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

Abstract

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.