Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-24T05:46:31.976Z Has data issue: false hasContentIssue false
  • English
  • Français

A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. Part 1. Perpendicular motion

Published online by Cambridge University Press:  19 April 2006

Peter Ganatos ,
Sheldon Weinbaum  and
Robert Pfeffer
Peter Ganatos
Affiliation:
The City College of The City University of New York, New York 10031
Sheldon Weinbaum
Affiliation:
The City College of The City University of New York, New York 10031
Robert Pfeffer
Affiliation:
The City College of The City University of New York, New York 10031
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents the first ‘exact’ solutions to the creeping-flow equations for the transverse motion of a sphere of arbitrary size and position between two plane parallel walls. Previous solutions to this classical Stokes flow problem (Ho & Leal 1974) were limited to a sphere whose diameter is small compared with the distance of the closest approach to either boundary. The accuracy and convergence of the present method of solution are tested by detailed comparison with the exact bipolar co-ordinate solutions of Brenner (1961) for the drag on a sphere translating perpendicular to a single plane wall. The converged series collocation solutions obtained in the presence of two walls show that for the best case where the sphere is equidistant from each boundary the drag on the sphere predicted by Ho & Leal (1974), using a first-order reflexion theory, is 40 per cent below the true value when the walls are spaced two sphere diameters apart and is one order-of-magnitude lower at a spacing of 1.1 diameters.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 99 , Issue 4 , 29 August 1980 , pp. 739 - 753
Copyright
© 1980 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

Arminski, L., Weinbaum, S. & Pfeffer, R. 1980 J. Theor. Biol. (in press).
Brenner, H. 1961 Chem. Engng Sci. 16, 242.
Erdelyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1954 Tables of Integral Transforms, vol. 2. McGraw-Hill.
Ganatos, P. 1979 Ph.D. dissertation, City University of New York.
Ganatos, P., Pfeffer, R. & Weinbaum, S. 1978 J. Fluid Mech. 84, 79.
Ganatos, P., Pfeffer, R. & Weinbaum, S. 1980 J. Fluid Mech. 99, 755–783.
Gluckman, M. J., Pfeffer, R. & Weinbaum, S. 1971 J. Fluid Mech. 50, 705.
Halow, J. S. & Wills, G. B. 1970 A.I.Ch.E. J. 16, 281.
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics, 2nd edn Noordhoff.
Ho, B. P. & Leal, L. G. 1974 J. Fluid Mech. 65, 365.
Leichtberg, S., Pfeffer, R. & Weinbaum, S. 1976 Int. J. Multiphase Flow 3, 147.
Leichtberg, S., Weinbaum, S., Pfeffer, R. & Gluckman, M. J. 1976 Phil. Trans. Roy. Soc. A 282, 585.
Lorentz, H. A. 1907 Abhand. Theor. Phys. 1, 23.
Weinbaum, S. & Caro, C. G. 1976 J. Fluid Mech. 74, 611.