An Inspection of Nonlinear Instability of Interface Between Two Bingham Flows Within Permeable Media: Impact of Periodic Magnetic Field

Studying Bingham flows in permeable media under a periodic magnetic field enhances the understanding of yield-stress fluids for applications like oil recovery and filtration. This study combines non-Newtonian behavior with porous-medium resistance and magnetic variations, facilitating the analysis of complex flow phenomena, including oscillatory yielding and improved flow control in porous structures. The viscous potential theory is employed to streamline the mathematical processes. The utilization of linear governing partial differential equations of motion, along with appropriate nonlinear boundary conditions, yields additional simplifications. The investigation yields a nonlinear Mathieu oscillator that governs the interfacial displacement. A non-perturbative method is used to convert this nonlinear ordinary differential equation into a linear equation. A non-dimensional formulation minimizes the fundamental variables required to characterize the system by establishing a collection of dimensionless physical characteristics. The study analyzes a nonlinear Mathieu oscillator with complex coefficients to explore system dynamics related to elevation. By simplifying the variable coefficients, it enhances the examination of stability and resonance behavior. Despite inherent complexities, the work effectively clarifies fundamental concepts, contributing to a more coherent understanding of the subject. The Hartman number, magnetic field, and magnetic permeability ratio exert a destabilizing effect. Conversely, the Bingham parameter, Weber number, and periodic frequency exert a stabilizing influence.