A Mathematical Model for Electro-Magnetohydrodynamic Cavitation Bubbles near a Rigid Wall

This study presents a mathematical model of the dynamics of a cavitation bubble oscillating near a rigid wall under an electromagnetic field. The model utilizes a modified Keller–Miksis equation incorporating the compressibility effects of the surrounding Newtonian conducting fluid. The rigid boundary’s effects, modeled using the image method, contributed to an additional pressure, which altered the cavitation bubble’s radial dynamics. Electromagnetic effects were incorporated through the Maxwell stresses induced by an external electric field, electrostatic pressure from surface charge accumulated at the bubble’s interface, and magnetic damping arising from the electric currents induced in the conducting fluid. The resulting nonlinear ordinary differential equation was solved using a fourth- and fifth-order Runge–Kutta scheme. Validation against previous theoretical and experimental studies showed good agreement, confirming the model’s reliability. A parametric analysis showed that the bubble–wall distance, electric field intensity, magnetic field strength, and surface charge magnitude considerably influence the behaviors of oscillating bubbles. Electric fields and surface charges promote bubble expansion, whereas magnetic fields and nearby surfaces restrict its size, thereby influencing its collapse. These behaviors can be attributed to the governing equation and the magnitude of its nonlinear terms. The proposed model provides a consistent mathematical framework for analyzing the electro-magnetohydrodynamic cavitation phenomena near rigid boundaries.