Theoretical Analysis of the Field and Force for Magnetic Bead-Based Transport Under a Localized Elliptical Cylinder Magnet

Precise control of micrometer-scale particles or cells is crucial for biomedical diagnosis, gene sequence detection, and intercellular communication analysis. Among these, the magnetophoretic circuit-based method offers a novel approach to achieving high-precision capture and separation of particles with small size differences. This method utilizes the high magnetic field gradient generated by magnetized soft magnets, combined with a rotating magnetic field to apply driving torque, enabling precise control of the motion of magnetic microspheres or cells labeled with magnetic microspheres. Currently, the majority of magnetophoresis circuits focus on elliptical micro-magnet arrays, and finite element methods (FEM) are generally adopted to determine the distribution of spatial magnetic potential energy. However, the accuracy of FEM is highly dependent on the accuracy of the mesh sizes, and it lacks the capability for inverse optimization of the magnetophoresis circuits in terms of its iteration. To address this limitation, this paper proposes an analytical method based on the equivalent magnetic charge method (EMC) to accurately analyze the field and force involved in magnetic bead-based transport. This analysis covers cases of localized elliptic cylindrical magnets with arbitrary magnetization directions and geometrical shapes. This method is independent of mesh size and computational area, making it suitable for high-precision calculations. It also significantly reduces computational time, enhancing efficiency. When the rotation frequency of the external magnetic field is sufficiently low, the magnetic bead consistently moves toward the location of minimum magnetic potential energy. This observation further illustrates that the high accuracy of field and force analysis in magnetic bead-based transport provides a robust theoretical foundation for optimizing magnetophoretic circuits and enhancing control over individual beads and cells.