Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-18T18:16:41.397Z Has data issue: false hasContentIssue false
  • English
  • Français

Drag on a sphere in slow shear flow

Published online by Cambridge University Press:  26 April 2006

Kunimasa Miyazaki ,
Dick Bedeaux  and
Josep Bonet Avalos
Kunimasa Miyazaki
Affiliation:
Department of Physical and Macromolecular Chemistry, Gorlaeus Laboratories, PO Box 9502, 2300RA Leiden, The Netherlands Present address: Department of Applied Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan.
Dick Bedeaux
Affiliation:
Department of Physical and Macromolecular Chemistry, Gorlaeus Laboratories, PO Box 9502, 2300RA Leiden, The Netherlands
Josep Bonet Avalos
Affiliation:
Institut Charles Sadron (CNRS-ULP), 6 rue Boussingault, 67083 Strasbourg Cedex, France Permanent address: Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain.
Get access Rights & Permissions [Opens in a new window]

Abstract

A general closed form for the mobility tensor of a sphere moving in a fluid in stationary homogeneous flow is derived using the induced force method up to the first order in the square root of the Reynolds number based on the velocity gradient of the unperturbed flow. The closed form for the mobility tensor is valid for the time-dependent case as well as for the stationary case. As a special case, we calculate it explicitly for a simple shear flow. The result for the x, z-component for the stationary case, which gives the lift force, agrees with the value calculated by Saffman.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 296 , 10 August 1995 , pp. 373 - 390
Copyright
© 1995 Cambridge University Press

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

Bedeaux, D. & Rubi, J. M. 1987 Drag on a sphere moving slowly through a fluid in elongational flow. Physica A 144, 285–298.Google Scholar
Drew, D. A. 1978 The force on a small sphere in slow viscous flow. J. Fluid Mech. 88, 393–400.Google Scholar
Gotoh, T. 1990 Brownian motion in a rotating flow. J. Statist. Phys. 59, 371–402.Google Scholar
Harper, E. Y. & Chang, I.-D. 1968 Maximum dissipation resulting from lift in a slow viscous shear flow. J. Fluid Mech. 33, 209–225.Google Scholar
Herron, I. H., Davis, S. H. & Bretherton, F. P. 1975 On the sedimentation of a sphere in a centrifuge. J. Fluid Mech. 68, 209–234.Google Scholar
Ishii, K. & Hasimoto, H. 1980 Lateral migration of a spherical particle in flows in a circular tube. J. Phys. Soc. Japan 48, 2144–2155.Google Scholar
Mazur, P. & Bedeaux, D. 1974 A generalization of Faxén theorem to nonsteady motion of a sphere through an incompressible fluid in arbitrary flow. Physica 76, 235–246.Google Scholar
Mazur, P. & Saarloos, W. VAN 1982 Many-sphere hydrodynamic interactions and mobilities in a suspension. Physica A 115, 21–57.Google Scholar
Mazur, P. & Weisenborn, A. J. 1984 The Oseen drag on a sphere and the method of induced force. Physica A 123, 209–226.Google Scholar
McLaughlin, J. B. 1991 Inertial migration of a small sphere in linear shear flow. J. Fluid Mech. 224, 261–274.Google Scholar
McLaughlin, J. B. 1993 The lift on a small sphere in wall-bounded linear shear flows. J. Fluid Mech. 246, 249–265.Google Scholar
Miyazaki, K. 1995 Dependence of the friction tensor on the rotation of a frame of reference. submitted to Physica A.
Onuki, A. & Kawasaki, K. 1980 Critical phenomena of classical fluid under flow. I. Prog. Theor. Phys. 63, 122–139.Google Scholar
Pérez-Madrid, A., Rubi, J. M. & Bedeaux, D. 1990 Motion of a sphere through a fluid in stationary homogeneous flow. Physica A 163, 778–790.Google Scholar
Rabin, Y., Wang, S. Q. & Creamer, D. B. 1989 Linearized velocity disturbances dynamic Oseen tensors in simple shear and elongational flows. J. Chem. Phys. 90, 570–574.Google Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400 (and Corrigendum, 1968, 31, 624).Google Scholar
Stokes, G. G. 1851 On the effect of the internal friction of fluids on the motion of pendulums. Camb. Phil. Trans. 9, 8–106.Google Scholar
Weisenborn, A. J. 1985 Drag on a sphere moving slowly in a rotating viscous fluid. J. Fluid Mech. 153, 215–227.Google Scholar