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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.
Scriven et al. (1964) studied this question.