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

We consider solutions where the surface tension of the solvent $\gamma _\mathrm{s}$ is smaller than the surface tension of the polymer $\gamma _\mathrm{p}$. 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 $e^{\ast }$ required to obtain this instability. We predict that a) $e^{\ast }$ is a decreasing function of the solvent vapor pressure $ p_\mathrm{v}(e^{\ast }\sim p_\mathrm{v}^{-1/2})$; b) $e^{\ast }$ should be very small (${}< 1$ micron) provided that the initial solution is rather dilute; c) 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 Benard-Marangoni instability induced by cooling