Confinement effects in dip coating

When a flat plate is withdrawn from a liquid pool, a liquid film is deposited on the plate. This simple process is called dip coating. In the case of vertically upward withdrawal, gravity competes with the surface tension and viscous drag, and the balance between those determine the meniscus shape and hence the film thickness. Most of the previous studies on dip coating assumed that the pool is sufficiently large so that the stationary container wall does not affect the film thickness. However, the cases where the stationary wall affects the entrained film have not been examined thoroughly so far. In this confined dip coating, the film thickness deviates from that of unconfined dip coating under the same conditions such as the withdrawal speed and the physical properties of the liquid. The meniscus in a confined pool is more curved than that in an unconfined pool owing to wetting on the stationary wall, which is parallel to the plate. Besides, a channel between the moving plate and the stationary wall appears; therefore, the flow inside the channel should be included in an analysis of confined dip coating. In the present study, we analyse the mechanism that determines the film thickness, both theoretically and numerically.