Enhanced dip coating on a soft substrate

A solid plate withdrawn from a wetting liquid bath entrains a thin liquid film, a process known as dip coating. We theoretically investigate the influence of a soft layer coated on the plate. The liquid-film thickness is found to be enhanced at low pulling velocity, when the elastic deformations of the soft layer are larger than the liquid-film thickness. A scaling relation of the film thickness with the velocity and the elastic modulus is analytically characterized using an asymptotic-matching method, and confirmed with numerical integration.