Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-18T13:54:30.397Z Has data issue: false hasContentIssue false
  • English
  • Français

Drag and lift forces on interface-contaminated bubbles spinning in a rotating flow

Published online by Cambridge University Press:  10 April 2009

MARIE RASTELLO ,
JEAN-LOUIS MARIÉ ,
NATHALIE GROSJEAN  and
MICHEL LANCE
MARIE RASTELLO*
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, Ecole Centrale de Lyon-CNRS-Université Claude Bernard Lyon 1-INSA Lyon, 36 Avenue Guy de Collongue, 69134 Ecully cedex, France
JEAN-LOUIS MARIÉ
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, Ecole Centrale de Lyon-CNRS-Université Claude Bernard Lyon 1-INSA Lyon, 36 Avenue Guy de Collongue, 69134 Ecully cedex, France
NATHALIE GROSJEAN
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, Ecole Centrale de Lyon-CNRS-Université Claude Bernard Lyon 1-INSA Lyon, 36 Avenue Guy de Collongue, 69134 Ecully cedex, France
MICHEL LANCE
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, Ecole Centrale de Lyon-CNRS-Université Claude Bernard Lyon 1-INSA Lyon, 36 Avenue Guy de Collongue, 69134 Ecully cedex, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The equilibrium position of a spherical air bubble in a solid body rotating flow around a horizontal axis is investigated experimentally. The flow without bubbles is checked to be solid body rotating. The area of influence of the bubble is characterized to determine for each bubble whether the incoming flow is perturbed or not. The demineralized water used is shown to Tbe contaminated, and spinning of the bubble's interface is observed and measured. From the measurement of the bubble's equilibrium position, drag and lift coefficients are determined. They appear to be dependent on two dimensionless numbers. Eo the Eötvös number and Rω the rotational Reynolds number (or Taylor number Ta) can be varied independently by changing the control parameters, and for that reason are the convenient choice for experiments. (Re, Ro) with Ro the Rossby number is an equivalent choice generally adopted in the literature for numerical simulations, and Re denotes the Reynolds number. When using this second representation, the Ro number appears to be an indicator of the influence on the force coefficients of the shear, of the curvature of the streamlines of the flow and of the bubble's spinning. The bubble's spinning effect on the lift force is far from trivial. Its contribution explains the important gap between lift values for a bubble (not spinning) in a clean fluid and for a bubble (spinning) in a contaminated fluid as present.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 624 , 10 April 2009 , pp. 159 - 178
Copyright
Copyright © Cambridge University Press 2009

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.)

References

REFERENCES

Alves, S. S., Orvalho, S. P. & Vasconcelos, J. M. T. 2005 Effect of bubble contamination on rise velocity and mass transfer. Chem. Engng Sci., 60, 1–9.CrossRefGoogle Scholar
Auton, T. R. 1987 The lift force on a spherical body in a rotational flow. J. Fluid Mech. 183, 199–218.CrossRefGoogle Scholar
Bagchi, P. & Balachandar, S. 2002 a Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate re. Phys. Fluids 14 (8), 2719–2737.CrossRefGoogle Scholar
Bagchi, P. & Balachandar, S. 2002 b Shear versus vortex-induced lift force on a rigid sphere at moderate re. J. Fluid Mech. 473, 379–388.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An introduction to fluid dynamics. Cambridge University Press.Google Scholar
Bel Fdhila, R. & Duineveld, P. C. 1996 The effect of surfactant on the rise of a spherical bubble at high Reynolds and Peclet numbers. Phys. Fluids 8, 310–321.CrossRefGoogle Scholar
Candelier, F., Angilella, J.-R. & Souhar, M. On the effect of the Boussinesq-Basset force on the radial migration of a stokes particle in a vortex. Phys. Fluids 16 (5), 1765–1776.CrossRefGoogle Scholar
Clift, R., Grace, J. R. & Weber, M. E.Bubbles, Drops and Particles. Academic Press.Google Scholar
Cuenot, B., Magnaudet, J. & Spennato, B. 1997 The effects of slightly soluble surfactants on the flow around a spherical bubble. J. Fluid Mech. 339, 25–53.CrossRefGoogle Scholar
Duineveld, P. C. 1995 The rise velocity and shape of bubbles in pure water at high Reynolds number. J. Fluid Mech. 292, 325–332.CrossRefGoogle Scholar
Hartunian, R. A. & Sears, W. R. 1957 On the instability of small gas bubbles moving uniformly in various liquids. J. Fluid Mech. 3, 27–47.Google Scholar
Juaneda, Y. & Colin, C. 9–13 July 2007 Bubble dynamics in a cylindrical Couette flow. In Sixth International Conference on Multiphase Flows, Leipzig.Google Scholar
Kim, I. & Pearlstein, A. J. 1990 Stability of the flow past a sphere. J. Fluid Mech. 211, 73–93.CrossRefGoogle Scholar
Lamb, H. 1934 Hydrodynamics, 6th edn. Dover.Google Scholar
Leal, L. G. 1989 Vorticity transport and wake structure for bluff bodies at finite Reynolds number. Phys. Fluids 1, 124–131.CrossRefGoogle Scholar
Legendre, D. & Magnaudet, J. 1997 A note on the lift force on a spherical bubble or drop in a low-Reynolds-number shear flow. Phys. Fluids 9 (11), 3572–3574.Google Scholar
Legendre, D. & Magnaudet, J. The lift force on a spherical bubble in a viscous linear shear flow. J. Fluid Mech. 368, 81–126.Google Scholar
Lunde, K. & Perkins, R. J. 1998 Shape oscillations of rising bubbles. Appl. Sci. Res. 58, 387–408.CrossRefGoogle Scholar
Magnaudet, J. & Eames, I. 2000 Dynamics of high re bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32, 659–708.CrossRefGoogle Scholar
Magnaudet, J. & Legendre, D. 1998 Some aspects of the lift force on a spherical bubble. Appl. Sci. Res. 58, 441–461.CrossRefGoogle Scholar
Mei, R., Klausner, J. & Lawrence, C. 1994 A note on the history force on a spherical bubble at finite Reynolds number. Phys. Fluids 6, 418–420.CrossRefGoogle Scholar
van Nierop, E. A., Luther, S., Bluemink, J. J., Magnaudet, J., Prosperetti, A. & Lohse, D. 2007 Drag and lift forces on bubbles in a rotating flow. J. Fluid Mech. 571, 439–454.CrossRefGoogle Scholar
Naciri, A. 1992 Contribution à l'étude des forces exercées par un liquide sur une bulle de gaz: portance, masse ajoutée et interactions hydrodynamiques. PhD thesis, Ecole Centrale de Lyon.Google Scholar
Rastello, M., Marié, J.-L., Grosjean, N. & Lance, M. 9–13 July 2007 Study of bubble's equilibrium in a rotating flow. In Sixth International Conference on Multiphase Flows, Leipzig.Google Scholar
Saffman, P. G. 1965 The lift force on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400. Corrigendum: J. Fluid Mech., 31, 624 (1968).CrossRefGoogle Scholar
Sakamoto, H. & Haniu, H. 1995 The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow. J. Fluid Mech. 287, 151–171.CrossRefGoogle Scholar
Sridhar, G. & Katz, J. 1995 Drag and lift forces on microscopic bubbles entrained by a vortex. Phys. Fluids 7 (2):389–399.CrossRefGoogle Scholar
de Vries, A. W. G., Biesheuvel, A. & van Wijngaarden, L. 2002 Notes on the path and wake of a gas bubble rising in pure water. Intl J. Multiphase Flow 28, 1823–1835.CrossRefGoogle Scholar