Drying of polymer solutions: formation of glassy crust and gelled skin

When a polymer solution film dries, a vertical concentration gradient may form, which leads to the formation of either a gelled skin or a thin glassy crust. The former is associated with a slight increase in the mutual diffusion coefficient, whereas the latter is associated with a sharp decrease in this coefficient. Starting from the equation that describes the drying of a thick film of a polymer solution, we show that the asymptotic regime is self-similar, and propose approximations for the evaporation rate and the concentration profile. We further introduce an analytical expression for the mutual diffusion coefficient of a polymer solution and deduce the conditions for the existence of a gel-like skin and a glassy crust, according to the molar mass and the initial polymer concentration. Finally, we derive analytical approximations for the growth rates of the two layers in the asymptotic regime, as well as for the evaporation rate and the surface activity, in good agreement with the numerical solution of the model.