Hostname: page-component-7c8c6479df-ph5wq Total loading time: 0 Render date: 2024-03-28T13:31:40.589Z Has data issue: false hasContentIssue false

Linear Rayleigh-Taylor stability of viscous fluids with mass and heat transfer

Published online by Cambridge University Press:  19 April 2006

S-P. Ho
Affiliation:
Division of Applied Mathematics, Brown University, R.I. 02912

Abstract

The linear Rayleigh–Taylor stability of superposed viscous fluids with interfacial transfer of mass and heat is first considered for layers of finite thickness. A dispersion relation is obtained. It is then employed to derive stability and instability criteria for the case of two semi-infinite layers as well as the case where one of the layers is finite. From these criteria one arrives at a critical dispersion relation and a new critical wavenumber. This new critical wavenumber is distinct from the classical value owing to the presence of a parameter which depends, in a very simple manner, upon the kinematic viscosity of the fluids, the surface tension and the rate of interfacial transfer of mass and energy. Also it is found that the stabilizing effect of the surface tension is neither affected by the arrangement of the system nor the direction of the temperature gradient. However, the effects of the viscosity and the gravity will depend upon the relative positions of the superposed fluids and the direction of the temperature gradient at the interface.

Type
Research Article
Copyright
© 1980 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

Beuriger, J. 1901 Zur Auflösung der biquadratischen Gleichungen. Program (Beilage) K Bonn: Gymnasium.
Burnside, W. S. & Panton, A. W. 1892 Theory of Equations, 3rd edn. Dublin University Press.
Chandrasekhar, S. 1955 Proc. Camb. Phil. Soc. 51, 162178.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability, ch. 10. Oxford University Press.
Harrison, W. J. 1908 Proc. Lond. Math. Soc. 6, 396405.
Hsieh, D. Y. 1972 Trans. A.S.M.E. D, J. Basic Engng 94, 156000.
Hsieh, D. Y. 1978 Phys. Fluids 21, 745748.
Lewis, W. J. 1950 Proc. Roy. Soc. A 202, 8198.
Palmer, H. J. 1976 J. Fluid Mech. 75, 487511.
Rayleigh, Lord 1900 Scientific Papers, vol. 2, pp. 200227. Cambridge University Press.
Taylor, G. I. 1950 Proc. Roy. Soc. A 201, 192196.