Magnetic interaction between magnetic particles is of great significance in the fields of magnetic separation and functional materials. A good understanding of interaction mechanism of magnetic particles would further boost its promising industrial applications. We hereby present our work which visualizes the movement behavior of magnetic spheres in magnetic fields employing high-speed imaging and simulates the dynamic behavior of spheres using an Arbitrary Lagrangian-Eulerian (ALE) based on finite element method. In this paper, we investigated the stress tensor, magnetic force, and dynamic behavior of magnetic spheres in magnetic fields, especially magnetic energy density in different domains. Results show that there are four relatively independent regions of magnetic energy density distribution in external spatial domains of a single sphere system. Attractive force will generate when the energy density in the spatial region between two spheres is relatively high, while a repulsive force will generate when the energy density in the spatial region between two spheres is relatively low. Every magnetic sphere spontaneously moves towards the region with high energy density and stays away from the region with low energy density. The total magnetic energy in magnetic spheres’ domains (V₁) and external spatial domains (V₂) increases, but the magnetic energy in the external spatial domain decreases over time during the aggregation process. The magnetic spheres ultimately arrange in chain-like structures oriented along magnetic field direction. We hereby proposed a novel and efficient approach to predict the movement trends and final state of magnetic particle swarm from the view of energy density.

磁性颗粒之间的磁相互作用在磁分离和功能材料领域具有重要意义。深入了解磁性粒子的相互作用机制将进一步促进其有前途的工业应用。我们在此介绍我们的工作，该工作使用高速成像可视化磁场中磁球的运动行为，并使用基于有限元方法的任意拉格朗日-欧拉 (ALE) 模拟球体的动态行为。在本文中，我们研究了磁场中磁球的应力张量、磁力和动态行为，特别是不同域的磁能密度。结果表明，在单个球体系统的外部空间域中存在四个相对独立的磁能密度分布区域。当两个球体之间的空间区域的能量密度较高时会产生吸引力，而当两个球体之间的空间区域的能量密度较低时会产生排斥力。每个磁球自发地向能量密度高的区域移动，远离能量密度低的区域。磁球域中的总磁能（每个磁球自发地向能量密度高的区域移动，远离能量密度低的区域。磁球域中的总磁能（每个磁球自发地向能量密度高的区域移动，远离能量密度低的区域。磁球域中的总磁能（V ₁ )和外部空间域( V ₂ )增加，但外部空间域的磁能在聚集过程中随时间减少。磁球最终排列成沿磁场方向定向的链状结构。我们在此提出了一种新颖有效的方法来从能量密度的角度预测磁粒子群的运动趋势和最终状态。