Modeling of mass transfer in a film of solution evaporating under the mask with holes

In this work, a model is developed for investigating the redistribution of colloidal particles in the film of an aqueous solution evaporating on a solid horizontal substrate under a mask with holes. Considering the characteristic horizontal film size as large and taking into account the symmetry in the arrangement of the holes in the mask the problem is solved for one film cell under a mask with a hole in its center. It is believed that vapour passes into the atmosphere only through the hole in the mask, the vapor flux density is calculated on the basis of the equation of steady-state diffusion of vapor in the atmosphere. The height-averaged velocity and volume fraction of colloidal particles are calculated using the conservation of mass, taking into account diffusion and deposition of particles onto the substrate. The calculation is performed using FlexPDE. We study the effect of the ratio of hole radius to hole spacing, the distance between the film and the mask, the diffusion, the deposition, the initial volume fraction of particles on the redistribution of particles in solution and on the substrate at the initial stage of film drying. These studies have shown that the behavior of the redistribution of particles in the solution and on the substrate depends primarily on the distance between the film and the mask, on the ratio of hole radius to hole spacing, on the diffusion coefficient of the particles. These parameters determine whether the particles will accumulate under the holes in the mask or will be distributed uniformly. The results agree with the experimental data.