Magnetophoresis of paramagnetic metal ions in porous media

We report a numerical investigation of the magnetophoresis of solutions containing paramagnetic metal ions. Using a simulated magnetic field of a superconducting magnet and the convection-diffusion model, we study the transport of transition metal salts through a porous medium domain. In particular, through a detailed comparison of the numerical results of magnetophoretic velocity and ion concentration profiles with prior published experiments, we validate the model. Subsequent to model validation, we perform a systematic analysis of the model parameters on the magnetophoresis of metal ions. Magnetophoresis is quantified with a magnetic Péclet number Pe_m. Under a non-uniform magnetic field, Pe_m initially rises, exhibiting a local maximum, and subsequently declines towards a quasi-steady value. Our results show that both the initial and maximum Pe_m values increase with increasing magnetic susceptibility, initial concentration of metal solutes, and ion cluster size. Conversely, Pe_m decreases as the porosity of the medium increases. Finally, the adsorption of metal salts onto the porous media surface is modeled through a dimensionless Damkohler number Da_ad. Our results suggest that the adsorption significantly slows the magnetophoresis and self-diffusion of the paramagnetic metal salts, with a net magnetophoresis velocity dependent on the kinetics and equilibrium adsorption properties of the metal salts. The latter result underscores the crucial role of adsorption in future magnetophoresis research.