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Convection onset for a binary mixture in a porous medium and in a narrow cell: a comparison

Published online by Cambridge University Press:  26 April 2006

Wolfgang Schöpf
Wolfgang Schöpf
Affiliation:
Physikalisches Institut der Universität Bayreuth, W-8580 Bayreuth, Germany
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Abstract

The hydrodynamic equations describing the fluid motion in a narrow cell and in a porous medium become identical in the limit of infinite height-to-width ratio (Hele-Shaw limit) in the first and zero permeability in the second case. The properties of the convection onset are, however, indistinguishable from an experimental point of view away from these limits. For realistic (rigid, impermeable) boundary conditions the critical Rayleigh number, the critical wavenumber and in the case of a Hopf bifurcation additionally the critical frequency are derived in both cases for a binary fluid mixture. For the porous medium the assumption of zero permeability is usually a very good approximation. The critical values for the porous medium are compared to those of the narrow cell for different height-to-width ratios and the connection with experiments is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 245 , December 1992 , pp. 263 - 278
Copyright
© 1992 Cambridge University Press

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References

Barten W., Lücke M., Hort, W. & Kamps M. 1989 Phys. Rev. Lett. 63, 376.
Batchelor G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bensimon D., Kolodner P., Surko C. M., Williams, H. & Croquette V. 1990 J. Fluid Mech. 217, 441.
Brand, H. R. & Steinberg V. 1983 Physica 119A, 327.
Bretherton, C. S. & Spiegel E. A. 1983 Phys. Lett. 96A, 152.
Chandrasekhar S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Chock, D. P. & Li C. 1975 Phys. Fluids 18, 1401.
Cross M. C. 1988 Phys. Rev. A 38, 3593.
Cross, M. C. & Kim K. 1988 Phys. Rev. A 37, 3909.
Dullien F. A. L. 1979 Porous Media, Fluid Transport and Pore Structure. Academic Press.
Elder J. W. 1967 J. Fluid Mech. 27, 29.
Frick, H. & Clever R. M. 1980 Z. angew. Math. Phys. 31, 502.
Gershuni, G. Z. & Zhukhovitskii E. M. 1976 Convective Stability of Incompressible Fluids. Jerusalem: Keter.
Hartline, B. K. & Lister C. R. B. 1977 J. Fluid Mech. 79, 379.
Hurle, D. T. J. & Jakeman E. 1971 J. Fluid Mech. 47, 667.
Irmay S. 1958 Trans. Am. Geophys. Union 39, 702.
Knobloch E. 1986 Phys. Rev. A 34, 1538.
Knobloch E. 1989 Phys. Rev. A 40, 1549.
Knobloch, E. & Moore D. R. 1988 Phys. Rev. A 37, 860.
Kolodner P., Glazier, J. A. & Williams H. 1990 Phys. Rev. Lett. 65, 1579.
Kvernvold, O. & Tyvand P. A. 1979 J. Fluid Mech. 90, 609.
Lapwood E. R. 1948 Proc. Camb. Phil. Soc. 44, 508.
Lee G. W. T., Lucas, P. & Tyler A. 1983 J. Fluid Mech. 135, 235.
Legros J. C., Longree D., Chavepeyer, G. & Platten J. K. 1975 Physica 80A, 76.
Lhost, O. & Platten J. K. 1988 Phys. Rev. A 38, 3147.
Lhost, O. & Platten J. K. 1989 Phys. Rev. A 40, 6415.
Linz, S. J. & Lücke M. 1987 Phys. Rev. A 35, 3997.
Moses, E. & Steinberg V. 1986 Phys. Rev. A 34, 693.
Nield D. A. 1967 J. Fluid. Mech. 29, 545.
Platten, J. K. & Legros L. C. 1983 Convection in Liquids. Springer.
Rehberg, I. & Ahlers G. 1985 Phys. Rev. Lett. 55, 500.
Schöpf, W. & Kramer L. 1991 Phys. Rev. Lett. 66, 2316.
Schöpf, W. & Rehberg I. 1992 Europhys. Lett. 17, 321.
Schöpf, W. & Zimmermann W. 1989 Europhys. Lett. 8, 41.
Sullivan, T. S. & Ahlers G. 1988 Phys. Rev. Lett. 61, 78.
Thual, O. & Fauve S. 1988 J. Phys. (Paris) 49, 1829.
van Saarlos, W. & Hohenberg, P. C. 1990 Phys. Rev. Lett. 64, 749.
Walden R. W., Kolodner P., Passner, A. & Surko C. M. 1985 Phys. Rev. Lett. 55, 496.
Westbrook D. R. 1969 Phys. Fluids 12, 1547.
Wooding R. A. 1960 J. Fluid. Mech. 7, 501.