Three-dimensional nonlinear dynamics of a thin liquid film on a spinning ellipsoid

Abstract

The present work investigates the three-dimensional flow of a thin liquid film distributed on the outer surface of an ellipsoid, rotating around the vertical axis at constant angular velocity. The lubrication approximation expressing the evolution of the film thickness, originally developed for stationary curved substrates, has been re-derived by including the non-inertial forces associated with the rotation. This comprehensive model, which incorporates the gravitational, centrifugal, and capillary forces, is employed for a parametric investigation via numerical simulations. The results validate and extend the conclusions of our former study covering the axisymmetric case and bring about an advanced understanding by exploring non-axisymmetric effects. The parametric analysis sheds light on the significance of rotation on a non-constant curvature substrate by comparing the thickness profiles with the static case.