Effect of Matrix Shape on the Capture of Fine Weakly Magnetic Minerals in High-Gradient Magnetic Separation

The magnetic matrix is the core component of the high-gradient magnetic separation (HGMS) system and plays a decisive role in the operation of the HGMS system. The cylindrical matrix is the most commonly used matrix in HGMS. The matrix shape is a very important parameter influencing the performance of the HGMS system. The special cross-section matrix may have better magnetic characteristics and present better performance in HGMS. However, previous studies of the basic principles of HGMS are basically limited to those employing a circular cross-section matrix. Investigations into the magnetic characteristic and performance of a special cross-section shape matrix are scarce. In this paper, the effect of matrix shape on the capture of fine weakly magnetic minerals in HGMS is investigated with the particle capture model. The matrix shape varies between circular cross section and elliptical cross section. The magnetic field and the flow field around the elliptic matrix are analytically calculated. The motion equations of particles around the elliptic matrix under different circumstances are derived and the particle motion trajectories are depicted. The particle capture radius and efficiency of the matrix with shape coefficient L-h/L-v (ratio of the horizontal axis to the vertical axis of the matrix cross section) ranging from 1/3 to 3 are calculated and compared, providing that the matrix area facing the incoming fluid is the same. The results indicate that there exists the optimal L-fh/L-v value at which the capture radius and efficiency reach the maximum. The optimal L-h/L-v value increases with the increase in particle size and the decrease in matrix size. Within the L-h/L-v range of 1/3-3, the maximum particle capture efficiency (at the optimal L-h/L-v or at L-h/L-v = 3) under some arrangements can be much higher than the circular matrix (at L-h/L-v = 1), but the increment decreases with the increase in matrix size, the arrangement parameter d/L-v, and the decrease in particle size. The results provide a theoretical basis for the application of the elliptical matrix in HGMS as well as a reference for the development of other novel magnetic matrices in HGMS.