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High gradient magnetic separation (HGMS) is an efficient way to removemagnetic and paramagnetic particles, such as heavy metals, from waste water. Asthe suspension flows through a magnetized filter mesh, high magnetic gradientsaround the wires attract and capture the particles, removing them from thefluid. We model such a system by considering the motion of a paramagnetictracer particle through a periodic array of magnetized cylinders. We show thatthere is a critical Mason number (ratio of viscous to magnetic forces) belowwhich the particle is captured irrespective of its initial position in thearray. Above this threshold, particle capture is only partially successful anddepends on the particle's entry position. We determine the relationship betweenthe critical Mason number and the system geometry using numerical andasymptotic calculations. If a capture efficiency below 100% is sufficient, ourresults demonstrate how operating the HGMS system above the critical Masonnumber but with multiple separation cycles may increase efficiency.

Particle Capture Efficiency in a Multi-Wire Model for High Gradient Magnetic Separation