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On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity

Published online by Cambridge University Press:  28 March 2006

L. E. Scriven  and
C. V. Sternling
L. E. Scriven
Affiliation:
Department of Chemical Engineering, University of Minnesota, Minneapolis, Minnesota
C. V. Sternling
Affiliation:
Chemical Engineering Department, Shell Development Company, Emeryville, California
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Abstract

The onset of steady, cellular convection driven by surface tension gradients on a thin layer of liquid is examined in an extension of Pearson's (1958) stability analysis. By accounting for the possibility of shape deformations of the free surface it is found that there is no critical Marangoni number for the onset of stationary instability and that the limiting case of ‘zero wave-number’ is always unstable. Surface viscosity of a Newtonian interface is found to inhibit stationary instability. A simple criterion is found for distinguishing visually the dominant force, buoyancy or surface tension, in cellular convection in liquid pools.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 19 , Issue 3 , July 1964 , pp. 321 - 340
Copyright
© 1964 Cambridge University Press

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References

Aris, R. 1962 Vectors, Tensors and the Basic Equations of Fluid Mechanics. Englewood Cliffs, N.J.: Prentice-Hall.
Bénard, H. 1900 Rev. Gen. Sci. pures et appl. 11, 1261–71, 1309–28.
Bénard, H. 1901 Ann. Chim. Phys. 23, 62–144.
Bénard, H. 1927 C.R. Acad. Sci., Paris, 185, 1109–11, 1256–59.
Bénard, H. 1928 Bull. Soc. Franc. Phys. no. 266, 112S-115S.
Bénard, H. 1930 Proc. 3rd Int. Congr. Appl. Mech. 1, 120.
Block, M. J. 1956 Nature, Lond., 178, 650–1.
Brooke Benjamin, T. 1957 J. Fluid Mech. 2, 554–74.
Brooke Benjamin, T. 1960 J. Fluid Mech. 4, 513–32.
Hickman, K. C. D. 1952 Indust. Engng Chem. 44, 1892–1902.
Jeffreys, H. 1951 Quart. J. Mech. Appl. Math. 4, 283–8.
Levengood, W. C. 1959 Astrophys. J. 129, 483–8.
Low, A. R. & Brunt, D. 1925 Nature, Lond., 115, 299–301.
Nakagawa, Y. 1957a Proc. Roy. Soc. A, 240, 108–13.
Nakagawa, Y. 1957b Proc. Roy. Soc. A, 242, 81–8.
Nakagawa, Y. 1959 Proc. Roy. Soc. A, 249, 138–45.
Pearson, J. R. A. 1958 J. Fluid Mech. 4, 489–500.
Pellew, A. & Southwell, R. V. 1940 Proc. Roy. Soc. A, 176, 312–43.
Rayleigh, Lord 1916 Phil. Mag. 32, 529–46. (Also Sci. Papers, 6, 432.)
Sani, R. L. & Scriven, L. E. 1964 (To be published.)
Scriven, L. E. 1960 Chem. Engng Sci. 12, 98–108.
Scriven, L. E. & Sterling, C.V. 1960 Nature, Lond., 187, 186–88.
Sternling, C. V. & Barr-David, F. H. 1959 M.S. no. P-769, Shell Development Company; submitted to A.I.Ch.E. Journal.Google Scholar
Sternling, C. V. & Scriven, L. E. 1959 Amer. Inst. Chem. Engrs J. 6, 514–23.
Vernotte, P. 1936a C.R. Acad. Sci., Paris, 202, 119, 733, 1764.
Vernotte, P. 1936b C.R. Acad. Sci., Paris, 203, 43, 985 (cf. Volkovisky).
Volkovisky, V. 1939 Publ. Sci. Tech. du Minist. de l'Air, no. 151.