Influence of a longitudinal and tilted vibration on stability and dewetting of a liquid film

We consider the dynamics of a thin liquid film in the attractive substrate potential and under the action of a longitudinal or a tilted vibration. Using a multiscale technique we split the film motion into the oscillatory and the averaged parts. The frequency of the vibration is assumed high enough for the inertial effects to become essential for the oscillatory motion. Applying the lubrication approximation for the averaged motion we obtain the amplitude equation, which includes contributions from gravity, van der Waals attraction, surface tension, and the vibration. We show that the longitudinal vibration leads to destabilization of the initially planar film. Stable solutions corresponding to the deflected free surface are possible in this case. Linear analysis in the case of tilted vibration shows that either stabilization or destabilization is possible. Stabilization of the dewetting film by mechanical action (i.e., the vibration) was first reported by us [Phys. Rev. E 77, 036320 (2008)]. This effect may be important for applications. Also, it is shown that the tilted vibration causes the averaged longitudinal fluid flow, which can be used to transport microparticles.