Inertial drag-out problem : sheets and films on a rotating drum

The so-called Landau-Levich-Derjagin problem treats the coating flow dynamics of thin viscous liquid films that form on freely-driven solid surfaces. Such flows are not only relevant to film coating and liquid entrainment in industrial processes but are also a starting block for lubrication theory. In this context, we use a simple experimental set-up consisting of a partially immersed rotating drum in a water tank to study the role of inertia, and also curvature, on the liquid entrainment phenomena. Using water and UCON mixtures, we point out a rich phenomenology in the presence of strong inertia. Instead of a $2$D, or axisymmetric, dynamic meniscus as seen in the classical problem, the inertial effects bring about one or more thin liquid sheets from which a liquid film develops on the drum's front end. In addition, this film then undergoes atomisation at the rear end of the drum due to the centrifugal acceleration. Both viscous and surface tension forces play a key role in deciding the film thickness as in the classical Landau-Levich problem until a critical Weber number based on Landau-Levich dynamic meniscus. Thereafter, strong inertial effects influence the film flow rate over the drum via lateral entrainment and via a modified inertial dynamic meniscus at large immersion-depth-to-radius ratio.