Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-15T21:57:08.012Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Degroot, S. R. & Mazur, P. 1962 Non-equilibrium Thermodynamics. North Holland.
Harris, D. L. & Reid, W. H. 1964 On the stability of viscous flow between rotating cylinders. Part 2. Numerical analysis J. Fluid Mech. 20, 95.Google Scholar
Hirschfelder, J. O., Curtiss, C. F. & Bird, R. B. 1954 Molecular Theory of Gases and Liquids. John Wiley.
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.Google Scholar
Kulinski, E. S. 1966 Rotating Couette flow of a binary liquid Phys. Fluids, 9, 1207.Google Scholar
Lanczos, G. 1961 Linear Differential Operators, chap. 9. Van Nostrand.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Saric, W. S. 1968 Hydrodynamic stability of heterogeneous Couette flows. Ph.D. thesis, Illinois Institute of Technology, Chicago, Illinois.
Snyder, H. A. 1968 Stability of rotating Couette flow. I. Asymmetric wave forms Phys. Fluids, 11, 728.Google Scholar
Sparrow, E. C., Munro, W. D. & Jonsson, V. K. 1964 Instability of the flow between rotating cylinders – the wide gap problem J. Fluid Mech. 20, 35.Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders Trans. Roy. Soc. A 223, 289.Google Scholar
Walowit, J., Tsao, S. & DiPrima, R. C. 1964 Stability of flow between arbitrarily spaced concentric cylindrical surfaces including the effect of a radial temperature gradient J. Appl. Mech. 31, 585.Google Scholar
Yih, C. S. 1961 Dual rule of viscosity in the instability of revolving fluids in variable density Phys. Fluids, 4, 806.Google Scholar
Yih, C. S. 1965 Dynamics of Nonhomogeneous Fluids. Macmillan.