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The hydrodynamic interactions between two spheres in a Brinkman medium

Published online by Cambridge University Press:  20 April 2006

Sangtae Kim  and
William B. Russel
Sangtae Kim
Affiliation:
Department of Chemical Engineering, Princeton University. NJ 08544 Present address: Department of Chemical Engineering and Mathematics Research Center, University of Wisconsin, Madison, WI 53706.
William B. Russel
Affiliation:
Department of Chemical Engineering, Princeton University. NJ 08544
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Abstract

The hydrodynamic interaction between two spheres in a Brinkman medium has been calculated using both the method of reflections and the boundary collocation technique. In particular, calculation of the forces and dipoles for two spheres in a uniform stream and linear field show that the method of reflections converges more rapidly than in the Stokes case, owing to screening of interactions, and that the boundary collocation technique produces accurate solutions at almost all separations (except touching) with relatively few collocation points.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 154 , May 1985 , pp. 253 - 268
Copyright
© 1985 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. 1964 Handbook of Mathematical Functions. National Bureau of Standards.
Batchelor, G. K. & Green, J. T. 1972 J. Fluid Mech. 56, 375.
Brenner, H. 1972 Chem. Engng Sci. 27, 1069.
Brinkman, H. C. 1947 Appl. Sci. Res. A1, 27.
Faxen, H. 1922 Ark. Mat. Astron. Fys. 17, no. 1.
Faxen, H. 1927 Ark. Mat. Astron. Fys. 20, no. 8.
Felderhof, B. U. 1975 Physica 80A, 63, 172.
Felderhof, B. U. & Deutch, J. M. 1975 J. Chem. Phys. 62, 2879, 2398.
Ganatos, P., Pfeffer, R. & Weinbaum, S. 1978 J. Fluid Mech. 84, 79.
Ganatos, P., Pfeffer, R. & Weinbaum, S. 1980 J. Fluid Mech. 99, 755.
Glendinning, A. B. & Russel, W. B. 1983 J. Coll. Interface Sci. 93, 95.
Gluckman, M. J., Pfeffer, R. & Weinbaum, S. 1971 J. Fluid Mech. 50, 705.
Goldman, A. J., Cox, R. G. & Brenner, H. 1966 Chem. Engng Sci. 21, 1151.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Higdon, J. J. L. & Kojima, M. 1981 Intl J. Multiphase Flow 7, 719.
Hobson, E. 1955 The Theory of Spherical and Ellipsoidal Harmonics. Chelsea.
Howells, I. D. 1974 J. Fluid Mech. 64, 449.
Kim, S. & Russel, W. B. 1985 J. Fluid Mech. 154, 269.
Koplik, J., Levine, H. & Zee, A. 1983 Phys. Fluids 26, 2864.
Leichtberg, S., Weinbaum, S., Pfeffer, R. & Gluckman, M. J. 1976 Phil. Trans. R. Soc. Lond. A 282, 585.
Stimson, M. & Jeffery, G. B. 1926 Proc. R. Soc. Lond. A 111, 110.
Stratton, J. A. 1941 Electromagnetic Theory. McGraw-Hill.