Modelling of evolution of redistribution of colloidal particles and shape of the film drying under the disk

Using the Lubrication theory, the conservation solvent and the advection-diffusion equation, drying processes of colloidal film on a solid substrate under a solid disk are studied. A model is proposed to describe temporal dynamics of both the shape of the film and the volume fraction of the colloidal spherical particles inside the film. Initially, the system is single-phase (liquid), then in the area, where the volume fraction of the colloidal particles reaches critical value, solid phase forms. This area holds the shape, prevents the hydrodynamic flows and evaporation from its free surface. In liquid area viscosity and diffusivity depend on the volume fraction of the particles. The rate of solvent mass loss per unite surface area per unite time from the film by evaporation under a disk was obtained numerically from the Laplace's equation for the vapor concentration in the area over the film. During the first desiccation stage the volume of the film under the disk is liquid, the rest of the film becomes solid. When the whole volume of the film becomes solid dried film has a dip below the disk.