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Slow motion of two spheres in a shear field

Published online by Cambridge University Press:  29 March 2006

C. J. Lin ,
K. J. Lee  and
N. F. Sather
C. J. Lin
Affiliation:
Department of Chemical Engineering, University of Washington, Seattle, Washington 98105
K. J. Lee
Affiliation:
Department of Chemical Engineering, University of Washington, Seattle, Washington 98105
N. F. Sather
Affiliation:
Department of Chemical Engineering, University of Washington, Seattle, Washington 98105
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Abstract

The exact solution of the Stokes equations for the creeping motion of two spheres of arbitrary size and arbitrarily oriented with respect to a shear field is obtained by use of spherical bipolar co-ordinates. Numerical results are given for two special cases: (1) the free motion of two equal-sized spheres in simple shear flow and (2) the free motion of a sphere near a wall in the rotational shear field between two parallel disks rotating at different rates. The sphere trajectories calculated for the first of these problems are found to agree fairly well with those observed experimentally.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 43 , Issue 1 , 17 August 1970 , pp. 35 - 47
Copyright
© 1970 Cambridge University Press

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References

Brenner, H. 1961 Chem. Engng Sci. 16, 24.
Darabaner, C. L. & Mason, S. G. 1967 Rheol. Acta, 6, 273.
Dean, W. R. & O'Neill, M. E. 1963 Mathematika, 10, 13.
Goldman, A. J., Cox, R. G. & Brenner, H. 1966 Chem. Engng Sci. 21, 115.
Goldman, A. J., Cox, R. G. & Brenner, H. 1967 a Chem. Engng Sci. 22, 63.
Goldman, A. J., Cox, R. G. & Brenner, H. 1967 b Chem. Engng Sci. 22, 65.
Jeffery, G. B. 1915 Proc. Lond. Math. Soc. (Ser. 2) 14, 327.
Lin, C. J. 1968 Doctoral Thesis, University of Washington, Seattle.
Maude, A. D. 1961 Br. J. Appl. Phys. 12, 29.
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. New York: McGraw-Hill.
O'Neill, M. E. 1964 Mathematika, 11, 67.
O'Neill, M. E. 1968 Chem. Engng Sci. 23, 129.
Stimson, M. & Jeffery, G. B. 1926 Proc. Roy. Soc. A 111, 110.
Wakiya, S. 1967 J. Phys. Soc. Japan, 22, 1101.
Supplementary material: PDF

C. J. Lin , K. J. Lee and N. F. Sather supplementary material

Supplementary material

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