Magnetically assisted separation of weakly magnetic metal ions in porous media. Part 2: numerical simulations

We present a numerical investigation of the magnetophoresis of metal ions in porous media under static, nonuniform magnetic fields. The multiphysics simulations couple momentum transport, mass diffusion, and magnetic field equations, with the porous medium modeled using two distinct approaches: a Stokes-based formulation incorporating effective diffusivity, and a Brinkman-based formulation that explicitly accounts for permeability and medium-induced drag. Comparison with recent experimental data [A. Nwachukwu, M. Garba, J. Ali, T. Siegrist, M. Humayun and H. Mohammadigoushki, arXiv, 2025, preprint, arXiv:2510.09360. DOI: 10.48550/arXiv.2510.09360] reveals that the Stokes model partially fails to capture key trends, while the Brinkman model, with permeability accurately reproduces observed transport behavior on various porous media. Our simulations predict that both paramagnetic (MnCl₂) and diamagnetic (ZnCl₂) ions may form field-induced clusters under magnetic gradients over a range of concentrations of 1-100 mM and magnetic field gradients of up to 100 T² m^-1. The dominant driving force is found to be the magnetic gradient (Kelvin) force, while the paramagnetic force from concentration gradients contributes minimally. In binary mixtures, hydrodynamic interactions between paramagnetic and diamagnetic clusters significantly alter transport dynamics. Specifically, paramagnetic clusters can pull diamagnetic clusters along the magnetic field gradient, enhancing diamagnetic migration and suppressing the motion of paramagnetic species. These findings highlight the importance of porous media modeling and interspecies interactions in predicting magnetophoretic transport of ionic mixtures.