Abstract Magnetic matrix is a key component of high gradient magnetic separation (HGMS) system. Special shape matrices have brought great attentions from researchers whereas only elliptic and circular matrices have been properly modeled and comprehensively investigated. Our previous study showed that diamond matrices present good magnetic characteristics in axial HGMS and are worthy of being comprehensively studied. In this paper, a 2D dynamic simulation model was developed to representatively describe particle capture for the 3D axial HGMS. Quantitative analysis on particle capture cross section (PCCS) revealed the matching relation between aspect ratio and magnetic induction for maximum particle capture by diamond matrix. It is found that the optimal aspect ratio decreases as magnetic induction increases, and is independent on particle size (in the size range of 1–30 μm). The advantage of favorable aspect ratio is more prominent for smaller particles under lower magnetic induction. Comparative study reveals that effect of aspect ratio on particle capture performance of diamond and elliptic matrices are quite similar, and their optimal aspect ratios are nearly identical under specific induction. Diamond matrix exhibits a slight superiority over elliptic matrix in most cases, making it a kind of promising matrix in axial HGMS. An empirical equation has been proposed to determine the optimal aspect ratio, and it is estimated that the optimal aspect ratio of elliptic and diamond matrices are about 0.75‧Ms/B0.

中文翻译：

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金刚石基体轴向高梯度磁选最佳纵横比研究

摘要 磁性基质是高梯度磁分离（HGMS）系统的关键组成部分。特殊形状的矩阵引起了研究人员的极大关注，而只有椭圆和圆形矩阵得到了适当的建模和综合研究。我们之前的研究表明，金刚石基体在轴向 HGMS 中表现出良好的磁特性，值得全面研究。在本文中，开发了一个 2D 动态仿真模型来代表性地描述 3D 轴向 HGMS 的粒子捕获。颗粒捕获截面（PCCS）的定量分析揭示了金刚石基体最大颗粒捕获的纵横比和磁感应强度之间的匹配关系。发现最佳纵横比随着磁感应强度的增加而减小，并且与粒径无关（在 1-30 μm 的尺寸范围内）。在磁感应强度较低的情况下，对于较小的颗粒，有利的纵横比优势更加突出。对比研究表明，纵横比对金刚石和椭圆基体颗粒捕获性能的影响非常相似，在特定诱导下它们的最佳纵横比几乎相同。金刚石基体在大多数情况下比椭圆基体略有优势，使其成为轴向HGMS中一种很有前途的基体。提出了一个经验公式来确定最佳纵横比，估计椭圆和菱形矩阵的最佳纵横比约为0.75‧Ms/B0。对比研究表明，纵横比对金刚石和椭圆基体颗粒捕获性能的影响非常相似，在特定诱导下它们的最佳纵横比几乎相同。金刚石基体在大多数情况下比椭圆基体略有优势，使其成为轴向HGMS中一种很有前途的基体。提出了一个经验公式来确定最佳纵横比，估计椭圆和菱形矩阵的最佳纵横比约为0.75‧Ms/B0。对比研究表明，纵横比对金刚石和椭圆基体颗粒捕获性能的影响非常相似，在特定诱导下它们的最佳纵横比几乎相同。在大多数情况下，金刚石基体比椭圆基体略有优势，使其成为轴向 HGMS 中一种很有前途的基体。提出了一个经验公式来确定最佳纵横比，估计椭圆和菱形矩阵的最佳纵横比约为0.75‧Ms/B0。使其成为轴向 HGMS 中一种很有前途的矩阵。提出了一个经验公式来确定最佳纵横比，估计椭圆和菱形矩阵的最佳纵横比约为0.75‧Ms/B0。使其成为轴向 HGMS 中一种很有前途的矩阵。提出了一个经验公式来确定最佳纵横比，估计椭圆和菱形矩阵的最佳纵横比约为0.75‧Ms/B0。