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The effects of surface tension and viscosity on the stability of two superposed fluids

Published online by Cambridge University Press:  24 October 2008

W. H. Reid
W. H. Reid
Affiliation:
Brown University, Providence, Rhode Island
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Abstract

The effect of surface tension on the stability of two superposed fluids can be described in a universal way by a non-dimensional ‘surface tension number’ S which provides a measure of the relative importance of surface tension and viscosity. When both fluids extend to infinity, the problem can be reduced to the finding of the roots of a quartic equation. The character of these roots is first analysed so as to obtain all possible modes of stability or instability. Two illustrative cases are then considered in further detail: an unstable case for which the density of the lower fluid is zero and a stable case for which the density of the upper fluid is zero, the latter case corresponding to gravity waves. Finally, the variational principle derived by Chandrasekhar for problems of this type is critically discussed and it is shown to be of less usefulness than had been thought, especially in those cases where periodic modes exist.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 2 , April 1961 , pp. 415 - 425
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Bellman, R., and Pennington, R. H., Quart. Appl. Math. 12 (1954), 151–62.CrossRefGoogle Scholar
(2)Carrier, G. F., and Chang, C. T., Quart. Appl. Math. 16 (1959), 436–9.CrossRefGoogle Scholar
(3)Chandrasekhar, S., Proc. Camb. Phil. Soc. 51 (1955), 162–78.CrossRefGoogle Scholar
(4)Dryden, H. L., Murnaghan, F. D., and Bateman, H., Hydrodynamics (Bulletin no. 84 of the National Research Council, Washington, 1932).Google Scholar
(5)Feldman, S., J. Fluid Mech. 6 (1959), 131–55.CrossRefGoogle Scholar
(6)Hide, R., Proc. Camb. Phil. Soc. 51 (1955), 179–201.CrossRefGoogle Scholar
(7)Hide, R., Quart. J. Mech. Appl. Math. 9 (1956), 22–34.CrossRefGoogle Scholar
(8)Rayleigh, Lord., Proc. Lond. Math. Soc. 14 (1883), 170–7;Google Scholar
also, Scientific Papers, vol. 2, pp. 200–7.Google Scholar
(9)Taylor, G. I., Proc. Roy. Soc. A, 201 (1950), 192–6.Google Scholar
(10)Tchen, C. -M., J. Appl. Phys. 27 (1956), 760–7.CrossRefGoogle Scholar