Full finite element analyses for leveling of a polymer/solvent film accompanying with drying shrinkage

A mathematical model for the leveling process of a polymer/solvent film coated on a flat substrate was constructed by employing a two-dimensional finite element analysis, in which the film thinning due to solvent evaporation was taken into account in addition to the spatial and temporal variations of the physical properties. Then, the effects of the solvent evaporation rate, the wavelength, and amplitude of disturbances on the leveling behavior were numerically investigated. As a result, the critical value of the Biot number, beyond which the coated film with irregular surface geometry is frozen due to the completion of solvent evaporation before the film surface becomes uniform by leveling, decreased with increasing wavelength of disturbances. Also, the leveling time at which the film becomes flat by leveling increases rapidly with the Biot number, and then the shortest drying time could be found as the time at which the leveling time coincides with the time of complete solvent evaporation.