Dynamics and equilibria of thin viscous coating films on a rotating sphere

Abstract

We examine the dynamics of a thin viscous liquid film on the outer surface of a solid sphere rotating around its vertical axis in the presence of gravity. An asymptotic model describing the evolution of the film thickness is derived in the rotating frame based on the lubrication approximation. The model includes the centrifugal and gravity forces and the stabilizing effect of surface tension. Depending on the values of the parameters, the problem admits different types of steady states: one with a uniformly positive film thickness, or those with one or two dry zones on the sphere. We prove that all steady states are energy minimizers and hence global attractors for axisymmetric states.