EHD nonlinear instability of a cylindrical interface between two williamson liquids

The investigation of electrohydrodynamic (EHD) nonlinear instability at a cylindrical interface concerning two Williamson fluids (W) is distinctive owing to its significance in industrial and biomedical contexts, including inkjet printing, electro-spinning, and enhanced oil recovery, where comprehending the stability of viscoelastic liquid interfaces under electric fields is significant for performance optimization and fluid behavior regulation. The study uses a nonlinear methodology to analyze the stability of a vertical cylindrical interface between two WF through porous media, concentrating on the impact of an axial uniform EF. The nonlinear methodology expresses the essential linear partial differential equations (PDEs) and implements the applicable nonlinear boundary conditions (BCs). This method produces a nonlinear distinguishing PDE. The non-perturbative approach (NPA) is employed to examine nonlinear stability. The main impartial of NPA is to transform a nonlinear ordinary differential equation (ODE) into a linear one. The NPA is differentiated from traditional perturbation techniques by its ability to precisely scrutinize the behavior of extremely nonlinear oscillators. This distinctive methodology is advanced by extending He's frequency formula (HFF) to orchestrate the movement of the interface. The study demonstrates that the structure stabilizes by elevating both the axial wavenumber and axial EF. It is found that the stability mechanism remains unchanged irrespective of whether the coefficients of the distinguishing ODE are real or complex. PolarPlots are generated independently for real and complex cases to grantee the impact of numerous variables and the effectiveness of the stability profile.