Abstract
The problem of a general non-axisymmetric Stokes flow of a viscous fluid past a porous sphere is considered. The expressions for the velocity and pressure, both inside and outside the sphere are given, when the flow outside satisfies the Stokes equations and the flow inside the sphere is governed by Darcy's law. The expressions for drag and torque are given. It is found that the drag is greater or smaller than the drag in the rigid case, depending on whether the undisturbed velocity is a pure biharmonic or a harmonic respectively. The torque is same as in the rigid case.
References
L. V. Wolfersdorf,Stokes flow past a sphere with permeable surface, ZAMM,69, 111–112 (1989).
A. I. Leonov,The slow stationary flow of a viscous fluid about a porous sphere, P.M.M.,26, 564–566 (1962).
D. D. Joseph and L. N. Tao,The effect of permeability on the slow motion of a porous sphere in a viscous liquid, ZAMM,44, 361–364 (1964).
B. S. Padmavathi, T. Amaranath and D. Palaniappan,Stokes flow past a permeable sphere, Non-axisymmetric case, ZAMM., (to appear).
D. Palaniappan, T. Amaranath, S. D. Nigam and R. Usha,Lamb's solution of Stokes equations: A sphere theorem, Quart. J. Mech. Appl. Math.,45, 1 (1992).
H. Faxén,Der Widerstand gegen die Bewegung einer 'starren Kugel in einer zähen Flüssigkeit, die zwischen zwei parallelen, ebenen Wänden eingeschlossen ist, Arkiv. Mat. Astron. Fys.,18, 3 (1924).
E. Almansi,Sull integrazione dell' equazione differenziale V2n=0, Ann. Mat. Pura App. Ser. III,2, 1–51 (1899).
D. Palaniappan, S. D. Nigam, T. Amaranath and R. Usha,A theorem for shear-free sphere in Stokes' flow, Mech. Res. Comm.,17, 429–435 (1990).
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Padmavathi, B.S., Amaranath, T. A solution for the problem of stokes flow past a porous sphere. Z. angew. Math. Phys. 44, 178–184 (1993). https://doi.org/10.1007/BF00914360
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DOI: https://doi.org/10.1007/BF00914360