Drying of a solution in a meniscus: a model coupling the liquid and the gas phases

A model simulating the drying of a solution in a meniscus in contact with a moving substrate is developed. It takes into account the hydrodynamics in the solution in the framework of the lubrication approximation, the vapor diffusion in the gas phase, and the variation of physical properties during drying. The free surface profile and spatial evaporation flux are not imposed a priori but result from the simulation of the mass transfer in the liquid/gas system (1.5-sided model). Several regimes are observed depending on the substrate velocity. For a large substrate velocity, the classical Landau-Levich regime is obtained. For smaller velocities, a drying front appears that is characterized by a strong concentration gradient and a peak in the evaporation flux. The coupling between the evaporation flux and the meniscus shape in this regime is analyzed. Another regime appears at a very low substrate velocity and seems to be driven by a competition between advection and diffusion. This macroscopic model simulates recent experimental results, namely, the dependence of the deposit thickness on the substrate velocity, which scales as 1/V in the regime dominated by evaporation.