Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-08T02:28:03.946Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of two plane walls on the motion of a small sphere in a viscous fluid

Published online by Cambridge University Press:  12 April 2006

Osamu Sano  and
Hidenori Hasimoto
Osamu Sano
Affiliation:
Department of Physics, Faculty of Science, University of Tokyo, Japan
Hidenori Hasimoto
Affiliation:
Department of Physics, Faculty of Science, University of Tokyo, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

A theoretical study is made of the motion of a small sphere in an incompressible viscous fluid bounded by two plane walls. The analysis is based on the Stokes equations of motion and the method of reflexions is employed to obtain the lowest-order wall effect on the sphere, which is allowed either to rotate or not as it translates in an arbitrary direction. The effect of two plane walls on the force and torque (or angular velocity) experienced by the sphere is not accurately estimated by superposing the contributions from the two individual walls.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 4 , 29 August 1978 , pp. 673 - 694
Copyright
© 1978 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

Brenner, H. 1962 J. Fluid Mech. 12, 35.
Brenner, H. 1964 J. Fluid Mech. 18, 144.
Brenner, H. & Happel, J. 1958 J. Fluid Mech. 4, 195.
Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1954 Tables of Integral Transforms, vol. 2. McGraw-Hill.
Faxén, H. 1921 dissertation, Uppsala University (see Happel & Brenner 1973).
Faxén, H. 1922 Ann. Phys. 68, 89.
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics. Noordhoff.
Hasimoto, H. 1976 J. Phys. Soc. Japan 41, 2143; 42, 1047.
Ho, B. P. & Leal, L. G. 1974 J. Fluid Mech. 65, 365.
Imai, I. 1973 Ryutai Rikigaku (Fluid Dynamics). Syokabo.
Kim, M. U. 1976 Ph.D. thesis, University of Tokyo.
Ladenburg, R. 1907 Ann. Phys. 23, 447.
Lorentz, H. A. 1907 Abh. Theor. Phys., Leipzig 1, 23.
Sano, O. 1977 Ph.D. thesis, University of Tokyo.
Sano, O. & Hasimoto, H. 1976 J. Phys. Soc. Japan 40, 884.
Sano, O. & Hasimoto, H. 1977 J. Phys. Soc. Japan 42, 306.
Wakiya, S. 1956 Res. Rep. Fac. Engng, Niigata Univ. (Japan) 5, 1.