Simulation of magnetophoresis of magnetic nanoparticles in liquids

Magnetophoresis, which is known as a process of driving magnetic particles to depart from the dispersion in the presence of an external inhomogeneous magnetic field, has gained substantial investigations due to its significance in various fields. The main objective of this paper is to analyze the magnetophoretic mechanism of magnetic nanoparticles in fluids with a Lagrangian approach. The equivalent current source method is used to calculate the magnetic field of a cylindrical permanent magnet, which provides a feasible way to simulate the magnetophoresis process. Then the magnetophoretic velocity of particles and the influence of various key factors, e.g. the dimension of a cylindrical permanent magnet, the saturation magnetization of particles and the viscosity of fluid, are investigated. Furthermore, an efficient algorithm is proposed to calculate the trajectory of particles, and to describe the capture efficiency of the particles and the distribution of the captured particles at different times. In addition, the applicability of the Lagrangian approach is also discussed.