A thin-film equation for a viscoelastic fluid, and its application to the Landau-Levich problem

Thin-film flows of viscoelastic fluids are encountered in various industrial and biological settings. We derive a thin-film equation for a second-order fluid, and use it to study the classical Landau-Levich dip-coating problem. We show how viscoelasticity of the fluid affects the thickness of the deposited film, and address some apparent discrepancies in the literature.