The drag-out problem in film coating theory

Summary

An important step towards the understanding of many industrial coating processes is a solution of the dragout problem, which is to determine the thickness of the film of liquid which clings to a plate when it is drawn steadily out of a bath of the liquid. An approximate solution, valid for small capillary numbers, was given by Landau and Levich, and considerable effort has been exerted to extend or refine this work. In this paper we show that the Landau-Levich result is an asymptotic solution valid as the capillary number tends to zero, a fact not properly appreciated hitherto, and show how correction terms may be obtained by the method of matched expansions. We also show how the results may be applied to the coating of a horizontal roller.