Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-16T06:01:43.059Z Has data issue: false hasContentIssue false
  • English
  • Français

Drag and lift forces on bubbles in a rotating flow

Published online by Cambridge University Press:  04 January 2007

ERNST A. VAN NIEROP ,
STEFAN LUTHER ,
JOHANNA J. BLUEMINK ,
JACQUES MAGNAUDET ,
ANDREA PROSPERETTI  and
DETLEF LOHSE
ERNST A. VAN NIEROP
Affiliation:
Faculty of Applied Sciences, Physics of Fluids, University of Twente, The Netherlands Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
STEFAN LUTHER
Affiliation:
Faculty of Applied Sciences, Physics of Fluids, University of Twente, The Netherlands
JOHANNA J. BLUEMINK
Affiliation:
Faculty of Applied Sciences, Physics of Fluids, University of Twente, The Netherlands
JACQUES MAGNAUDET
Affiliation:
Institut de Mécanique des Fluides de Toulouse, (IMFT), Allée du Professeur Camille Soula, 31400 Toulouse, France
ANDREA PROSPERETTI
Affiliation:
Faculty of Applied Sciences, Physics of Fluids, University of Twente, The Netherlands Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
DETLEF LOHSE
Affiliation:
Faculty of Applied Sciences, Physics of Fluids, University of Twente, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

The motion of small air bubbles in a horizontal solid-body rotating flow is investigated experimentally. Bubbles with a typical radius of 1 mm are released in a liquid-filled horizontally rotating cylinder. We measure the transient motion of the bubbles in solid-body rotation and their final equilibrium position from which we compute drag and lift coefficients for a wide range of dimensionless shear rates 0.1<Sr<2 (Sr is the velocity difference over one bubble diameter divided by the slip velocity of the bubble) and Reynolds numbers 0.01<Re<500 (Re is based on the slip velocity and bubble diameter). For large Sr, we find that the drag force is increased by the shear rate. The lift force shows strong dependence on viscous effects. In particular, for Re<5, we measure negative lift forces, in line with theoretical predictions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 571 , 25 January 2007 , pp. 439 - 454
Copyright
Copyright © Cambridge University Press 2007

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

Ashmore, J., del Pino, C. & Mullin, T. 2005 Cavitation in a lubrication flow between a moving sphere and a boundary. Phys. Rev. Lett. 94, 124501.CrossRefGoogle Scholar
Auton, T. 1987 The lift force on a spherical body in a rotational flow. J. Fluid Mech. 183, 199–218.CrossRefGoogle Scholar
Auton, T., Hunt, J. & Prud'Homme, M. 1988 The force exterted on a body in inviscid unsteady non-uniform rotational flow. J. Fluid Mech. 197, 241–257.Google Scholar
Bagchi, P. & Balachandar, S. 2002 Shear versus vortex-induced lift force on a rigid sphere at moderate Re. J. Fluid Mech. 473, 379–388.Google Scholar
Bluemink, J. J., van Nierop, E. A., Luther, S., Deen, N. G., Magnaudet, J., Prosperetti, A. & Lohse, D. 2005 Asymmetry-induced particle drift in a rotating flow. Phys. Fluids 17, 072106.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles. Academic.Google Scholar
Climent, E. & Magnaudet, J. 2006 Dynamics of a two-dimensional up flowing mixing layer seeded with bubbles. Bubble dispersion and effect of two-way coupling, Phys. Fluids 18, 103304.Google Scholar
Galindo, V. & Gerbeth, G. 1993 A note on the force on an accelerating spherical drop at low-Reynolds number. Phys. Fluids A 5, 3290–3292.CrossRefGoogle Scholar
Gotoh, T. 1990 Brownian motion in a rotating flow. J. Stat. Phys. 59, 371–402.Google Scholar
Guet, S., Ooms, G., Oliemans, R. & Mudde, R. 2004 Bubble size effect on low liquid input drift-flux parameters. Chem. Engng Sci. 59, 3315–3329.CrossRefGoogle Scholar
Herron, I., Davis, S. & Bretherton, F. 1975 On the sedimentation of a sphere in a centrifuge. J. Fluid Mech. 68, 209–234.Google Scholar
Lamb, H. 1934 Hydrodynamics, 6th edn. Dover.Google Scholar
Legendre, D. & Magnaudet, J. 1998 The lift force on a spherical bubble in a viscous linear shear flow. J. Fluid Mech. 368, 81–126.Google Scholar
Lohse, D. & Prosperetti, A. 2003 Controlling bubbles. J. Phys. Condens. Matter 15, S415.CrossRefGoogle Scholar
McLaughlin, J. B. 1991 Inertial migration of a small sphere in linear shear flows. J. Fluid Mech. 224, 261–274.Google Scholar
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32, 659–708.Google Scholar
Magnaudet, J. & Legendre, D. 1998 Some aspects of the lift force on a spherical bubble. Appl. Sci. Res. 58, 441–461.CrossRefGoogle Scholar
Maxworthy, T., Gnann, C., Kürten, M. & Durst, F. 1996 Experiments on the rise of air bubbles in clean viscous liquids. J. Fluid Mech. 321, 421.Google Scholar
Mazzitelli, I., Lohse, D. & Toschi, F. 2003a The effect of microbubbles on developed turbulence. Phys. Fluids 15, L5–L8.CrossRefGoogle Scholar
Mazzitelli, I., Lohse, D. & Toschi, F. 2003b On the relevance of the lift force in bubbly turbulence. J. Fluid Mech. 488, 283–313.Google 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
Naciri, M. 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 Central de Lyon.Google Scholar
Rensen, J., Bosman, D., Magnaudet, J., Ohl, C., Prosperetti, A., Tögel, R., Versluis, M. & Lohse, D. 2001 Spiraling bubbles: How acoustic and hydrodynamic forces compete. Phys. Rev. Lett. 86, 4819–4822.Google Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385. Corrigendum: 31, p. 624, 1968.CrossRefGoogle Scholar
Seddon, J. R. T. & Mullin, T. 2006 Reverse rotation of a cylinder near a wall. Phys. Fluids 18, 041703.Google Scholar
Sridhar, G. & Katz, J. 1995 Drag and lift forces on microscopic bubbles entrained by a vortex. Phys. Fluids 7, 389–399.Google Scholar
Taylor, G. 1928 The forces on a body placed in a curved converging stream of fluid. Proc. R. Soc. Lond. A 120, 260.Google Scholar
Toegel, R., Luther, S. & Lohse, D. 2006 Viscosity destabilizes sonoluminescing bubbles. Phys. Rev. Lett. 96, 114301.Google Scholar
Tomiyama, A. 2002 Transverse migration of single bubble in simple shear flows. Chem. Engng Sci. 57, 1849–1858.Google Scholar
Tryggvason, G., Bunner, B., Esmaelli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S. & Jan, Y.-J. 2001 A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169, 708–759.Google Scholar
Yang, S. M. & Leal, L. G. 1991 A note on the memory-integral contributions to the force on an accelerating spherical drop at low Reynolds number. Phys. Fluids A 3, 1822–1824.Google Scholar