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

TL;DR

This paper models the particle capture process in high gradient magnetic separation systems, identifying a critical force ratio that determines whether particles are captured or escape, and explores how system geometry influences this threshold.

Contribution

It introduces a mathematical model for particle motion in HGMS, revealing the critical Mason number for capture and analyzing the effects of system geometry on efficiency.

Findings

Critical Mason number exists for particle capture.

Capture efficiency depends on particle entry position above this threshold.

Multiple separation cycles can improve overall efficiency.

Abstract

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.