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On convective instability induced by surface-tension gradients

Published online by Cambridge University Press:  28 March 2006

K. A. Smith
K. A. Smith
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology
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Abstract

The linearized stability problem for steady, cellular convection resulting from gradients in surface tension is examined in some detail. Earlier work by Pearson (1958) and Sternling & Scriven (1959, 1964) has been extended by considering the effect of gravity waves. In order to avoid the use of an assumed coupling mechanism at the interface, the relevant dynamical equations were retained for both phases. It is shown that the existence of a critical Marangoni number is assured, and that for many situations this critical value is essentially that which is appropriate to the case of a non-deformable interface. Usually, surface waves are important only at very small wave-numbers, but they are dominant for unusually thin layers of very viscous liquids.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 24 , Issue 2 , February 1966 , pp. 401 - 414
Copyright
© 1966 Cambridge University Press

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References

Bénard, H. 1900 Rev. Gen. Sci. Pures et Appl. 11, 1261, 1309.
Bénard, H. 1901 Ann. Chem. Phys. 23, 6.
Pearson, J. R. A. 1958 J. Fluid Mech. 4, 48.
Scriven, L. E. & Sternling, C. V. 1964 J. Fluid Mech. 19, 32.
Sternling, C. V. & Scriven, L. E. 1959 Amer. Inst. Chem. Engrs J. 6, 51.