Final shape of a drying thin film

Drying processes of polymer solutions on a solid substrate enclosed by bank are studied in the slow limit of the solvent evaporation. A simple model is proposed to examine the final shape of the film after drying. Analytical expressions of the final shape in terms of the initial parameters are obtained. It is shown that the craterlike and basinlike shapes appear as final shapes of the film depending on the initial parameters. The "shape diagrams" which show parameter dependence of the final shape are presented in the absence/presence of diffusion. The final shape of the film in the geometry without bank is also discussed.