Insights in the nonlinear instability of an annular jet inclosing an electrified Eyring–Powell viscoelastic fluid

Abstract

The exploration of nonlinear instability in an annular jet containing an electrified Eyring–Powell viscoelastic fluid (EPF) is essential in industrial and biological applications, enhancing fluid control and optimizing intricate processes. The current model is pervaded by the impact of a uniform axial electric field (EF). Additionally, the flow is assumed to flow in a permeable media. The study explores the impact of EF effects on jet breakup and stability, providing new criteria of instability thresholds and deformation patterns. It is well known that the implementation of an axial EF may produce multiple instability modes, potentially leading to breakdown or formation of complex structures within the annular jet. The viscous potential theory (VPT) is exploited to abbreviate the mathematical intricacy. The nonlinear methodology foundations in solving the linear governing partial differential equations (PDEs) of motion are resolved through the applicable nonlinear boundary conditions (BCs) to yield coupled nonlinear ordinary differential equations (ODEs) that judge the interface displacements. The study scrutinizes the surface tensions (STs) in a broad context, together with the symmetric and anti-symmetric perturbation modes. He's frequency formulation (HFF) strengthens the innovative non-perturbative approach (NPA). It is employed to transform conventional nonlinear ODEs into linear ones. A set of non-dimensional physical parameters is accomplished. The validation between the nonlinear and linear ODEs is constructed by consuming the Mathematica Software (MS). A series of graphs are provided to illustrate the impact of various non-dimensional physical parameters in the stability configuration. The efficacy and accuracy of the NPA are validated by some figures and tables. It is found that the structure becomes gradually stable as the permeability of the medium; the inner and outer radii grow. Simultaneously, it converts fewer stable with the rise of the electric Bond number and the non-Newtonian parameter. Consistent decay behavior is seen in the temporal histories of the periodic solutions, suggesting that the outcomes are stable. Additionally, the associated phase plane curves are shown in a variety of plots that resemble symmetric closed curves and feature spiral curves pointing inward at a single point.