A New Mechanism of Coffee-Ring Formation Deduced from Numerical Simulations with Considering Deformation and Wettability

Abstract

A mathematical model describing the drying behavior of solution droplets deposited on a substrate is numerically solved to predict the morphology of the formed solid layer. The model includes the fluid dynamics, heat transfer, and mass transfer, and also considers wettability of the substrate and deformation of the free surface. The calculated morphologies of solid films agree reasonably with those formed experimentally from polystyrene/anisole solution droplets. The model predicts drying behavior that has not been previously reported. First, when a coffee ring is formed, solutal Marangoni forces deform the free surface while the solvent fully remains. Second, the deformation yields an outward bulk flow, enhancing solute transport toward the edge. Third, the effect of droplet size on the receding distance is related to the deformation. Consequently, the effects of droplet size, surface tension, viscosity, evaporation rate and wettability on film morphology can be explained by the deformation behavior.