Theory and experimental verification of a model for high gradient magnetic separation.

A mathematical model of high gradient magnetic separation (HGMS) is presented, along with data on a characterized and sized feed material. The data are fitted to the model which uses elliptical co-ordinates to approximate the ribbon-like nature of the fibers. Magnetic force terms are developed for both paramagnetic and ferromagnetic particles in the vicinity of idealized matrix fibers which can either be magnetically saturated or unsaturated. The fluid flow is simulated by superimposing a boundary layer upon the solution for potential flow thus extending the range of validity to low Reynolds Numbers. Single particle trajectories are calculated in a piecewise linear manner by considering the force balance of magnetic, hydrodynamic, gravitational and inertial forces over each increment of the trajectory. By taking orientation of the fiber with respect to the field and flow direction into account, loading can be allowed for by assuming elliptical deposits. Experimental data were generated using high grade hematite prepared in ten separate size fractions. Correlation with the model is generally fairly good except for large particles where mechanical entrapment dominates the process. Considerable discussion of the results is included by analysing the physical concepts upon which the model is based. The validity of various assumptions pertinent to HGMS modeling is tested.