Nonlinear dynamics of thin liquid films subjected to mixed-frequency electrical field

Abstract

The nonlinear dynamics of the interface between both perfect and leaky dielectric liquid films interposed between two parallel electrodes are investigated under the effect of mixed-frequency electric fields. A coupled system of evolution equations is derived in dimensionless form by employing the long-wave approximation. The linear stability analysis is implemented in accordance with the characteristics of each specific case namely the constant (DC) and the altering (AC) fields. In particular the response of the system to the multi-mode AC electrical field is analyzed. Assisted by the conclusions of the theoretical investigation the initial-boundary-value problem associated with the coupled system of evolution equations is solved numerically for several parameter sets. The system behavior is studied by monitoring the evolution process and by examining the steady/quasi-steady pillar formations in the nonlinear regime. The possibility to generate interface profiles of diverse topological forms to manipulate their features and to control the time dependent progress and the film rupture by imposing different combinations of frequencies and/or amplitudes of the corresponding mode is confirmed.