Stability analysis of a thin liquid film on an axially oscillating cylindrical surface in the high-frequency limit.

We consider an axisymmetric liquid film on a horizontal cylindrical surface subjected to axial harmonic oscillation in the high-frequency limit. We derive and analyze the nonlinear evolution equation describing the nonlinear dynamics of this physical system in terms of the averaged film thickness. The method used for the derivation of the evolution equation is based on long-wave theory and the separation of the relevant fields into fast and slow components. We carry out the linear stability analysis for a film of a constant thickness which shows that axial forcing of the cylinder may result in either stabilization or destabilization of the axisymmetric flow with respect to the unforced one, depending on the choice of the parameter set. The analysis is extended to the weakly nonlinear stage and it reveals that the system bifurcates subcritically from the equilibrium.