Outlining the impact of structural properties of a multilayered porous channel with oscillating velocities and fields

Abstract

In this study, we analyze the multilayered viscous potential flow, in which the effects of primary and combined resonances on the interfacial stability due to oscillating velocities and a periodic field are carried out. Fluids are assumed to be immiscible and incompressible with different electrical and dynamic properties and move through a porous nature. Viscosity occurs at the surface through the surface dynamic condition, where it is assumed to be weak in the fluid bulk and can be ignored. Given the boundary and surface conditions, the linear solutions of the motion and field equations led to simultaneous differential equations with complex periodic coefficients, which are a generalization of Mathieu’s equations. The special case of uniform velocity and the constant field is discussed where a quadruple algebraic equation has complex coefficients is obtained. The method of multiple time scales is applied to obtain analytical approximate solutions and perform the stability criteria for both the non-resonant and resonant states. The impacts of flow velocities and associated electric field properties, as well as the permeability of porous media and fluid sheet geometry, were taken into consideration. Through numerical discretization by varying the values of the quantities of the model, essential conclusions can be made that support an understanding of the stabilization process. For the primary resonance, it is found that there is an important role in increasing the thickness of the layers to the stability of the fluid sheet, while the porosity of the layers has a dual role phenomenon depending on the thickness of the upper layer. In the case of combined resonance, it was mentioned that increasing the dielectric constant between the lower layer and middle one tends to assist the system to instability, but it is worth noting that it supports it slowly, on the other hand, the electric horizontal field helps the system to be more stable.