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. Under a non-uniform magnetic field, Pe initially rises, exhibiting a local maximum, and subsequently declines towards a quasi-steady value. Our results show that both the initial and maximum Pe values increase with increasing magnetic susceptibility, initial concentration of metal solutes, and ion cluster size. Conversely, Pe 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. 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.