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High gradient magnetic separation (HGMS) has been widely applied in many scientific and industrial fields. The performance of matrix in HGMS varied greatly before and after reaching magnetization saturation. Particle capture models of unsaturated and saturated matrices had been established in previous studies. Problems remained that how to determine the demarcation of applied magnetic induction for selecting the right capture models in specific studies. This is remarkably essential for the investigation of effect of matrix shape (aspect ratio) on performance of matrix in HGMS. In the present paper, magnetization process of circular matrix with increasing applied magnetic induction was investigated through numerical simulation and theoretical calculations. A convenient method to determine the demarcation point was proposed. The internal magnetic induction of matrix is equal to magnetization before reaching saturation and has the same growth rate as applied magnetic induction after reaching saturation. The demagnetization of matrix is half of the magnetization before and after reaching saturation. Validity of the coefficients adopted in the particle capture models in the whole range of applied induction is investigated with the internal magnetic induction, aiming to determine the demarcation point for selecting the right particle capture models. Results showed that the demarcation of the applied magnetic induction for circular matrix is M s /2. Particle capture models of unsaturated and saturated matrix should be selected when applied magnetic induction is lower and higher than M s /2, respectively. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a design and the corresponding mathematical study for the construction of a spatial geometric structure that we denominate the building block. The construction procedure is simple. Starting with two squares, we define and construct what we call the module. Next, we consider a fixed number of modules that generate the structure of the building block. We study the different possible connections among the building blocks, through which we define the so called matrix. We also demonstrate that this interconnection process turns out to be mathematically consistent. Finally, we propose a list of possible applications for the studied structures (involving areas such as education, sport sciences, molecular and architectural designs, etc.). [Copyright &y& Elsevier]