The drying of liquid films on cylindrical and spherical substrates

The drying of liquid films from binary solid–solvent mixtures on cylindrical and spherical substrates is investigated by solving the diffusion equation on the cylindrical or spherical domains with account for the shrinkage of the systems due to the solvent evaporation. As a main result of the gas phase analysis, d2-laws for both the cylindrical and the spherical cases are found. The spatio-temporal evolution of the component mass fractions in the liquid are obtained for varying initial film thickness and drying conditions. Large mass fraction gradients, formed at high drying rates, lead to a skin-core morphology with low product quality. Initially very thin films dry very uniformly, which is analogous to the flat temperature profiles in unsteady heat conduction at small Biot numbers. The maximum initial film thickness allowable to ensure flat solute mass fraction profiles in the films, and thus high quality of the dry films, is computed for varying drying rates. From these results a guideline for the drying of liquid films on cylindrical and spherical substrates is deduced.