Instabilities during the evaporation of a film: non glassy polymer + volatile solvent

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We consider solutions where the surface tension of the solvent is smaller than the surface tension of the polymer. In an evaporating film, a plume of solvent rich fluid, then induces a local depression in surface tension, and the surface forces tend to strengthen the plume. We give an estimate (at the level of scaling laws) for the minimum thickness required to obtain this instability. We predict that the thickness a) is a decreasing function of the solvent vapor pressure b) should be very small (<1 micron) provided that the initial solution is rather dilute. The overall evaporation time for the film should be much longer than the growth time of the instability. The instability should lead to distortions of the free surface and may be optically observable. It should dominate over the classical Bernard-Marangoni instability induced by cooling.