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 oc cur during the drying process make the implementation of practical and effi cient numerical models rather difficult. In this paper we present a three-d imensional mathematical and numerical model based on the lubrication approx imation for the flow of drying paint films on horizontal substrates. The pa int is modeled as a multicomponent liquid with one nonvolatile and one vola tile component, termed the "resin" and the "solvent" respectively. Our mode l 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 co ncentration is also incorporated in the model. A closed-form Linearized sol ution has been found for coating layers that are of almost uniform thicknes s. The numerical solution agrees closely with the linear solution in the ap propriate Limit. A model simulation demonstrates the effect of surface tens ion gradients due to compositional changes in a three-dimensional flow fiel d, and we suggest methods by which these gradients may be used to obtain a more uniform final coating layer.