Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-18T16:53:51.007Z Has data issue: false hasContentIssue false
  • English
  • Français

The motion of a small sphere in fluid near a circular hole in a plane wall

Published online by Cambridge University Press:  20 April 2006

Takeshi Miyazaki  and
Hidenori Hasimoto
Takeshi Miyazaki
Affiliation:
Division of Atmospheric Environment, The National Institute for Environmental Studies, Tsukuba, Ibaraki, Japan
Hidenori Hasimoto
Affiliation:
Department of Physics, University of Tokyo, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

The Stokes flow due to the motion of a small particle in arbitrary directions is investigated in the presence of a circular hole in an infinite thin plane wall separating a quiescent viscous fluid.

The solutions of the boundary-value problem are obtained in closed forms to the point-force approximation in toroidal coordinates, by the use of the Green and Neumann functions supplemented by the edge function to remove the singularity at the rim of the hole. The volume flux through the hole and the force and torque experienced by the small spherical particle are determined on the basis of this solution. The case of linear motion parallel to the plane of the wall is discussed in detail.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 145 , August 1984 , pp. 201 - 221
Copyright
© 1984 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

Bateman, H. 1932 Partial Differential Equations, p. 461. Cambridge University Press.
Brenner, H. 1964 J. Fluid Mech. 18, 144.
Dagan, Z., Weinbaum, S. & Pfeffer, R. 1982 J. Fluid Mech. 117, 143.
Davis, A. M. J. 1983 Intl J. Multiphase Flow 9, 575.
Davis, A. M. J., O'Neill, M. E. & Brenner, H. 1981 J. Fluid Mech. 103, 183 (and Corrigendum 111, 1981, 499).
Happell, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics, chaps 5 and 7. Prentice-Hall.
Hasimoto, H. 1978 Mixed boundary value problem in fluid mechanics. Inst. Math. Sci. Kyoto Univ. Lecture Note 335, p. 1. (In Japanese)Google Scholar
Hasimoto, H. 1979 Mixed boundary value problem in fluid mechanics. Inst. Math. Sci. Kyoto Univ. Lecture Note 360, p. 1. (In Japanese)Google Scholar
Hasimoto, H. 1981 J. Phys. Soc. Japan 50, 4068.
Hasimoto, H., Kim, M. & Miyazaki, T. 1983 J. Phys. Soc. Japan 52, 1996.
Hasimoto, H. & Sano, O. 1980 Ann. Rev. Fluid Mech. 12, 335.
Imai, I. 1973 Ryutai Rikigaku (Fluid Mechanics), Tokyo p. 428 Syokabo. (In Japanese)
Kim, M. 1979 J. Phys. Soc. Japan 47, 1670.
Miyazaki, T. & Hasimoto, H. 1982 J. Phys. Soc. Japan 51, 2343.
Sano, O. & Hasimoto, H. 1976 J. Phys. Soc. Japan 40, 884.
Sano, O. & Hasimoto, H. 1977 J. Phys. Soc. Japan 42, 306.
Sano, O. & Hasimoto, H. 1978 J. Fluid Mech. 87, 673.
Wendt, G. 1958 In Handbuch der Physik (ed. S. Flugge), vol. 16, p. 144. Springer.