年間 4 号発行
ISSN 印刷: 2151-4798
ISSN オンライン: 2151-562X
Indexed in
SLOW MOTION OF A POROUS SPHERE OF VARIABLE PERMEABILITY IN A BOUNDED MEDIUM: EFFECT OF STRESS JUMP CONDITION
要約
In this paper, we present the study of the slow motion of a porous sphere of variable permeability in a spherical container, filled by a viscous incompressible fluid, at an instant it passes the center of the container. Flow in the spherical container and the porous sphere is governed by the Stokes equation and Brinkman's equation, respectively. Two cases are considered here: (i) when the permeability of the porous sphere varies quadratically with radial distance and (ii) when the permeability of the sphere is uniform. An analytical solution of the problem is obtained for both cases of permeability variation by using continuity of the velocity and normal stress and jump in tangential shear stress at the interface of the fluid and porous sphere as a boundary condition. Exact expression of the relevant hydrodynamical quantities such as streamlines, velocity, pressure, wall correction factor Wc, and drag D on the surface of the sphere are obtained. The influence of various parameters, such as stress jump coefficient β permeability parameter a and separation parameter λ, on streamlines, wall correction factor, and drag force, have been discussed and exhibited graphically. One figure shows that the drag force and wall correction parameter on the porous sphere increase with the decrease in stress jump coefficient β. We find that this parameter has a remarkable effect on Wc and drag D. Also, we compare the obtained results for both cases of permeability variation.
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