Evaporation-assisted magnetic separation of rare earth ions in aqueous solutions

This work aims to answer the question of why an enrichment of paramagnetic ions can be observed in a magnetic field gradient despite the presence of a counteracting Brownian motion. For that purpose, we study a rare earth chloride (DyCl3) solution in which weak evaporation is adjusted by means of small differences in the vapor pressure. The temporal evolution of the refractive index field of this solution, as a result of heat and mass transfer, is measured by means of a Mach-Zehnder interferometer. We develop a numerical algorithm which splits the refractive index field into two parts, one space-dependent and conservative and the other time-dependent and transient. By using this algorithm in conjunction with a numerical simulation of the temperature and concentration field, we are able to show that 90\% of the refractive index in the evaporation-driven boundary layer is caused by an increase in the concentration of Dy(III) ions. A simplified analysis of the gravitational and magnetic forces, entering the Rayleigh number, leads to a diagram of the system's instability. Accordingly, the enrichment layer of elevated Dy(III) concentration is placed in a spatial zone dominated by a field gradient force. This leads to the unconditional stability of this layer in the present configuration. The underlying mechanism is the levitation and reshaping of the evaporation-driven boundary layer by the magnetic field gradient.