Journal of Fluid Mechanics



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


L. E.  Scriven a1 and C. V.  Sternling a2
a1 Department of Chemical Engineering, University of Minnesota, Minneapolis, Minnesota
a2 Chemical Engineering Department, Shell Development Company, Emeryville, California

Article author query
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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.

(Published Online March 28 2006)
(Received July 28 1962)
(Revised September 9 1963)



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