Effects of magnetic field and slippages on oscillating rigid spheres in magnetorheological ferrofluids

This study investigates the intricate dynamics of synchronized and desynchronized oscillations of rigid spheres with varying diameters immersed in magnetorheological ferrofluids. It delineates two distinct motion types: synchronized oscillation, where spheres resonate in unison due to magnetic forces, and desynchronized oscillation, characterized by out-of-phase movements stemming from disparate frequencies and hydrodynamic interactions. Employing Stokes flow theory, the research formulates a spherical solution and applies boundary conditions through a sophisticated collocation technique. Noteworthy findings indicate that drag force coefficients rapidly converge to definitive parameters, including the ratio of sphere diameters, the Hartmann number, frequency parameters, and slippage conditions, signifying independent motion at sufficient inter-sphere separations. Furthermore, the study rigorously examines the influence of variations in fluid properties and magnetic fields on sphere interactions, while also evaluating the precision of the numerical methodologies employed. The implications of this research are profound, offering significant insights for applications necessitating meticulous control over particle dynamics.