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Journal of Porous Media
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ISSN Imprimer: 1091-028X
ISSN En ligne: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v11.i6.50
pages 575-588

Rotation of a Solid Sphere in a Viscous Fluid Bounded by a Concentric Spherical Porous Medium

Parul Saxena
Department of Mathematics and Astronomy, University of Lucknow, Lucknow, Uttar Pradesh 226007, India
A. C. Srivastava
Department of Mathematics & Astronomy, Lucknow University, Lucknow - 226007, India


The flow of a viscous fluid in a spherical annulus formed by a solid sphere rotating with a constant angular velocity and a concentric spherical porous medium has been discussed for small Reynolds numbers. The porous medium is fully saturated with the viscous fluid. It is assumed that the flow in the annular region of the width d in which a clear fluid flows is governed by the Navier-Stokes equation and that in the porous medium by Brinkman equation. Two flows are matched at the interface by the conditions suggested by Ochoa-Tapia and Whitaker. It has been found that the rotational velocity in both the media increases with the increase of permeability and with the decrease of d. It is maximum at the interface and then decreases exponentially. The effects of the decrease of d and increase of the ratio of effective viscosity in the porous medium and the viscosity of the fluid are to increase the torque on the rotating sphere. The torque on the rotating sphere also increases with the decrease of the permeability of the porous medium.