A numerical simulation on magnetophoresis of transition metal ions in porous media

Magnetic particles in solution tend to aggregate under non-uniform magnetic fields during magnetophoresis, a process applied in drug delivery, biocatalysis, pollutant removal, and separations. Despite its broad utility, the underlying transport mechanisms in porous environments remain underexplored. This study numerically investigates magnetically driven motion of paramagnetic and diamagnetic ions in saturated porous media under static magnetic field gradients. A multiphysics model is developed that couples fluid flow, species transport, and magnetic forces. Two porous-medium approaches are compared: a Stokes-based model with effective diffusivity and a Brinkman model accounting for permeability and viscous drag. Results, benchmarked against recent experiments, show that the Brinkman model better captures transport trends. Simulations reveal that both ion types form field-induced aggregates under gradients up to 100 T²/m at concentrations of 1–100 mM. The Kelvin force dominates transport; concentration-gradient magnetic forces are negligible. In binary systems, paramagnetic clusters can entrain diamagnetic species, enhancing their motion while reducing the net drift of paramagnetic ions. These findings emphasize the importance of accurate porous-flow modeling and interspecies interactions in magnetophoretic transport.