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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.v20.i9.30
pages 807-821

STOKES FLOW OVER A NON-NEWTONIAN ENCAPSULATED DROP OF ANOTHER LIQUID: EFFECT OF STRESS JUMP

Bharat Raj jaiswal
AKS University
Bali Ram Gupta
Department of Mathematics, JaypeeUniversity of Engineering and Tech., Guna 473226, M. P., India.

RÉSUMÉ

The translational motion of an incompressible viscous fluid over a composite sphere, consisting of a liquid core enveloped by a porous shell, is sought using the stress jump boundary condition (Oacha-Tapia) for tangential stress at the liquid-porous interface together with the continuity of velocity and normal stress components. The flow outside the porous shell (Region I) is governed by the Stokes' equation, inside the porous region (Region II) by the Brinkman equation, and within the non-Newtonian liquid sphere, the stream function is obtained by expanding it in a power series of S, characterizing the cross-viscosity of a Reiner-Rivlin fluid. The effect of stress jump coefficient β on the flow field has been studied analytically. The drag exerted by the fluid on the encapsulated drop is calculated and represented graphically with respect to permeability (k), cross-viscous parameter (S), and relative viscosity (λ). It is found that the effect of stress has a dual nature on drag force for varying β. It is also noticed that permeability of the porous shell decreases the drag on the body. Flow patterns have also been displayed through streamlines for diverse values of different parameters. Some earlier useful results have been also deduced from the ongoing study.


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