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Stokes Flow of Viscous Fluid Past a Micropolar Fluid Spheroid

Part of: Incompressible viscous fluids Foundations, constitutive equations, rheology

Published online by Cambridge University Press:  11 July 2017

M. Krishna Prasad  and
Manpreet Kaur
M. Krishna Prasad*
Affiliation:
National Institute of Technology, Department of Mathematics Raipur-492010, Chhattisgarh, India
Manpreet Kaur*
Affiliation:
National Institute of Technology, Department of Mathematics Raipur-492010, Chhattisgarh, India
*
*Corresponding author. Email:madaspra.maths@nitrr.ac.in, kpm973@gmail.com (M. K. Prasad), manpreet.kaur22276@yahoo.com (M. Kaur)
*Corresponding author. Email:madaspra.maths@nitrr.ac.in, kpm973@gmail.com (M. K. Prasad), manpreet.kaur22276@yahoo.com (M. Kaur)
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Abstract

The Stokes axisymmetric flow of an incompressible viscous fluid past a micropolar fluid spheroid whose shape deviates slightly from that of a sphere is studied analytically. The boundary conditions used are the vanishing of the normal velocities, the continuity of the tangential velocities, continuity of shear stresses and spin-vorticity relation at the surface of the spheroid. The hydrodynamic drag force acting on the fluid spheroid is calculated. An exact solution of the problem is obtained to the first order in the small parameter characterizing the deformation. It is observed that due to increase spin parameter value, the drag coefficient decreases. Well known results are deduced and comparisons are made with classical viscous fluid and micropolar fluid.

Keywords

Stokes flowmicropolar fluiddrag forcespheroidspin vorticity relation

MSC classification

Secondary: 76A05: Non-Newtonian fluids 76D07: Stokes and related (Oseen, etc.) flows
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 5 , October 2017 , pp. 1076 - 1093
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Eringen, A. C., Theory of micropolar fluids, J. Math. Mech., 16 (1966), pp. 1–18.Google Scholar
[2] Eringen, A. C., Microcontinuum Field Theories II: Fluent Media, Springer, New York, 2001.Google Scholar
[3] Ariman, T., Turk, M. A. and Sylvester, N. D., Applications of microcontinuum fluid mechanics, Int. J. Eng. Sci., 12 (1974), pp. 273–293.CrossRefGoogle Scholar
[4] Lukaszewicz, G., Micropolar Fluids: Theory and Applications, Birkhäuser, Basel, 1999.CrossRefGoogle Scholar
[5] Rybczynski, W., On the translatory motion of a fluid sphere in a viscous medium, Bull Acad. Sci. Cracow. Ser. A, 40 (1911), pp. 40–46.Google Scholar
[6] Hadamard, J. S., Mécanique-mouvement permanent lent d’une sphère liquide et visqueuse dans un liquide visqueux, CR Acad. Sci., 152 (1911), pp. 1735–1738.Google Scholar
[7] Hetsroni, G. and Haber, S., The flow in and around a droplet or bubble submerged in an unbounded arbitrary velocity field, Rheol Acta, 9 (1970), pp. 488–496.CrossRefGoogle Scholar
[8] Bart, E., The slow unsteady settling of a fluid sphere toward a flat fluid interface, Chem. Eng. Sci., 23 (1968), pp. 193–210.CrossRefGoogle Scholar
[9] Wacholder, E. and Weihs, D., Slow motion of a fluid sphere in the vicinity of another sphere or a plane boundary, Chem. Eng. Sci., 27 (1972), pp. 1817–1828.CrossRefGoogle Scholar
[10] Lee, T. C. and Keh, H. J., Creeping motion of a fluid drop inside a spherical cavity, Euro. J. Mech. B/Fluids, 34 (2012), pp. 97–104.CrossRefGoogle Scholar
[11] Rao, S. K. L. and Rao, P. B., Slow stationary flow of a micropolar liquid past a sphere, J. Eng. Math., 4 (1970), pp. 209–217.CrossRefGoogle Scholar
[12] Rao, S. K. L. and Iyengar, T. K. V., The slow stationary flow of incompressible micropolar fluid past a spheroid, Int. J. Eng. Sci., 19 (1981), pp. 189–220.CrossRefGoogle Scholar
[13] Iyengar, T. K. V. and Srinivasacharya, D., Stokes flow of an incompressible micropolar fluid past an approximate sphere, Int. J. Eng. Sci., 31 (1993), pp. 115–123.CrossRefGoogle Scholar
[14] Ramkissoon, H. and Majumdar, S. R., Drag on axially symmetric body in the Stokes flow of micropolar fluid, Phys. Fluids, 19 (1976), pp. 16–21.CrossRefGoogle Scholar
[15] Sawada, T., Kamata, T., Tanahashi, T. and Ando, T., Stokesian flow of a micropolar fluid past a sphere, Keio Science and Technology Reports, 36 (1983), pp. 33–47.Google Scholar
[16] Ramkissoon, H., Flow of a micropolar fluid past a Newtonian fluid sphere, Z. Angew. Math. Mech., 65 (1985), pp. 635–637.CrossRefGoogle Scholar
[17] Ramkissoon, H. and Majumdar, S. R., Micropolar flow past a slightly deformed fluid sphere, Z. Angew. Math. Mech., 68 (1988), pp. 155–160.CrossRefGoogle Scholar
[18] Hoffmann, K. H., Marx, D. and Botkin, N. D., Drag on spheres in micropolar fluids with nonzero boundary conditions for microrotations, J. Fluid. Mech., 590 (2007), pp. 319–330.CrossRefGoogle Scholar
[19] Niefer, R. and Kaloni, P. N., On the motion of a micropolar fluid drop in a viscous fluid, J. Eng. Math., 14 (1980), pp. 107–116.CrossRefGoogle Scholar
[20] Sherief, H. H., Faltas, M. S. and Ashmawy, E. A., Axi-symmetric translational motion of an arbitrary solid prolate body in a micropolar fluid, Fluid Dyn. Research, 42 (2010), 065504.CrossRefGoogle Scholar
[21] Iyengar, T. K. V. and Radhika, T., Stokes flow of an incompressible micropolar fluid past a porous spheroidal shell, Bulletin of the Polish Academy of Sciences: Technical Sciences, 59 (2011), pp. 63–74.CrossRefGoogle Scholar
[22] Saad, E. I., Cell models for micropolar flow past a viscous fluid sphere, Meccanica, 47 (2012), pp. 2055–2068.CrossRefGoogle Scholar
[23] Jaiswal, B. R. and Gupta, B. R., Stokes flow of Micropolar fluid past a Non-Newtonian liquid spheroid, Int. J. Fluid Mech. Research, 42 (2015), pp. 170–189.CrossRefGoogle Scholar
[24] Sherief, H. H., Faltas, M. S., Ashmawy, E. A. and Nashwan, M. G., Stokes flow of a micropolar fluid past an assemblage of spheroidal particle-in-cell models with slip, Phys. Scripta, 90 (2015), 055203.CrossRefGoogle Scholar
[25] Faltas, M. S. and Saad, E. I., Slow motion of spherical droplet in a micropolar fluid flow perpendicular to a planar solid surface, Euro. J. Mech. B/Fluids, 48 (2014), pp. 266–276.CrossRefGoogle Scholar
[26] Happel, J. and Brenner, H., Low Reynolds Number Hydrodynamics, NJ: Prentice-Hall, Englewood Cliffs, 1965.Google Scholar