High-gradient magnetic chromatography of rare-earth elements

High-gradient magnetic chromatography (HGMC) is the chromatographic separation of a mixture of magnetic particles using high-gradient magnetic separation (HGMS) systems. However, unlike HGMS which has traditionally been used to separate magnetic from non-magnetic particles, the goal of HGMC is to separate different types of magnetic particles which have relatively close but different magnetic susceptibility, mass and volume. In this article we develop a simple mathematical model for the design of HGMC separation systems. The model takes into consideration the magnetostatic interactions between magnetic particles and wires (which form the stationary phase) and the effect of gravitation, Brownian motion of magnetic particles, and the viscous forces between particles and fluid. Using this model, we are able to derive analytical equations for the stability curves of the magnetic particles and use these curves in computing the recovery rates and purity of separation.