Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-18T13:13:33.886Z Has data issue: false hasContentIssue false
  • English
  • Français

On convection cells induced by surface tension

Published online by Cambridge University Press:  28 March 2006

J. R. A. Pearson
J. R. A. Pearson
Affiliation:
Imperial Chemical Industries Limited, Akers Research Laboratories, The Frythe, Welwyn, Herts.
Get access Rights & Permissions [Opens in a new window]

Abstract

A mechanism is proposed by which cellular convective motion of the type observed by H. Bénard, which hitherto has been attributed to the action of buoyancy forces, can also be induced by surface tension forces. Thus when a thin layer of fluid is heated from below, the temperature gradient is such that small variations in the surface temperature lead to surface tractions which cause the fluid to flow and thereby tend to maintain the original temperature variations. A small disturbance analysis, analogous to that carried out by Rayleigh and others for unstable density gradients, leads to a dimensionless number B which expresses the ratio of surface tension to viscous forces, and which must attain a certain minimum critical value for instability to occur. The results obtained are then applied to the original cells described by Bénard, and to the case of drying paint films. It is concluded that surface tension forces are responsible for cellular motion in many such cases where the criteria given in terms of buoyancy forces would not allow of instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 4 , Issue 5 , September 1958 , pp. 489 - 500
Copyright
© 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

Batchelor, G. K. 1954 Quart. J. Roy. Met. Soc. 80, 339.
Bénard, H. 1900 Rev. Gen. des Sci. pures et appl. 1261, 1309.
Bénard, H. 1901 Ann. Chim. Phys. (7), 23, 62.
Christopherson, D. G. 1940 Quart. J. Math. 11, 63.
Jeffreys, H. 1926 Phil. Mag. (7), 2, 833.
Jeffreys, H. 1928 Proc. Roy. Soc. A, 118, 201.
Lin, C. C. 1955 Theory of Hydrodynamic Stability. Cambridge University Press.
Low, A. R. 1929 Proc. Roy. Soc. A, 125, 180.
Pellew, A. & Southwell, R. V. 1940 Proc. Roy. Soc. A, 176, 312.
Prandtl, L. 1952 Fluid Dynamics. London: Blackie.
Rayleigh, Lord 1916 Scientific Papers, vol. 6, p. 432. Cambridge University Press.
Volkovisky, V. 1939 Publ. Sci. Tech. Minist. de l’Air, no. 151.