Gravity and inertia effects in plate coating

Coating processes are of technological interest. We focus here on the extraction of a vertical plate out of a wetting liquid. We first summarize the Landau-Levich-Derjaguin theory, including the gravity corrections which have been proposed in particular by White and Tallmadge. We propose a new numerical solution to the problem. Then, we discuss further developments: for liquids of low viscosity, it is shown that above a threshold in capillary number, the film is thickened because of inertia. A simple scaling argument is proposed for predicting the location of the threshold.