  High gradient magnetic separation (HGMS) is an efficient way to remove
magnetic and paramagnetic particles, such as heavy metals, from waste water. As
the suspension flows through a magnetized filter mesh, high magnetic gradients
around the wires attract and capture the particles, removing them from the
fluid. We model such a system by considering the motion of a paramagnetic
tracer particle through a periodic array of magnetized cylinders. We show that
there is a critical Mason number (ratio of viscous to magnetic forces) below
which the particle is captured irrespective of its initial position in the
array. Above this threshold, particle capture is only partially successful and
depends on the particle's entry position. We determine the relationship between
the critical Mason number and the system geometry using numerical and
asymptotic calculations. If a capture efficiency below 100% is sufficient, our
results demonstrate how operating the HGMS system above the critical Mason
number but with multiple separation cycles may increase efficiency.
