The Discretized Motion of an Anisotropic Magnetic Particle under a Non-Uniform AC Magnetic Field*

An anisotropic magnetic particle or cluster near a surface in liquid can perform a translational motion under a non-uniform alternating magnetic field. Unlike a permanent magnet pulling a magnetic particle, the particle moves away from the magnetic source. The moving speed can be tuned by varying the magnetic field strength and gradient, its alternating frequency, and the particle size, magnetic moment and its orientation. When the orientation of the magnetic moment of the particle changes 90^o, the motion of the particle evolves from rolling to precession, then to tumbling. Systematic investigations on the translational velocity versus the magnitude and frequency of the applied magnetic field show that the overall motion of the particle can be divided into four different zones: Brownian motion zone, synchronized zone, asynchronized zone, and oscillation zone. High speed movies reveal that both the tumbling and precession motions of the particles have a discretized nature. An intrinsic quality factor q for the motion of a magnetically driven particle is defined, and based on the nature of the discretized motion, an analytic expression for q is found to be determined by the shape of the particle, the hydrodynamics near a wall, and the magnetic properties of the particle.