Temporal evolution of demarcations between the unsteady and steady regions and between the film and meniscus during dip coating with vertical withdrawal of Newtonian fluids

Thus far studies on dip coating focus on the asymptotic layer thickness which is reached only in the lower part of the layer when the withdrawal time is sufficiently long. This work attempts to offer a complete description of the evolution of layer thickness profile with withdrawal time for vertical withdrawal of Newtonian fluids using simulation and the Buckingham π theorem. The results show that over time, the withdrawal process successively undergoes two regimes: (I) an unsteady film region and an unsteady meniscus region and (II) an unsteady film region connected to a steady meniscus region through an unsteady meniscus region. The controlling factors for the two regimes are identified at different values of capillary number and Reynolds number. Models are proposed to predict the heights of the demarcations between different regions. The models agree well with experimental results when the controlling forces are viscous force and gravity.