Mathematical modeling of a dip-coating process using concentrated dispersions

Abstract

Industrial dip coating is a simple and easy to access technique that can be considered as a self-metered coating process. Practical applications of films obtained by this method include decorative, protective, and functional purposes. The objective of this work was to develop a 2D mathematical model of the fluid-dynamic variables of the dip-coating draining stage of a finite vertical plate, considering nonevaporative and isothermal conditions. Concentrated dispersions were considered, such as those whose rheological behavior was described by an extension of a theoretical rheological model proposed by Quemada. As a result, an analytical and simple mathematical model that relates the main fluid parameters could be obtained. The model was achieved based upon rigorous mass and momentum balances applied to the draining stage of a monophasic, isothermal, and nonevaporative system, where the highest forces are viscous and gravitational. Parameters that were estimated are the velocity profile, average velocity, flow rate, local thickness, and average thickness of the film. Finally, experimental validation was performed by using experimental data (rheological properties, densities, and average film thickness values) of several representative concentrated dispersions (emulsions and suspensions) obtained in this work and from the literature. All the information achieved in this study can be useful to control and predict the thickness and homogeneity of the film during an industrial coating process, in order to satisfy the quality requirements of the final product.