Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-17T16:16:44.905Z Has data issue: false hasContentIssue false
  • English
  • Français

The three-dimensional hydrodynamic interaction of a finite sphere with a circular orifice at low Reynolds number

Published online by Cambridge University Press:  21 April 2006

Zong-Yi Yan ,
Sheldon Weinbaum ,
Peter Ganatos  and
Robert Pfeffer
Zong-Yi Yan
Affiliation:
Department of Mechanical Engineering, The City College of The City University of New York, NY 10031, USA Current address: Department of Mechanics, Peking University, Beijing, China.
Sheldon Weinbaum
Affiliation:
Department of Mechanical Engineering, The City College of The City University of New York, NY 10031, USA
Peter Ganatos
Affiliation:
Department of Mechanical Engineering, The City College of The City University of New York, NY 10031, USA
Robert Pfeffer
Affiliation:
Department of Chemical Engineering, The City College of The City University of New York, NY 10031, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes a combined multipole-series representation and integral-equation method for solving the low-Reynolds-number hydrodynamic interaction of a finite sphere at the entrance of a circular orifice. This method combines the flexibility of the intergral-equation method in treating complicated geometries and the accuracy and computational efficiency of the multipole-series-representation technique. For the axisymmetric case, the hydrodynamic force has been solved for the difficult case where the sphere intersects the plane of the orifice opening, which could not be treated by previous methods. For the three-dimensional case, the first numerical solutions have been obtained for the spatial variation of the twelve force and torque correction factors describing the translation or rotation of the sphere in a quiescent fluid at a pore entrance or the Sampson flow past a fixed sphere. Restricted by excessive computation time, accurate three-dimensional solutions are presented only for a sphere which is one-half the orifice diameter. However, based on an analysis of the behaviour of the force and torque correction factors for this case, approximate interpolation formulas utilizing the results on or near the orifice axis and in the far field are proposed for other diameter ratios, thus greatly extending the usefulness of the present solution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 174 , January 1987 , pp. 39 - 68
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

Batchelor, G. K. 1976 J. Fluid Mech. 74, 1.
Brenner, H. 1961 Chem. Engng Sci. 16, 242.
Brenner, H. & Gaydos, L. J. 1977 J. Colloid Interface Sci. 58, 312.
Dagan, Z., Pfeffer, R. & Weinbaum, S. 1982 J. Fluid Mech. 122, 273.
Dagan, Z., Weinbaum, S. & Pfeffer, R. 1982a J. Fluid Mech. 115, 505.
Dagan, Z., Weinbaum, S. & Pfeffer, R. 1982b J. Fluid Mech. 117, 143.
Dagan, Z., Weinbaum, S. & Pfeffer, R. 1983 Chem. Engng Sci. 38, 4.
Davis, A. M. J. 1983 Intl J. Multiphase Flow 9, 575.
Davis, R. E. & Acrivos, A. 1966 Chem. Engng Sci. 21, 681.
Ganatos, P., Pfeffer, R. & Weinbaum, S. 1978 J. Fluid Mech. 84, 79.
Ganatos, P., Pfeffer, R. & Weinbaum, S. 1980 J. Fluid Mech. 99, 755.
Ganatos, P., Weinbaum, S. & Pfeffer, R. 1982 J. Fluid Mech. 124, 27.
Gluckman, M. J., Pfeffer, R. & Weinbaum, S. 1971 J. Fluid Mech. 50, 705.
Goldman, A. J., Cox, R. G. & Brenner, H. 1967 Chem Engng Sci. 22, 637.
Haberman, W. L. & Sayre, R. M. 1958 David W. Taylor Model Basin Rep. No. 1143. Washington D.C.
Happel, J. & Brenner, H. 1973 Low Reynolds Number Hydrodynamics, 2nd edn. Noordhoff.
Ladyzhenskaya, O. A. 1963 The Mathematical Theory of Viscous Incompressible Flow, Chap. 3, Gordon & Breach.
Leal, L. G. & Lee, S. H. 1982 Adv. Colloid Interface Sci. 17, 61.
Lee, S. H. & Leal, L. G. 1982 J. Colloid Interface Sci. 87, 81.
Leichtberg, S., Pfeffer, R. & Weinbaum, S. 1976 Intl J. Multiphase Flow 3, 147.
Lewellen, P. C. 1982 Hydrodynamic analysis of microporous mass transport, Ph.D. dissertation, University of Wisconsin-Madison.
Miyazaki, T. & Hasimoto, H. 1984 J. Fluid Mech. 145, 201.
Rallinson, J. M. & Acrivos, A. 1978 J. Fluid Mech. 89, 191.
Sadhal, S. S. & Johnson, R. E. 1983 J. Fluid Mech. 126, 237.
Wang, Y., Kao, J., Weinbaum, S. & Pfeffer, R. 1986 On the inertial impaction of small particles at the entrance to a pore including hydrodynamic and molecular wall interaction effects. Chem. Engng Sci. (in press).Google Scholar
Weinbaum, S. 1981 Lectures on Mathematics in Life Sciences. Am. Math. Soc. 14, 110.Google Scholar
Yan, Z. 1985 Three-dimensional hydrodynamic and osmotic pore entrance phenomena, Ph.D. dissertation, The City University of New York.
Yan, Z., Shan, H. & Dagan, Z. 1987 The axisymmetric rise of a bubble at the exit of a circular orifice in the presence of insoluble surfactant caps. Int Conf. on Fluid Mech., The Chinese Soc. of Theo. and Appl. Mech., Beijing, China, June 16–19, 1987.
Yan, Z., Weinbaum, S. & Pfeffer, R. 1986 On the fine structure of osmosis at the entrance and exit of biological membrane pores, J. Fluid Mech. 162, 415.Google Scholar
Youngren, G. K. & Acrivos, A. 1975 J. Fluid Mech. 69, 377.
Youngren, G. K. & Acrivos, A. 1976 J. Fluid Mech. 76, 433.