Abstract
The Marangoni instability of a thin liquid sheet driven by the surface tension gradient (due to variations of temperature or of mass concentration) is studied by means of a linear theory. It is found that the critical Marangoni number for the steady mode can be expressed by a simple function of the wave-number when the two boundaries of the sheet are flat. When the surface deformations are taken into account, another type of instability may occur for small values of the Biot number. The effect of deviation of the surface tension coefficient from the mean value at the free surfaces and the resulting surface patterns made up by the surface deformations at small wave-numbers are also discussed.
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