Nonlinear electro-rheological instability of two moving cylindrical fluids: An innovative approach

Abstract

The present article examines the nonlinear stability of two viscoelastic electrified cylindrical fluids immersed in permeable media. The current structure consists of two endless vertical cylinders containing two electrified fluids. An axial unchanged electric field (EF) is applied to the entire construction; additionally, the impact of the surface tension is reflected. The main driving force for understanding this challenge has increasing significance in atmospheric and oceanic dynamics. The viscous potential theory is employed to ease the mathematical processes. The fundamental hydrodynamic equations are combined with Maxwell's equations in the quasi-static approximation to set the boundary-value problem. The appropriate boundary conditions (BCs) are expressed in a nonlinear form; this nonlinearity is achieved by addressing the linearized controlling equations of the motion. The viscoelastic impacts are considered to illustrate how the BCs produce their contributions. Consequently, the equations of motion are tackled without the effects of viscoelasticity parameters. The interface displacement consequently interacts vertically along with the cylindrical axis. The Rayleigh Helmholtz–Duffing oscillator describes the propagation of the interface between the two fluids. The non-perturbative approach (NPA), based on the He's frequency formula, transforms the typical nonlinear differential equation (NDE) into a linear one. The non-dimensional analysis reveals a lot of dimensionless physical numerals. These non-dimensional physical characteristics can be utilized to study the fundamental character of the liquid movement. They are also used to reduce the quantity of variables that are needed to comprehend the framework. A quick explanation of NPA is also presented. The stability study reveals the real/complex coefficients of the NDE. The numerical simulations show that there is a consistent solution and that the increases in the axial EF, as well as axial wavenumber, stabilize the system. The obtained findings help to understand and explain diverse nonlinear progressions that have taken place in fluid mechanics. To show the impact of the different factors and the efficiency of the stability approach, diverse PolarPlot diagrams are graphed for both actual and hypothetical portions.