A mathematical model for crater defect formation in a drying paint layer

Certain deep indentations observed in dry coatings are referred to as "crar ers." They are believed to arise from gradients in the coating surface tens ion. A mathematical model of surface-tension-gradient-driven Row, using the lubrication approximation for thin layers, is developed to study the forma tion of craters. The paint is modeled as consisting of an evaporating "solv ent" part and a nonvolatile "resin" part Surface tension gradients on the c oating surface arise due to a nonuniform distribution of surfactant. Axisym metric numerical simulations using the model are performed to explore two c andidate crater production mechanisms: an initial release of concentrated s urfactant and a steady surfactant source. The effects of changes in various properties, such as the paint drying rate, the surfactant diffusivity, and the viscosity increase during drying, are examined, The model produces cra ters with large diameters, pronounced rims, and central peaks, similar to t hose seen in practice. Drying rate has a large influence on crater diameter and depth, by limiting Row due to surface tension gradients within a given time. Reduction of the paint viscosity increase during drying causes incre ased flow rates, leading to larger craters. A preexisting layer of surfacta nt on the paint surface sharply reduces the extent of cratering. Surfactant diffusion also tends to reduce the severity of cratering by alleviating su rface tension gradients. In some cases, a simplified form of the drying mod el may be used to quickly approximate the results of the full model. The mo del provides useful insights into the craters seen in industrial coating ap plications. (C) 2000 Academic Press.