Modeling magnetic separation of metal ions in aqueous solutions

Abstract

Although the techniques for the magnetic separation of large (micrometer size) ferromagnetic and paramagnetic particles are well developed and commercially used on a large scale, the magnetic separation of nanoparticles is not well studied. In this article, we develop a mathematical model to describe the transport of small paramagnetic and diamagnetic particles in liquids under a non-uniform magnetic field. Special emphasis is given to thermal diffusion, which is shown to play an important role in the transport of nanoparticles. The model describes the magnetic particles and the solvent as two interpenetrating continua: the magnetic particle continuum, which interacts with the external magnetic field, lacks inertia, and moves through the solvent while experiencing a force of resistance from the solvent; and the solvent continuum which is assumed non-magnetic and inert. The two continua are described using the Navier-Stokes and drift–diffusion equations, respectively. Using our model, we analyze the effects of drag, gravitation, thermal diffusion and magnetophoresis on the dynamics of the particles and look at the conditions under which these phenomena dominate their transport properties. The model is in good qualitative agreement with experiments published in the literature.