Thin Liquid Film Dynamics on a Spinning Spheroid

The present work explores the impact of rotation on the dynamics of a thin liquid layer deposited on a spheroid (bi-axial ellipsoid) rotating around its vertical axis. An evolution equation based on the lubrication approximation was derived, which takes into account the combined effects of the non-uniform curvature, capillarity, gravity, and rotation. This approximate model was solved numerically, and the results were compared favorably with solutions of the full Navier-Stokes equations. A key advantage of the lubrication approximation is the solution time, which was shown to be at least one order of magnitude shorter than for the full Navier-Stokes equations, revealing the prospect of controlling film dynamics for coating applications. The thin film dynamics were investigated for a wide range of geometric, kinematic, and material parameters. The model showed that, in contrast to the purely gravity-driven case, in which the fluid drains downwards and accumulates at the south pole, rotation leads to a migration of the maximum film thickness towards the equator, where the centrifugal force is the strongest.