Bending and Position Hysteresis of Magnetic Microfibers in Nonuniform Magnetic Fields

Abstract

Magnetic microfibers are fibers that behave as a flexible paramagnetic body, for example, polymer fibers filled with superparamagnetic particles. A cantilevered magnetic microfiber will bend in response to an applied magnetic field. In a nonuniform field, generated for example by a single electromagnet or by a magnetic dipole, a magnetic microfiber displays position hysteresis as the field strength increases and decreases. This paper presents a model for determining stable shapes of a cantilevered magnetic microfiber in a nonuniform magnetic field. The model determines stable shapes by finding local minima of the potential energy using a Rayleigh-Ritz method. The model predicts the position hysteresis behavior observed in magnetic microfibers. Experimental data ware collected using two electromagnets with different geometries. The model simulation and experimental data compare well both qualitatively and quantitatively. The model will be useful for designing actuators based on magnetic microfibers and for characterizing the magnetic properties of fabricated fibers. A rigid bar model is also introduced, which captures the qualitative behavior of the fiber and illustrates the source of the position hysteresis behavior.

Sharpening the surface of magnetic paranematic droplets

“…1b) [13,14] .The formation time of a micron size magnetic cluster can be made comparable or even shorter than that of a commercial printing device. Therefore, the suggested physical principle is of industrial importance and can be used for formation of magnetic fibers [12][13][14] and for printing magnetic droplets [15][16][17][18]. A colloidal suspension of nickel nanorods of 200nm in diameter and 20 μm in length was prepared in ethylene glycol as described in Refs.…”

Preliminary design of a model-based position controller for magnetic microfibers

“…Because the bending of the fiber is continuous along it's length, a complete dynamic model would require continuum dynamics. In [2], a simplified one dimensional static model was found to adequately predict tip location of the fiber. In this paper, the static model is extended to the dynamic case, which will serve as the basis for control design.…”

“…A high bandwidth sensor was developed to measure fiber position, ensuring good estimated of the first and second derivatives. The magnetic torque on the rigid bar at angle θ is the derivative of the magnetic energy of the bar with respect to θ , computed using the magnetic model described in [2]. Therefore, Equation 6 is linear in unknown parameters, so a, b and 3/mL 2 can be determined using least squares.…”

“…The magnetic torque and hence c(θ ) can be computed numerically [2] and the static equilibria can be predicted for various values of coil current u by finding solutions to Equation 4. Figure 2 shows the plot of the solutions of Equation 4 for different coil currents.…”

“…A detailed static model of a cantilevered fiber placed in a nonuniform magnetic field was presented in [2]. The static equilibria of the fiber in a magnetic field for a given coil current are obtained by solving for the fiber shape with the minimum potential energy.…”