Abstract
This work aims to demonstrate the dynamical properties of the free interface separating two bounded layers of electrified Newtonian fluids inside a parametrically excited boxed basin. The mathematical model of the investigated problem is contacted with the linearized Navier–Stokes equation of viscous fluids and Maxwell equations together with the boundary conditions that are solved utilizing Laplace transform. Solutions of the governing equations in time domain are then numerically calculated by using Durbin's numerical inverse Laplace transform scheme. Graphical illustrations of the accomplished numerical results are provided to examine the influence of some selected parameters on the stability picture of the interfacial waves as well as the electric surface charge distribution. The numerical results proposed that the electric Euler number Eu, promotes the instability of the wave motion whatever the values of the frequency of oscillation and the destabilizing effect of Eu becomes weaker at larger values of the frequency; while a dual effect (in) stabilizing of the frequency of oscillations is reported whether the electric effects exist or not. This irregular influence of the frequency oscillation has also been monitored regarding to the forces exerted on the side wall of the container.
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