Skip to main content Accesibility Help

Clean versus contaminated bubbles in a solid-body rotating flow

  • Marie Rastello (a1) (a2), Jean-Louis Marié (a1) and Michel Lance (a1)

The behaviour of clean and contaminated bubbles in solid-body rotating flows is compared in terms of drag and lift forces. Both spherical and deformed bubbles are considered. For that comparison, we have completed the data published in Rastello et al. (J. Fluid Mech., vol. 624, 2009, pp. 159–178; J. Fluid Mech., vol. 682, 2011, pp. 434–459) by a new series of measurements. When they are contaminated, bubbles are subject to an additional lift force due to the spinning of their surfaces, while the clean ones are not. A detailed description of this spinning motion is presented and an expression for the Magnus-like lift it induces is given in the light of the new information. The component of the lift induced by flow rotation depends on the Rossby number $Ro$ , contrary to the case of clean bubbles. Including the ‘spin’ induced lift component in the dynamical equations provides a better prediction of the bubble’s trajectory in contaminated fluid. The presence of contaminants immobilizes the rear part of the bubble and reduces significantly the deformation. The laws of deformation according to the nature of the surface are presented. The way deformation influences the drag and lift coefficients in pure and contaminated fluids is quantified and discussed. Expressions for these various coefficients are proposed.

Corresponding author
Email address for correspondence:
Hide All
Adoua, R., Legendre, D. & Magnaudet, J. 2009 Reversal of the lift force on an oblate bubble in a weakly viscous shear flow. J. Fluid Mech. 628, 2341.
Adoua, S. R.2007 Hydrodynamique d’une bulle déformée dans un écoulement cisaillé. PhD thesis, Institut National Polytechnique de Toulouse.
Aoyama, S., Hayashi, K., Hosokawa, S., Lucas, D. & Tomiyama, A. 2017 Lift force acting on single bubbles in linear shear flows. Intl J. Multiphase Flow 96, 113122.
Aoyama, S., Hayashi, K., Hosokawa, S. & Tomiyama, A. 2016 Shape of ellipsoidal bubbles in infinite stagnant liquids. Intl J. Multiphase Flow 79, 2330.
Bagchi, P. & Balachandar, S. 2002 Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate Re . Phys. Fluids 14 (8), 27192737.
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, 310321.
Blanco, A. & Magnaudet, J. 1995 The structure of the axisymmetric high-Reynolds number flow around an ellipsoidal bubble of fixed shape. Phys. Fluids 7, 12651274.
Bluemink, J. J., Lohse, D., Prosperetti, A. & Van Wijngaarden, L. 2008 A sphere in a uniformly rotating or shearing flow. J. Fluid Mech. 600, 201233.
Bluemink, J. J., Lohse, D., Prosperetti, A. & Van Wijngaarden, L. 2010 Drag and lift forces on particles in a rotating flow. J. Fluid Mech. 643, 131.
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles. Academic.
Cuenot, B., Magnaudet, J. & Spennato, B. 1997 The effects of slightly soluble surfactants on the flow around a spherical bubble. J. Fluid Mech. 339, 2553.
Duineveld, P. C. 1995 The rise velocity and shape of bubbles in pure water at high Reynolds number. J. Fluid Mech. 292, 325332.
Giacobello, M., Ooi, A. & Balanchandar, S. 2009 Wake structure of a transversely rotating sphere at moderate Reynolds numbers. J. Fluid Mech. 621, 103130.
Haberman, W. L. & Morton, R. K.1953 An experimental investigation of the drag and shape of air bubbles rising in various liquids. Tech. Rep. 802, David W. Taylor Model Basin.
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 1970.
Joseph, D. D. 2006 Rise velocity of a spherical cap bubble. J. Fluid Mech. 488, 213223.
Lamb, H. 1932 Hydrodynamics, 6th edn. Dover.
Legendre, D. & Magnaudet, J. 1998 The lift force on a spherical bubble in a viscous linear shear flow. J. Fluid Mech. 368, 81126.
Legendre, D., Zenit, R. & Velez-Cordero, J. R. 2012 On the deformation of gas bubbles in liquids. Phys. Fluids 24, 043303.
Loth, E. 2008 Quasi-steady shape and drag of deformable bubbles and drops. Intl J. Multiphase Flow 34 (6), 523546.
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32, 659708.
Magnaudet, J. & Legendre, D. 1998 Some aspects of the lift force on a spherical bubble. Appl. Sci. Res. 58, 441461.
Magnaudet, J., Rivero, M. & Fabre, J. 1995 Accelerated flows past a rigid sphere or a spherical bubble. J. Fluid Mech. 284, 97135.
McLaughlin, J. B. 1996 Numerical simulation of bubble motion in water. J. Colloid Interface Sci. 184, 613625.
Mei, R., Klausner, J. & Lawrence, C. 1994 A note on the history force on a spherical bubble at finite Reynolds number. Phys. Fluids 6, 418420.
Moore, D. W. 1959 The rise of a gas bubble in a viscous liquid. J. Fluid Mech. 6, 113130.
Moore, D. W. 1965 The velocity rise of distorted gas bubbles in a liquid of small viscosity. J. Fluid Mech. 23, 749766.
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.
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, 439454.
Rastello, M., Marié, J. L., Grosjean, N. & Lance, M. 2009 Drag and lift forces on interface-contaminated bubbles spinning in a rotating flow. J. Fluid Mech. 624, 159178.
Rastello, M., Marié, J. L. & Lance, M. 2011 Drag and lift forces on clean spherical and ellipsoidal bubbles in a solid-body rotating flow. J. Fluid Mech. 682, 434459.
Schiller, L. & Naumann, A. Z. 1933 Uber die grundlegenden Berechnungen bei der Schwerkraftaufbereitung. Ver. Deut. Ing. 77, 318320.
Taylor, T. D. & Acrivos, A. 1964 On the deformation and drag of a falling viscous drop at low Reynolds number. J. Fluid Mech. 18, 466476.
Zhang, Z. & Prosperetti, A. 2005 A second-order method for three-dimensional particle simulation. J. Comput. Phys. 210, 292324.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed