Ribbing instability in rotating Landau-Levich drag-out problem.

The liquid flux entrained on the outside of a rotating drum is a fundamental problem involving complex, multi-scale, multi-phase flow physics in film coating processes, tribology (journal bearings), etc. Here, we study this so-called rotating drag-out problem in the limit wherein the liquid inertia dominates meniscus surface tension forces. In both experiments and direct numerical simulations, this condition leads to multiple liquid sheets along the drum's axis at its rising side that could be interpreted as inertial analogues of the well-known axial modulation of coating film thickness in low Reynolds number meniscus coating flows. However, the liquid sheet height is proportional to U²/g, where U is the linear drum speed. By properly controlling the gap between the drum's bottom and the floor, along with the drum's immersion depth, we measure the mean rib spacing as a function of drum speed U. In order to further clarify the underlying mechanism, we also solve the incompressible two-phase Navier-Stokes equations with an explicit interface capturing (VOF method). In particular, a simplified configuration of the drag-out problem involving an inclined plate with high-speed withdrawal is investigated. Thereby, the origin of the incipient ribbing instability is elucidated.