Analytical solutions for the free-draining flow of a Carreau-Yasuda fluid on a vertical plate

Abstract

Free-draining flow is observed in many practical and industrial situations. It is considered as a stage of a batch dip-coating process, where the draining of the fluid will form a liquid film over a substrate by gravity. The objective of this work was to develop a mathematical model and to obtain analytical solutions for the fluid-dynamic variables of a free-draining flow during a dip-coating draining stage of a finite vertical plate using a fluid whose rheological behavior is described by the Carreau-Yasuda model. Mathematical expressions have been obtained assuming a monophasic, isothermal, and nonevaporative system, where the most important forces are viscous and gravitational. The studied phenomena occurred far away from the meniscus formed at the surface of the fluid reservoir. The main operative variables that were estimated are velocity profile, flow rate, local thickness, and average thickness of the film. A validation was performed by using experimental data of average film thickness values of several representative food-grade fluids with coating capacity (emulsions and suspensions) obtained from the literature. The information published in this work will be useful for researchers and technicians to control and predict film characteristics (thickness and uniformity) and operational variables (velocity and flow rate) during laboratory and industrial coating processes where free-draining flow takes place.