Modeling Transport of Transition Metal Solutes in different Porous Media under a non-uniform Magnetic Field*

Magnetic particles in solution are reported to form clusters when subjected to a non-uniform magnetic field during Magnetophoresis. Magnetophoresis finds application in drug delivery (magnetic targeting), bio-catalysis, pollution capture, extraction, and protein isolation. Previous experimental studies showed that paramagnetic and diamagnetic metal ion systems undergo magnetophoresis in a porous medium under the influence of a non-uniform magnetic field of a permanent magnet. In this work, we present a Multiphysics numerical simulation to provide an in-depth understanding of the experimental results. Our numerical simulations indicate that both the paramagnetic and diamagnetic ions may form clusters of sub-micrometer size under influence of the magnetic field. Also, with same porosity, the porous media's pore size has been observed to influence the amount of enrichment or depletion of the magnetic particles. Additionally, we examined the impact of magnetic diffusion and magnetic convection fluxes and observe that the magnetic convection flux is dominant during magnetomigration. Furthermore, our simulations suggest that the cluster size is a function of time and magnetic susceptibility of the ions, and the effect of pore size could be understood in the context of friction between the cluster and the solid walls of the porous media. We provide an approximate form of cluster size and friction factor coefficient by fitting the simulations to experimental results.