Trajectory Analysis of Single Magnetic Bead Under Elliptic Cylindrical Magnet and Rotating Field

Abstract

The magnetophoretic circuit-based method offers a novel approach to achieving high-precision capture and separation of magnetic beads or magnetic bead-labelled cells with small size differences for applications in biomedical diagnosis, gene sequence detection, cell separation, and etc. At present, most magnetophoretic circuits use cylindrical magnets or ellipsoidal magnets, which offer limited adjustable geometrical parameters. Additionally, their field distribution is typically calculated based on the finite element method, which is highly dependent on the accuracy of the mesh sizes and can’t be used to predict the trajectory of magnetic beads in magnetophoretic circuit system. Considering that, this paper proposes an analytical method based on the equivalent magnetic charge approach to accurately analyze the magnetic field and force under an elliptical cylindrical magnet and a rotating field. This method is independent of mesh size and computational area, reducing computational time and enhancing efficiency. Moreover, a Lagrangian-Eulerian model is proposed to predict the magnetic bead trajectory under an elliptical cylindrical magnet combined with a rotating magnetic field, taking into account the coupling between the magnetic beads and the fluid. The influence of the magnet geometrical parameters and the rotating field frequency on the single magnetic bead trajectory is also investigated. This work is a proof of concept that we can use the Lagrangian-Eulerian model to analyze the trajectory of magnetic beads under arbitrary-shaped soft-magnetic elements and external rotating field, providing a robust theoretical foundation for optimizing the design of the magnetophoretic circuits and enhancing control over single magnetic bead and bead-labelled cell.

Keywords: elliptical cylinder magnet, magnetophoretic circuits, magnetic bead, equivalent magnetic charge method, Lagrangian-Eulerian model