Using a recently developed image representation for Stokes flow in a half-space bounded by a planar wall [Cichocki and Jones, Physica A 258, 273 (1998)], the image system is constructed for the flow field produced by a force multipole in the space bounded by two parallel walls. The image singularities are expressed in terms of products of double-reflection matrices, and the expansion is simplified using symmetries of the double-reflection operation. Our analysis yields recurrence relations for the strengths of the image multipoles. The relations are solved explicitly, and a complete image system is obtained for an arbitrary source-force multipole. Applications of our image representation for evaluating the hydrodynamic friction and mobility matrices of particles interacting with two parallel planar walls are indicated.
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November 2002
Research Article|
November 01 2002
Image system for Stokes-flow singularity between two parallel planar walls
S. Bhattacharya;
S. Bhattacharya
Department of Mechanical Engineering, Yale University, P.O. Box 20-8286, New Haven, Connecticut 06520-8286
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J. Bławzdziewicz
J. Bławzdziewicz
Department of Mechanical Engineering, Yale University, P.O. Box 20-8286, New Haven, Connecticut 06520-8286
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J. Math. Phys. 43, 5720–5731 (2002)
Article history
Received:
May 30 2002
Accepted:
July 08 2002
Citation
S. Bhattacharya, J. Bławzdziewicz; Image system for Stokes-flow singularity between two parallel planar walls. J. Math. Phys. 1 November 2002; 43 (11): 5720–5731. https://doi.org/10.1063/1.1508812
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