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Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow

  • D. J. Jeffrey (a1) (a2) and Y. Onishi (a3)

Two unequal rigid spheres are immersed in unbounded fluid and are acted on by externally applied forces and couples. The Reynolds number of the flow around them is assumed to be small, with the consequence that the hydrodynamic interactions between the spheres can be described by a set of linear relations between, on the one hand, the forces and couples exerted by the spheres on the fluid and, on the other, the translational and rotational velocities of the spheres. These relations may be represented completely by either a set of 10 resistance functions or a set of 10 mobility functions. When non-dimensionalized, each function depends on two variables, the non-dimensionalized centre-to-centre separation s and the ratio of the spheres’ radii λ. Two expressions are given for each function, one a power series in s−1 and the other an asymptotic expression valid when the spheres are close to touching.

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Adler, P. M. 1981 J. Coll. Interface Sci. 84, 461.
Batchelor, G. K. 1974 Ann. Rev. Fluid Mech. 6, 227.
Batchelor, G. K. 1976 J. Fluid Mech. 74, 1.
Batchelor, G. K. 1982 J. Fluid Mech. 119, 379.
Brenner, H. 1963 Chem. Engng Sci. 18, 1.
Brenner, H. 1964 Chem. Engng Sci. 19, 599.
Brenner, H. & O'NEILL, M. E. 1972 Chem. Engng Sci. 27, 1421.
Cooley, M. D. A. & O'NEILL, M. E. 1969a Mathematika 16, 37.
Cooley, M. D. A. & O'NEILL, M. E. 1969b Proc. Camb. Phil. Soc. 66, 407.
Ganatos, P., Pfeffer, R. & Weinbaum, S. 1978 J. Fluid Mech. 84, 79.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Hobson, E. W. 1931 Spherical and Ellipsoidal Harmonics. Cambridge University Press.
Jeffery, G. B. 1915 Proc. Lond. Math. Soc. 14, 327.
Jeffrey, D. J. 1973 Proc. R. Soc. Lond. A, 335, 355.
Jeffrey, D. J. 1982 Mathematika 29, 58.
Jeffrey, D. J. & Acrivos, A. 1976 AIChE J. 22, 417.
Jeffrey, D. J. & Onishi, Y. 1984 Z. angew. Math. Phys. (submitted).
Lorentz, H. A. 1906 Abhandl. theoret. Phys. 1, 23.
Majumdar, S. R. 1967 Mathematika 14, 43.
Nir, A. & Acrivos, A. 1973 J. Fluid Mech. 59, 209 and Corrigendum 61, 829.
O'Neill, M. E. 1969 Proc. Camb. Phil. Soc. 65, 543.
O'Neill, M. E. & Majumdar, S. R. 1970a Z. angew. Math. Phys. 21, 164.
O'Neill, M. E. & Majumdar, S. R. 1970b Z. angew. Math. Phys. 21, 180.
O'Neill, M. E. & Stewartson, K. 1967 J. Fluid Mech. 27, 705.
Oseen, C. W. 1927 Hydrodynamic. Leipzig: Acad. Verlag.
Smoluchowski, M. 1911 Bull. Inter. acad. Polonaise sci. lett. 1A, 28.
Van Dyke, M. D. 1975 Perturbation Methods in Fluid Mechanics. Parabolic.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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