Drainage on a rough surface

We discuss the drainage of a wetting film deposited on a vertical solid covered with a regular array of microposts. It is shown that the classical Jeffreys' law, observed on flat solid, is deeply modified by the texture: 1) the film thickness does not follow anymore a scaling law, as a function of time; 2) below a critical thickness on the order of the pillar height, the film thickness drastically decreases; 3) at long time, a residual film remains trapped in the network of posts. All these facts are interpreted by considering the interaction between the "free film" flowing above the posts, and the "trapped film" inside the roughness. Beside a general description of the drainage of film on rough surfaces, our study shows that textures can be used to influence, or even block, the flow of liquid films on inclines.