The rare earth minerals in Bayan Obo are poor, fine, scattered and variegated, so it is very difficult to achieve efficient separation. Superconducting magnetic separation technology is an efficient separation technology for refractory minerals. In this paper, the magnetic field induced by a matrix in a superconducting magnetic field is studied based on a finite element method and a separate numerical calculation method, and a model for the trajectories of rare earth mineral particles in Bayan Obo is obtained. The matching relationship between the matrix parameters and the capture radius is obtained through model calculation, as is the optimal capture radius and capture efficiency. The results show that the magnetic field gradient and magnetic field force decrease with increasing distance from the surface of the matrix and that the critical distance of the magnetic field induced by the matrix is 1.5 times the diameter of the matrix. The particle capture radius and capture efficiency are inversely proportional to the matrix diameter. When the matrix diameter is 0.06 mm, the capture efficiency is higher than at other diameters. The theoretical capture efficiency of rare earth mineral particles of size 20–38 µm is approximately 98%, but for particles below 10 µm, the capture efficiency is only 30%. The research results provide a quantitative selective capture law for the matrix diameter and particle diameter, which provides theoretical guidance for production practice.
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