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Finite amplitude cellular convection induced by surface tension

Published online by Cambridge University Press:  28 March 2006

J. W. Scanlon
Affiliation:
Rensselaer Polytechnic Institute, Troy, New York
L. A. Segel
Affiliation:
Rensselaer Polytechnic Institute, Troy, New York

Abstract

A non-linear analysis of cellular convection driven by surface tension in a semi-infinite liquid layer heated from below has been made. The purpose is to determine whether or not one can predict the emergence of the hexagonal flow pattern from the interaction of a certain large class of important disturbances. The principal conclusion is that, compared with gravity driven convection, there is generally a much greater band of imposed temperature difference associated with hexagonal convective patterns. Partial results for the more realistic assumption of finite depth support this conclusion.

Type
Research Article
Copyright
© 1967 Cambridge University Press

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References

Berg, J. C. & Acrivos, A. 1965 Chem. Engng. Sci. 20, 737.
Block, M. J. 1956 Nature, Lond. 178, 650.
Bray, R. W. 1966 Ph.D. Thesis, Dept. of Math., University of Essex.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Davis, S. H. 1964 Ph.D. Thesis, Dept. of Math., Rensselaer Polytechnic Institute.
Davis, S. H. & Segel, L. A. 1965 Rand Corporation Rept., RM-4709-PR.
Friedman, B. 1956 Principles and Techniques of Applied Mathematics, p. 205. New York: Wiley.
Jeffreys, H. 1951 Quart. J. Mech. and Appl. Math. 4, 283.
Koschmieder, E. L. 1966 Beitr. Phys. Atmos. 39, 1.
Nield, D. A. 1964 J. Fluid Mech. 19, 341.
Palm, E. 1960 J. Fluid Mech. 8, 183.
Pearson, J. R. 1958 J. Fluid Mech. 4, 489.
Scriven, L. E. & Sternling, C. V. 1960 Nature, Lond. 187, 186.
Segel, L. A. 1965a J. Fluid Mech. 21, 345.
Segel, L. A. 1965b J. Fluid Mech. 21, 359.
Segel, L. A. & Stuart, J. T. 1962 J. Fluid Mech. 13, 289.
Smith, K. A. 1966 J. Fluid Mech. 24, 401.
Sternling, L. E. & Scriven, C. V. 1964 J. Fluid Mech. 19, 321.
Stuart, J. T. 1960 J. Fluid Mech. 9, 353.
Vidal, A. & Acrivos, A. 1966 Phys. Fluids 9, 615.
Watson, J. 1960 J. Fluid Mech. 9, 371.