large-scale vortices generated near the bubble rim that remain essentially stationary to an observer in the laboratory reference frame. The change in wake geometry and the transition to an ellipsoidal bubble shape as fluid viscosity increases is documented.

The airfoil shape of the boundary of the circularly capped bubble and its closed primary wake is modelled using a Joukowski transformation in which the Joukowski constant is adjusted to match the experimental and potential-flow pressures along the bubble cap. The model successfully predicts the frontal pressure field, and the wake size and shape. The Davies & Taylor bubble-cap boundary condition is also verified.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 185 , December 1987 , pp. 137 - 151
Copyright
© 1987 Cambridge University Press

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References

Batchelor, G. K. 1956a On steady laminar flow with closed streamlines at high Reynoldsnumber. J. Fluid Mech. 1, 177.Google Scholar
Batchelor, G. K. 1956b A proposal concerning laminar wakes behind bluff bodies at large Reynolds number. J. Fluid Mech. 1, 388.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bessler, W. F. 1984 Analytical and experimental studies of wakes behind circularly capped bubbles. Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, NY.
Calderbank, P. H. 1967 Gas absorption from bubbles. The Chemical Engineer No. 212, CE 209.
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles. Academic.
Collins, R. 1965a Structure and behaviour of wakes behind two dimensional air bubbles in water. Chem. Engng Sci. 20, 851.Google Scholar
Collins, R. 1965b A simple model of a plane gas bubble in a liquid. J. Fluid Mech. 22, 763.Google Scholar
Collins, R. 1966 A second approximation for the velocity of a large gas bubble rising in an infinite liquid. J. Fluid Mech. 25, 469.Google Scholar
Collins, R. 1974 Models of spherical-cap bubbles. In Proc. Int. Coll. on Bubbles and Drops. Cal. Inst. Tech. and Jet Prop. Lab., 28–30 Aug. 1974, Vol. II, pp. 414.
Coppus, J. H. C., Rietema, K. & Ottengraf, S. P. P. 1977 Wake phenomena behind spherical-cap bubbles and solid spherical cap bodies. Trans. Instn Chem. Engrs 55, 122.Google Scholar
Crabtree, J. R. & Bridgwater, J. 1967 The wakes behind two dimensional air bubbles. Chem. Engng Sci. 22, 1517.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.Google Scholar
Haberman, W. L. & Morton, R. K. 1953 An experimental investigation of the drag and shape of air bubbles rising in various liquids. David Taylor Model Basin Rep. 802, NS715–102.Google Scholar
Harper, J. F. 1972 The motion of bubbles and drops through liquids. Adv. Appl. Mech. 12, 59.Google Scholar
Hills, J. 1975 The two-dimensional elliptical cap bubble. J. Fluid Mech. 68, 503.Google Scholar
Lazarek, G. M. 1972 Pressure fields due to large circularly capped air bubbles rising in water. Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, NY.
Lazarek, G. M. & Littman, H. 1974 The pressure field due to a large circular-capped air bubble rising in water. J. Fluid Mech. 66, 673.Google Scholar
Lindt, J. T. 1972 On the periodic nature of the drag on a rising bubble. Chem. Engng Sci. 27, 1775.Google Scholar
Manieri, C. C. & Mendelson, H. D. 1968 The rise velocity of bubbles in tubes and rectangular channels. AIChE J. 14, 295.Google Scholar
Maxworthy, T. 1967 A note on the existence of wakes behind large rising bubbles. J. Fluid Mech. 27, 368.Google Scholar
Moore, D. W. 1959 The rise of a gas bubble in a viscous liquid. J. Fluid Mech. 6, 113.Google Scholar
Rippin, D. W. & Davidson, J. F. 1967 Free streamline theory for a large gas bubble in a liquid. Chem. Engng Sci. 22, 217.Google Scholar
Ryskin, G. & Leal, L. G. 1984 Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent liquid. J. Fluid Mech. 148, 19.Google Scholar
Saffman, P. G. & Tanveer, S. 1984 Prandlt-Batchelor flow past a flat plate with a forward-facing flap. J. Fluid Mech. 143, 351.Google Scholar
Slaughter, I. & Wraith, A. E. 1968 The wake of a large gas bubble. Chem. Engng Sci. 23, 932.Google Scholar
Walters, J. K. & Davidson, J. F. 1962 The initial motion of a gas bubble formed in an inviscid liquid. Part 1. The two-dimensional bubble. J. Fluid Mech. 12, 408.Google Scholar
Wegener, P. P. & Parlange, J. Y. 1973 Spherical-cap bubbles. Ann. Rev. Fluid Mech. 4, 79.Google Scholar
Wegener, P. P., Sundell, R. E. & Parlange, J. Y. 1971 Spherical cap bubbles rising in liquids. Z. Flugwiss. 19, 247.Google Scholar