Interaction of magnetic spheres in magnetic fields from the view of magnetic energy density: A 3D finite element analysis (FEA)

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.