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Wall effects on a rotating sphere

  • QIANLONG LIU (a1) and ANDREA PROSPERETTI (a1) (a2)
Abstract

The flow induced by a spherical particle spinning in the presence of no-slip planar boundaries is studied by numerical means. In addition to the reference case of an infinite fluid, the situations considered include a sphere rotating near one or two infinite plane walls parallel or perpendicular to the axis of rotation and a sphere centred within a cube. The hydrodynamic force and couple acting on the sphere exhibit a complex behaviour under the sometimes competing, sometimes cooperating action of viscous, inertial and centrifugal effects.

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Corresponding author
Email address for correspondence: prosperetti@jhu.edu
References
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Banks W. H. H. 1976 The laminar boundary layer on a rotating sphere. Acta Mech. 24, 273287.
Barrett K. E. 1967 On the impulsively started rotating sphere. J. Fluid Mech. 27, 779788.
Besseris G. J., Miller I. F. & Yeates D. B. 1999 Rotational magnetic particle microrheometry: the Newtonian case. J. Rheol. 43, 591608.
Bickley W. G. 1938 The secondary flow due to a sphere rotating in a viscous fluid. Phil. Mag. 25, 746752.
Brenner H. 1964 Slow viscous rotation of an axisymmetric body within a circular cylinder of finite length. Appl. Sci. Res. A 13, 81120.
Bush J. W. M., Stone H. A. & Tanzosh J. P. 1994 Particle motion in rotating viscous fluids: historical survey and recent developments. Curr. Top. Phys. Fluids 1, 337355.
Chaoui M. & Feuillebois F. 2003 Creeping flow around a small sphere in a shear flow close to a wall. Q. J. Mech. Appl. Nath. 56, 381410.
Collins W. D. 1955 On the steady rotation of a sphere in a viscous fluid. Mathematika 2, 4247.
Cox R. G. & Brenner H. 1967 a Effect of boundaries on the Stokes resistance of an arbitrary particle. Part 3. Translation and rotation. J. Fluid Mech. 28, 391411.
Cox R. G. & Brenner H. 1967 b The slow motion of a sphere through a viscous fluid towards a plane surface. II. Small gap widths, including inertial effects. Chem. Engng Sci. 22, 17531777.
Damiano E. R., Long D. S., El-Khatib F. H. & Stace T. M. 2004 On the motion of a sphere in a Stokes flow parallel to a Brinkman medium. J. Fluid Mech. 500, 75101.
Dean W. R. & O'Neill M. E. 1963 A slow rotation of viscous liquid caused by the rotation of a solid sphere. Mathematika 10, 1324.
Dennis S. C. R. & Duck P. W. 1988 Unsteady flow due to an impulsively started rotating sphere. Comput. Fluids 16, 291310.
Dennis S. C. R., Ingham D. B. & Singh S. N. 1981 The steady flow of a viscous fluid due to a rotating sphere. Q. J. Mech. Appl. Math. 34, 361381.
Dennis S. C. R., Singh S. N. & Ingham D. B. 1980 The steady flow due to a rotating sphere at low and moderate Reynolds numbers. J. Fluid Mech. 101, 257279.
Feuillebois F. & Lasek A. 1978 On the rotational historic term in non-stationary Stokes flow. Q. J. Mech. Appl. Math. 31, 435443.
Fletcher C. 1988 Computational Techniques for Fluid Dynamics. Springer.
Ganatos P., Pfeffer R. & Weinbaum S. 1980 a Strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. Part 2. Parallel motion. J. Fluid Mech. 99, 755783.
Ganatos P., Weinbaum S. & Pfeffer R. 1980 b Strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. Part 1. Perpendicular motion. J. Fluid Mech. 99, 739754.
Garrett S. J. & Peake N. 2002 The stability of the boundary layer on a rotating sphere. J. Fluid Mech. 456, 199218.
Gavze E. 1990 The accelerated motion of rigid bodies in non-steady Stokes flow. Intl J. Multiphase Flow 16, 153166.
Goldman A. J., Cox R. G. & Brenner H. 1967 Slow viscous motion of a sphere parallel to a plane wall. Part I. Motion through a quiescent fluid. Chem. Engng Sci. 22, 637651.
Happel J. & Brenner H. 1973 Low-Reynolds Number Hydrodynamics, with Special Applications to Particulate Media, 2nd edn. Noordhoff.
Hollerbach R., Wiener R. J., Sullivan I. S., Donnelly R. J. & Barenghi C. F. 2002 The flow around a torsionally oscillating sphere. Phys. Fluids 14, 41924205.
Jeffery G. B. 1915 On the steady rotation of a solid of revolution in a viscous fluid. Proc. Lond. Math. Soc. 14, 327338.
Keh H. J. & Chen P. Y. 2001 Slow motion of a droplet between two parallel plane walls. Chem. Engng Sci. 56, 68636871.
Kim S. & Karrila S. 1991 Microhydrodynamics. Butterworth (reprinted by Dover 2005).
Kohama Y. & Kobayashi R. 1983 Boundary-layer transition and the behaviour of spiral vortices on rotating spheres. J. Fluid Mech. 137, 153164.
Lamb H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Landau L. & Lifshitz E. 1987 Fluid Mechanics, 2nd edn. Pergamon.
Leach J., Mushfique H., Keen S., Di Leonardo R., Ruocco G., Cooper J. M. & Padgett M. 2009 Comparison of Faxn's correction for a microsphere translating or rotating near a surface. Phys. Rev. E 79, 026301.
Loper D. E. 2001 On the structure of a Taylor column driven by a buoyant parcel in an unbounded rotating fluid. J. Fluid Mech. 427, 131165.
Malysa K. & van de Ven T. G. M. 1986 Rotational and translational motion of a sphere parallel to a wall. Intl J. Multiphase Flow 12, 459468.
Milne-Thomson L. 1968 Theoretical Hydrodynamics, 5th edn. MacMillan.
Minkov E., Ungarish M. & Israeli M. 2000 The motion generated by a rising particle in a rotating fluid – numerical solutions. Part 1. A short container. J. Fluid Mech. 413, 111148.
Minkov E., Ungarish M. & Israeli M. 2002 The motion generated by a rising particle in a rotating fluid – numerical solutions. Part 2. The long container case. J. Fluid Mech. 454, 345364.
O'Neill M. E. 1964 A slow motion of viscous liquid caused by a slowly moving solid sphere. Mathematika 11, 6774.
Parkin S. J. W., Knner G., Nieminen T. A., Heckenberg N. R. & Rubinsztein-Dunlop H. 2007 Microrheology of microlitre samples: probed with rotating optical tweezers. Proc. SPIE 6644, 66440O.
Peyret R. & Taylor T. 1983 Computational Methods for Fluid Flow. Springer.
Sawatzki O. 1970 Das strömungsfeld um eine rotierende kugel. Acta Mech. 9, 159214.
Shail R. 1997 Some regular perturbation solutions in fluid mechanics. Q. J. Mech. Appl. Math. 50, 128147.
Takagi H. 1974 Slow rotation of two touching spheres in viscous fluid. J. Phys. Soc. Japan 36, 875877.
Taniguchi H., Kobayashi T. & Fukunishi Y. 1998 Stability of the boundary layer on a sphere rotating in still fluid. Acta Mech. 129, 243253.
Walters K. & Waters N. D. 1963 On the use of a rotating sphere in the measurement of elasto-viscous parameters. Brit. J. Appl. Phys. 14, 667671.
Walters K. & Waters N. D. 1964 The interpretation of experimental results obtained from a rotating-sphere elasto-viscometer. Brit. J. Appl. Phys. 15, 989991.
Wimmer M. 1988 Viscous flows and instabilities near rotating bodies. Prog. Aerospace Sci. 25, 43103.
Wu X., Cen K., Luo Z., Wang Q. & Fang M. 2008 a Measurement on particle rotation speed in gas–solid flow based on identification of particle rotation axis. Exp. Fluids 45, 11171128.
Wu X., Wang Q., Luo Z., Fang M. & Cen K. 2008 b Theoretical and experimental investigations on particle rotation speed in a CFB riser. Chem. Engng Sci. 63, 39793987.
Xin J. & Megaridis C. 1996 Droplet spindown in a high-temperature gas environment. Intl J. Heat Fluid Flow 17, 567578.
Zhang Z. Z. & Prosperetti A. 2005 Sedimentation of 1.024 particles. In Proceedings of the ASME Fluids Engineering Division Summer Conference, Paper no. FEDSM2005–77133. ASME.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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