(518h) Electrostatic Faraday Instability in Thin Films

Pattern formation at the free interface of a fluid when subject to normal periodic vibrations has been studied since the time of Faraday. Such interfacial patterns owe their origin to an instability arising due to resonance between the external forcing frequency and the inherent natural frequency of the fluid interface. The natural frequency arises as a result of the interaction between the dynamics of the free interface and the fluid inertia. The external forcing on the other hand may be mechanical, acoustic or electrostatic in nature. In this work, we study interfacial pattern formation in thin liquid films subject to a periodic electrostatic forcing. In such a case, the instability arises primarily due to the Maxwell stresses at the fluid interface. The fluid is considered to be either perfect conductor or a perfect dielectric. A long-wave thin film model retaining the effects of inertia is developed using the method of weighted residual integral boundary layer. A linear stability analysis based on the Floquet theory as well as nonlinear simulations of the long wave model is carried out. It is shown that for gravitationally stable films, the interface becomes unstable to harmonic waves at the onset of instability. Different modes of interface pattern maybe obtained at the onset depending on the forcing frequency. Gravitationally unstable film with appropriate electrical properties when periodically forced, may be stabilized linearly (returns to stable at configuration) as well as non-linearly (evolves to time-periodic non-ruptured configurations). While for certain other choice of fluid films, periodic forcing only enhances the Rayleigh-Taylor instability.