Confinement effects in dip coating Onyu Kim and Jaewook Nam* Department of Chemical Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon-si, Gyeonggi-do 16419, Korea Presented at the 18 th International Coating Science and Technology Symposium September 18-21, 2016 Omni William Penn Hotel, Pittsburg, PA, USA ISCST shall not be responsible for statements or opinions contained in papers or printed in its publications. 1. Introduction Perhaps the simplest way to produce a thin film is to deposit a layer of liquid onto a plate via withdrawal from a liquid pool. The physics of process is known as the drag-out problem or the Landau-Levich-Derjaguin (LLD) problem, after pioneering studies by Landau & Levich (1942) and Derjaguin (1943). The obtained prototypical dip coating flow is popular because of its simplicity, not only in laboratory experiments, but also in industry. Dip coating and related methods are sufficiently flexible to produce films on various geometries and can be applied to fluids with various properties. Most previous studies on this topic have assumed that the pool width l is infinitely large. For this “infinite” dip coating flow, most of the pool remains static, except in the small region near the plate, where the flow can be recognized inside the extremely curved meniscus viewed in the far field (Krechetnikov & Homsy 2006). In this idealized setup, Landau & Levich (1942) have derived the equation without gravitational drainage for slow substrate withdrawal: (1.1) where h w is the film thickness, Ca = μu s /σ is the capillary number, with u s being the plate speed, μ being the fluid viscosity, and σ being the surface tension, and l c = (σ/ρg) 1/2 is the capillary length. Despite the considerable literature on “infinite” dip coating flows, the results of those studies cannot be directly applied to many practical situations in which the pool is confined, such as coating on fiber (Quéré 1999) or laboratory experiments (Brinker et al. 1992). The infinite pool assumption is only valid in the absence of a stationary wall influencing the film thickness h w (i.e. h w ≪ l). Otherwise, the pool is confined. A confined pool can be achieved either via a small pool width l due to a small container or through large h w due to a fast moving plate on which a thick film is deposited. Note that an unconfined pool can become confined as Ca increases with increased film thickness. Under these conditions, l becomes the proper characteristic length.