Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-20T07:11:23.534Z Has data issue: false hasContentIssue false
  • English
  • Français

The general solution for an ellipsoid in low-Reynolds-number flow

Published online by Cambridge University Press:  21 April 2006

Sangtae Kim  and
P. V. Arunachalam
Sangtae Kim
Affiliation:
Department of Chemical Engineering, University of Wisconsin, 1415 Johnson Drive, Madison, WI 53706, USA
P. V. Arunachalam
Affiliation:
Mathematics Research Center, University of Wisconsin, 610 Walnut Street, Madison, WI 53705, USA Permanent address: Department of Mathematics, Sri Venkateswara University, Tirupati 517502, India.
Get access Rights & Permissions [Opens in a new window]

Abstract

The general solution for low-Reynolds-number flow about an ellipsoid is derived by the singularity method and by representation in ellipsoidal harmonics. It is shown that, as in potential flow, the focal ellipse is the image system for the ellipsoid. A simple transformation which resembles a step in the derivation of the Dirichlet potential is introduced and its implications are explored. This transformation converts the velocity representation for an nth-order ambient field into that for the (n + 1)th-order field. The method furnishes an explanation for the invariance of the domain of the singularity distribution (the focal ellipse) with respect to the ambient field. Faxén relations for all multipole moments for arbitrary Stokes flow are derived in both integral and symbolic operator forms.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 178 , May 1987 , pp. 535 - 547
Copyright
© 1987 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. 1966 Chem. Engng Sci. 21, 97.
Brenner, H. 1972 Prog. Heat Mass Transfer 5, 89.
Brenner, H. & Haber, S. 1983 Physicochem. Hydrodyn. 4, 271.
Chwang, A. T. 1975 J. Fluid Mech. 72, 17.
Chwang, A. T. & Wu, T. Y. 1974 J. Fluid Mech. 63, 607.
Chwang, A. T. & Wu, T. Y. 1975 J. Fluid Mech. 67, 787.
Edwardes, D. 1892 Q. J. Maths 26, 70.
Giesekus, H. 1962 Rheol. Acta 2, 50.
Gluckman, M. J., Pfeffer, R. & Weinbaum, S. 1971 J. Fluid Mech. 50, 705.
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics. Martinus Nijhoff.
Hinch, E. J. & Leal, L. G. 1972 J. Fluid Mech. 52, 683.
Hinch, E. J. & Leal, L. G. 1979 J. Fluid Mech. 92, 591.
Jeffery, G. B. 1922 Proc. R. Soc. Lond. A 102, 161.
Kim, S. 1985 Intl J. Multiphase Flow 11, 713.
Kim, S. 1986 Intl J. Multiphase Flow 12, 469.
Liao, W. & Krueger, D. 1980 J. Fluid Mech. 96, 223.
Miloh, T. 1974 S I A M J. Appl. Maths 26, 334.
Oberbeck, A. 1876 Crelles J. 81, 62.
Rallison, J. M. 1978 J. Fluid Mech. 88, 529.
Russel, W. B. 1976 J. Colloid Interface Sci. 55, 590.
Zeichner, G. R. & Schowalter W. R., 1977 Aiche J. 23, 243.