Mathematical analysis of flow gradient-induced flake alignment in coatings during deposition

Abstract

The orientation of flake-shaped pigments in a finished coating is of critical importance to customers, coating researchers, manufacturers, and formulators due to its effect on appearance, especially perceived color travel. Alignment of flake with the underlying surface is primarily caused by the flow during the spreading of depositing paint droplets. It has been shown that, in contrast to conventional knowledge, the uniform orientation of flake observed in liquid coatings cannot be induced by uniform flow in depositing droplets, nor does uniform flow occur. This article investigates the effects of observed and relevant non-uniform Couette-like flow gradients in a flowing paint droplet on flake orientation. The increased flow of a depositing coating droplet along the top of a flake induces a torque and an acceleration toward the horizontal plane of the underlying substrate. The flake then rotates along with the depositing viscous material after a short initial acceleration and quickly reaches a horizontal configuration. The contained mathematical analysis explains correctly the complete alignment of flake with the plane of the underlying surface observed in typical paint application.