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.