Modeling transport of paramagnetic ions in porous materials

A mathematical model based on a drift–diffusion theory is proposed to describe the transport of paramagnetic ions under magnetic field gradients in porous materials. The model takes into consideration the magnetic and gravitational drifts and thermal diffusion, and uses Bruggeman equations to describe the effective properties of the porous medium. Metal-ion adsorption phenomena are considered through a simplified Langmuir model. In agreement with previously published experimental data, our simulation results demonstrate that adsorption in porous systems coupled with magnetophoresis could be employed to move individual transition-metal ions in solutions and also holds promise for the magnetic separation of rare-earth elements.