On the inertial Landau-Levich-Deryaguin problem over a rotating disc

The so-called Landau-Levich-Deryaguin (LLD) problem treats thin viscous liquid film flows entrained by a moving solid surface. Here, we use a partially-immersed rotating disc in a liquid tank to study the role of inertia in the LLD problem. At first, we point out a rich phenomenology in the presence of strong inertia : formation of multiple liquid sheets on disc's front side, atomization of the liquid flux entrained over the disc's rim. Then, we focus on a single liquid sheet and the related average liquid flow rate entrained over a thin disc for various depth-to-radius ratio (h/R < 1). We illustrate that the liquid sheet is created through a ballistic mechanism as liquid is lifted out of the pool by the rotating disc. Also, by varying liquid viscosity, the entrained flow rate is shown to be given by the classical LLD lubrication flow approach based on both viscous and surface tension effects only, despite the large Reynolds numbers that result in 3D, non-uniform and unsteady entrained film flows. However, when the related Weber number becomes significant, strong inertial effects influence the entrained liquid flux over the disc at large radius-to-immersion-depth ratio via 3D flow stuctures wherein, a modified-LLD scaling based on ballistic fluid particle trajectory is proposed.