Matrices In High Gradient Magnetic Separation Research Articles

Simulation of particle accumulation in high gradient magnetic separation based on static buildup model (SBM)

Static buildup model (SBM) is an analytical approach to predict upstream buildup profile of circular matrix in high-gradient magnetic separation (HGMS). But it was confined to single-wire system in idealized fluid and magnetic field, and was not applicable for more complicated or generalized systems. As better separation performance can be obtained by introducing composite force field or employing novel structural matrices in HGMS, it is necessary to develop models that are more adaptable for predicting particle buildup. In this paper, a simulation model based on SBM was developed to extend its application to complicated situation. The boundary of the buildup was updated by judging whether a particle released from locations near buildup surface would stay or not. And a characterized thickness within boundary layer was proposed to ensure that the released particles were subjected to forces of the same expression as that in SBM. The established model was proved to obtain close results with SBM when HGMS system was in idealized condition. Experimental results testified the model’s ability to predict saturated buildup profile of both circular and elliptic matrices in a realistic system. Since fluid and magnetic field information are processed by the simulation software, this model is also believed applicable for more complicated conditions such as multi-wire system and novel structure matrix system, which will be investigated in follow-up studies.

Effect of matrix saturation magnetization on particle capture in high gradient magnetic separation

The performance of high gradient magnetic separation (HGMS) system is influenced by many configuration and operation parameters. We have previously investigated the effect of these influencing parameters such as applied magnetic induction, fluid velocity, matrices size and shape etc. We derived extended particle capture models for cylinder matrices in HGMS, considering both the case that matrices were unsaturated and saturated by applied induction. A convenient method relating to matrix saturation magnetization Ms for judging magnetization state of matrices was proposed. Matrix saturation magnetization Ms is a very important parameter in HGMS and is worthy of being investigated. In this paper, effect of matrix saturation magnetization on particle capture performance in HGMS is studied through numerical simulation and theoretical calculation. The induced magnetic field and particle capture cross section of SUS 430, pure iron and cobalt steel matrices are equivalent and increase with saturation magnetization Ms when the matrices are unsaturated and saturated by applied induction, respectively. Matrices with larger aspect ratio λ have wider applied induction range within which higher saturation magnetization Ms will present superiority. Adopting matrices with relatively large aspect ratio and high saturation magnetization can enhance recovery of fine weakly magnetic minerals in vertical ring high gradient magnetic separator. This is also applicable to horizontal ring magnetic separator in which grooved plates (prone to saturation) are adopted.

Analyze the multi-wire magnetic field of HGMS by semi-analytical method

Abstract In this paper, a semi-analytical method (SAM) to analyze the magnetic field distribution in High-Gradient Magnetic Separation (HGMS) was promoted, constituting a combination of conform mapping (includes Schwarz-Christoffel (S-C) mapping) and finite elements (FEM). Following the establishment of a 2-D physical model of cylindrical matrices in HGMS, the procedure including 4 steps was elaborated in this paper. The magnetic field of the cross-section cylindrical matrices could be regarded as a combination of hexagonal units, while it could also be divided into an attraction zone a discrete area and a repulsion action zone. Due to its specially meshed grids in the calculation, the solution was effective and accurate. Subsequently, the comparisons on the magnetic force and separation result of mediums with various parameters were studied, whereas the results indicated that the cross-section matrix was more suitable for HGMS than the paralleled matrices. The matrix spacing that perpendicular to the field direction (d) was suggested to be similar to the bar medium diameter (R).

Rapid determination of the magnetization state of elliptic cross-section matrices for high gradient magnetic separation

Our previous studies showed that the performance of the matrices varied greatly before and after reaching magnetization saturation and we expanded the particle capture models of circular and elliptic matrices in high gradient magnetic separation (HGMS), considering both the case that the matrices were unsaturated and saturated. Problem remained that at which condition the matrices will reach magnetization saturation in HGMS. A method to determine the magnetization state of the matrices for selecting the applicable particle capture models (models for unsaturated or saturated matrices) in specific studies should be developed. This is particularly essential for studying the effect of matrix shape (aspect ratio) on the particle capture performance of matrices in HGMS, as the magnetization sate of the matrices varies greatly with the aspect ratio. In the present paper, the magnetization process of elliptic matrices was investigated and a rapid and convenient method of judging the demarcation for selecting the applicable particle capture models was proposed and was validated with numerical simulation. Generalized relation between magnetization coefficients and the matrix shape coefficient γ (ratio of axis along the magnetization direction to that perpendicular to the magnetization direction) before and after reaching magnetization saturation were quantitatively presented. The demarcation for judging the magnetization sate of elliptic matrices in HGMS can be determined by the simple equation B0 = Ms/(γ + 1). Based on the equation, the magnetization state of the matrix can be rapidly determined and the applicable particle capture models can be selected accordingly in specific studies.

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 $L_{f{h}}/L_{v}$ 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.

Investigation of the particle capture of elliptic cross-sectional matrix for high gradient magnetic separation

High gradient magnetic separation (HGMS) is an effective method to recover fine weakly magnetic particles from a suspension. Magnetic matrices are the crucial components of the HGMS system. The most commonly used matrices in HGMS are cylinder matrices of high magnetic permeability. Special cross-section shape matrix may have better magnetic characteristics and show better performance than circular cross-section matrix in HGMS. The particle capture of elliptic cross-section matrix in the three configurations of HGMS are modeled and investigated, aiming at revealing the application possibility of elliptic cross-section matrix in HGMS and providing a research clue for the development of novel high efficiency magnetic matrix for scientific researchers. The magnetic field and the flow field around the elliptic matrix are analytically calculated. The particle motion equations in the three configurations of HGMS are derived. The particle motion trajectories around the elliptic matrices are plotted. The particle capture radius and efficiency of the elliptic matrix are calculated and compared with those of the circular matrix, providing that the diameter of the circular matrix is equal to the short axis of the elliptic matrix. In the three configurations, the elliptic matrix can present higher particle efficiency than the circular matrix under some circumstances. The results indicate the promising application prospect of elliptic cross-section matrix in HGMS. The particle capture efficiency is influenced by many factors. In the development of novel high efficiency magnetic matrix, the magnetic characteristics, the flow characteristics and the arrangement of the matrix should all be taken into consideration.

Particle capture of elliptic cross-section matrices for parallel stream high gradient magnetic separation

Purpose – The purpose of this paper is to model the particle capture of elliptic magnetic matrices for parallel stream type high magnetic separation, which can be a guidance for the development of novel elliptic cylinder matrices for high-gradient magnetic separation (HGMS). Design/methodology/approach – The magnetic field distribution around the elliptic matrices is investigated quantitatively and the magnetic field and gradient were calculated. The motion equations of the magnetic particles around the matrices were derived and the particle capture cross-section of elliptic matrices was studied and was compared with that of the conventional circular matrices. Findings – Elliptic matrices can present larger particle capture cross-section than the conventional circular matrices and can be a kind of promising matrices to be applied to HGMS. Originality/value – There is little literature investigating the magnetic characteristics and the particle capture of the elliptic matrices in HGMS, the study is of great significance for the development of novel elliptic magnetic matrices in HGMS.