Evaporation-induced stratification in colloidal solutions

When a liquid film of a colloidal solution consisting of particles of different sizes is dried on a substrate, the colloids often stratify, where smaller colloids are laid upon larger colloids. This phenomenon is counterintuitive because larger colloids which have a smaller diffusion constant, are expected to remain near the surface during the drying process, leaving a layer of larger colloids on top of smaller colloids. Here we show that the phenomenon is caused by the interaction between the colloids, and can be explained by a diffusion model accounting for the interaction between the colloids. By studying the evolution equations both numerically and analytically, we derive the condition at which the stratified structures are obtained.