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TECHNICAL PAPERS

Torque and Bulk Flow of Ferrofluid in an Annular Gap Subjected to a Rotating Magnetic Field

[+] Author and Article Information
Arlex Chaves, Fernando Gutman

Department of Chemical Engineering,  University of Puerto Rico, Mayagüez, P.O. Box 9046, Mayagüez, PR 00681

Carlos Rinaldi1

Department of Chemical Engineering,  University of Puerto Rico, Mayagüez, P.O. Box 9046, Mayagüez, PR 00681crinaldi@uprm.edu

1

Author to whom correspondence should be addressed.

J. Fluids Eng 129(4), 412-422 (Nov 29, 2006) (11 pages) doi:10.1115/1.2567918 History: Received July 31, 2006; Revised November 29, 2006

We report analysis and measurements of the torque and flow of a ferrofluid in a cylindrical annulus subjected to a rotating magnetic field perpendicular to the cylinder axis. The presence of the inner cylinder results in a nonuniform magnetic field in the annulus. An asymptotic analysis of the ferrohydrodynamic torque and flow assuming linear magnetization and neglecting the effect of couple stresses indicated that the torque should have a linear dependence on field frequency and quadratic dependence on field amplitude. To the order of approximation of the analysis, no bulk flow is expected in the annular gap between stationary cylinders. Experiments measured the torque required to restrain a polycarbonate spindle surrounded by ferrofluid in a cylindrical container and subjected to the rotating magnetic field generated by a two-pole magnetic induction motor stator, as a function of the applied field amplitude and frequency, and for various values of the geometric aspect ratios of the problem. The ultrasound velocity profile method was used to measure the azimuthal and axial velocity profiles in the ferrofluid contained in the annular gap of the apparatus. Flow measurements show the existence of a bulk azimuthal ferrofluid flow between stationary coaxial cylinders with a negligible axial velocity component. The fluid was found to corotate with the applied magnetic field. Both the torque and flow measurements showed power-of-one dependence on frequency and amplitude of the applied magnetic field. This analysis and these experiments indicate that the action of antisymmetric stresses is responsible for the torque measured on the inner cylinder, whereas the effect of body couples is likely responsible for bulk motion of the ferrofluid.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Magnetization curve for the water-based ferrofluid (Ferrotec EMG 705). The inset shows the low field response of the ferrofluid.

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Figure 2

TEM image of magnetite nanoparticles in the water-based ferrofluid (Ferrotec EMG 705)

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Figure 3

Torque required to restrain the spindle from rotating when surrounded by ferrofluid filling the annular space between the spindle and outer container, as a function of magnetic-field amplitude and frequency, and for radial aspect ratios of (a) γ1=0.32 and (b) γ2=0.52

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Figure 4

Sketch of experimental geometry used to obtain the relation between parallel and azimuthal velocity components in a cylindrical container, assuming there is no radial flow

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Figure 5

Illustration of the experimental setup for measuring torques and velocity profiles of ferrofluids filling an annular space and subjected to a rotating magnetic field. Left: Annular container with ultrasonic transducers located inside a two-pole induction motor stator. Right: Top view showing transducers at different incident angles. The transducers are separated from the ferrofluid by a thin polycarbonate wall.

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Figure 6

Velocity profile for ferrofluid filling the annular gap between stationary coaxial cylinders obtained with three transducers at different angles with respect to the diagonal and magnetic field amplitude of 8.3mT rms. The external radius is 24.64mm, and the internal radius is 9.4mm.

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Figure 7

Velocity profiles in the (a) azimuthal direction using fixed transducers placed at four different heights (h=63.5mm) of the container for 60Hz frequency and 8.3mT rms amplitude of the applied magnetic field, and (b) in the axial direction obtained using a transducer placed in the cover of the container in the middle of the annular gap (r=17.2mm). The external radius is 24.64mm, and the internal radius is 9.4mm.

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Figure 8

Velocity profile dependence on (a) magnetic field frequency with constant amplitude of 12.5mT rms and on (b) magnetic field amplitude with constant frequency of 80Hz. In (b), profiles are shown for two distinct inner cylinder radii, with dashed lines added to aid in distinguishing between the two inner and outer radii. In (a) and (b), the external radius is 24.64mm. In (a), the internal radius is 9.4mm.

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Figure 9

Phenomenological model of ferrofluid torque on cylindrical walls in a rotating magnetic field H: (a) Axially directed torque induced by rotation of magnetic nanoparticles and (b) torque produced by viscous shear stress at the spindle due to magnetic field induced flow

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Figure 10

Log-log plot of the complete dimensionless torque data set versus (a) dimensionless frequency from 25Hzto500Hz and (b) dimensionless amplitude of the magnetic field from 0.61mT rms to 17mT rms. A value of τB=2.1×10−6s has been used to calculate the theoretical torque.

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Figure 11

Log-log plot of the scaled azimuthal velocity at r=17.2mm versus dimensionless amplitude of the magnetic field for experiments made with the water-based ferrofluid (with ϕ=0.039) and an internal cylinder radius of Ri=9.4mm. A value of τB=2.1×10−6s has been used to calculate the dimensionless velocity.

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