Coating of a textured solid

We discuss how a solid textured with well-defined micropillars entrains a film when extracted out of a bath of wetting liquid. At low withdrawal velocity V, it is shown experimentally that the film exactly fills the gap between the pillars; its thickness h(d) is independent of V and corresponds to the pillar height h(p). At larger velocity, h(d) slowly increases with V and tends towards the Landau-Levich-Derjaguin (LLD) thickness h(LLD) observed on a flat solid. We model the entrainment by adapting the LLD theory to a double layer consisting of liquid trapped inside the texture and covered by a free film. This model allows us to understand quantitatively our different observations and to predict the transition between h(p) and h(LLD).