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Flow of a viscous fluid past an array of spheres

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Abstract

The Stokes flow of a viscous incompressible fluid through a periodic array of impenetrable spheres with linear friction on the boundary is considered. A solution and an expression for the drag are obtained to terms of order c5/3 compared with unity (c is the volume concentration of the spheres). The proposed algorithm permits solution with any required degree of accuracy. The solution contains as limits the cases of perfect slip and no-slip on the surfaces of the spheres. In the problem with the no-slip condition, an asymptotically exact lower bound for the drag, which is valid for all values of the concentration c, is constructed.

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Literature cited

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Authors and Affiliations

  1. Moscow

    A. L. Berdichevskii

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  1. A. L. Berdichevskii
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 37–44, July–August, 1981.

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Berdichevskii, A.L. Flow of a viscous fluid past an array of spheres. Fluid Dyn 16, 518–524 (1981). https://doi.org/10.1007/BF01094593

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  • DOI: https://doi.org/10.1007/BF01094593

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