A numerical model for the transport and drying of solutions in thin porous media — Coffee-stain effect and solute ring formation

Abstract

We have developed a comprehensive numerical model for the transport and drying of solutions in thin porous media that consist of permeable fibers such as paper. We explicitly account for the gas-phase transport dynamics. Moreover, we introduce an empirical relation for the concentration- and molecular-weight dependence of the pore-fiber transport rate of the solutes. These two key elements enable us for the first time to realistically model two important phenomena relevant to inkjet printing technology. The first is the equivalent of the coffee-stain effect for dilute solutions in porous media. The second is the formation of solute rings for concentrated aqueous mixtures of compounds with a molecular weight significantly above that of water. Whereas the first is governed by spatially non-uniform solvent evaporation, the second case is dominated by solvent-mediated pore-fiber transport. We achieved a good qualitative agreement with the available experimental data.