Three-Dimensional Direct Numerical Simulation of Surface-Tension-Gradient Effects on the Leveling of an Evaporating Multicomponent Fluid

Mathematical and numerical modeling of drying coating layers is of interest to both industrial and academic communities. Compositional changes that occur during the drying process make the implementation of practical and efficient numerical models rather difficult. In this paper we present a three-dimensional mathematical and numerical model based on the lubrication approximation for the flow of drying paint films on horizontal substrates. The paint is modeled as a multicomponent liquid with one nonvolatile and one volatile component, termed the “resin” and the “solvent” respectively. Our model includes the effects of surface tension and gravitational forces as well as surface tension gradient effects which arise due to solvent evaporation. The dependence of viscosity, diffusivity, and evaporation rate on resin concentration is also incorporated in the model. A closed-form linearized solution has been found for coating layers that are of almost uniform thickness. The numerical solution agrees closely with the linear solution in the appropriate limit. A model simulation demonstrates the effect of surface tension gradients due to compositional changes in a three-dimensional flow field, and we suggest methods by which these gradients may be used to obtain a more uniform final coating layer.