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Stability of circular Couette flow of binary mixtures

Published online by Cambridge University Press:  29 March 2006

William S. Saric  and
Zalman Lavan
William S. Saric
Affiliation:
Sandia Laboratories, Albuquerque, New Mexico
Zalman Lavan
Affiliation:
Illinois Institute of Technology, Chicago, Illinois
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Abstract

The hydrodynamic stability of an ideal mixture of two viscous, dissimilar liquids contained between two concentric rotating cylinders is analyzed. The basic flow of the mixture is determined by coupling the mass and momentum equations with an equation for the equilibrium concentration distribution. Infinitesimal, axisymmetric disturbances are assumed, and the disturbance equations are written for the limiting case of large Schmidt numbers (no diffusion).

The presence of density and viscosity variations leads to a twelfth-order eigenvalue problem with two-point boundary conditions that has the appearance of a combined Taylor and density-stratified shear flow problem. A numerical technique is devised to determine the stability boundary and to calculate Taylor numbers and oscillation frequencies for different growth rates.

It is found that very small mean density gradients alter the critical Taylor number and that oscillations occurring in both the growing and neutral solutions are the dominant mode.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 47 , Issue 1 , 14 May 1971 , pp. 65 - 80
Copyright
© 1971 Cambridge University Press

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