Abstract
The 3-D motion of a weak-viscous dielectric liquid inside a partially-filled excited rectangular container in the presence of a uniform electric field is investigated using potential viscous theory. A Mathieu-like equation prescribe the evolution of modes is reached. The interaction between two surface modes is considered. According to linear approach, the normal field and dielectric constant destabilize the flow whereas surface tension stabilizes it. However, the wave number plays a dual role according to the waves kind. The discussion for fixed points as well as the phase space and time evolution of modes predicts a case of global instability due to the resonance condition βˆ1=0. Also, it reveals an unstable role of the forcing indicator whereas detuning parameter tends to enhance the stability. The approximate and numerical solutions of Mathieu-like equation compare well in regard with a qualitative behaviour. The greater the viscosity is, the less important disturbances become. The conclusion with respect to field as well as relative permittivity agrees with that of the linear approach. The paper concludes that considering more higher-order nonlinear terms can increase the accuracy of the results of the analytical method. In addition, a device can be designed to achieve optimal conditions for model stability by controlling available physical parameters.
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