Nonlinear Sloshing Waves between Two Immiscible Electrified Liquids in an Oscillating Rectangular Container

Abstract The sloshing response of a liquid layer in a rigid rectangular container subjected to a vertical excitation is investigated taking into accounts the effect of both interfacial tension and electrical voltage difference between the vertical container walls. The discussion is dealing with demonstrating the structure of resonated three modes of surface waves on the liquid free interface. The non-dimensional mathematical equations governing the problem together with the associated boundary conditions are formulated up to the second order of nonlinearity. The evolution equations of the resonated waves are derived, then the method of multiple time scales is utilized to construct a third order dynamical system governing the amplitudes of the resonated waves including the second interaction terms. Such a system, in which the effects of several model parameters on the dynamical properties of flow pattern are studied, is solved numerically. The numerical computations revealed that the electric voltage difference applied to the container’ side walls as well as the electric permittivities of the two fluids plays a significant role in damping the interfacial waves and trend to stabilize the liquid motion, whereas the amplitudes of the external excitation that the container exposed trends to enhances the instability of flow motion where they tend to disrupt fluid movement, increase the pressure on the container body, and pose a significant risk to the integrity of the container.