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Couette flow of two fluids between concentric cylinders

Published online by Cambridge University Press:  20 April 2006

Yuriko Renardy  and
Daniel D. Joseph
Yuriko Renardy
Affiliation:
Mathematics Research Center, University of Wisconsin-Madison, 610 Walnut Street, Madison WI 53705
Daniel D. Joseph
Affiliation:
Department of Aerospace Engineering, 107 Akerman Hall, 110 Union Street S.E., University of Minnesota, MN 55455
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Abstract

We consider the flow of two immiscible fluids lying between concentric cylinders when the outer cylinder is fixed and the inner one rotates. The interface is assumed to be concentric with the cylinders, and gravitational effects are neglected. We present a numerical study of the effect of different viscosities, different densities and surface tension on the linear stability of the Couette flow. Our results indicate that, with surface tension, a thin layer of the less-viscous fluid next to either cylinder is linearly stable and that it is possible to have stability with the less dense fluid lying outside. The stable configuration with the less-viscous fluid next to the inner cylinder is more stable than the one with the less-viscous fluid next to the outer cylinder. The onset of Taylor instability for one-fluid flow may be delayed by the addition of a thin layer of less-viscous fluid on the inner wall and promoted by a thin layer of more-viscous fluid on the inner wall.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 150 , January 1985 , pp. 381 - 394
Copyright
© 1985 Cambridge University Press

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References

Hooper, A. P. & Boyd W. G. C.1983 Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech. 128, 507–528.Google Scholar
Joseph D. D., Nguyen, K. & Beavers G. S.1984 Non-uniqueness and stability of the configuration of flow of immiscible fluids with different viscosities. J. Fluid Mech. 141, 319–345.Google Scholar
Joseph D. D., Renardy, M. & Renardy Y.1984 Instability of the flow of immiscible liquids with different viscosities in a pipe. J. Fluid Mech. 141, 309–317.Google Scholar
Joseph D. D., Renardy Y., Renardy, M. & Nguyen K.1985 Stability of rigid motions and rollers in bicomponent flows of immiscible liquids. J. Fluid Mech. (to appear).Google Scholar
Krueger E. R., Gross, A. & DiPrima R. C.1966 On the relative importance of Taylor-vortex and non-axisymmetric modes in flow between rotating cylinders. J. Fluid Mech. 24, 521–538.Google Scholar
Orszag S. A.1971 Accurate solution of the Orr-Sommerfeld stability equation. J. Fluid Mech. 50, 689–703.Google Scholar
Renardy, M. & Joseph D. D.1984 Hopf bifurcation in two-component flow. Maths Res. Center Tech. Summary Rep. 2689.Google Scholar
Yih C.-S.1967 Instability due to viscosity stratification. J. Fluid Mech. 27, 337–352.Google Scholar