Schematic representation of the axisymmetric problem solved using FEMM. The computational area is outlined with a dashed line. The magnetic character of the particles was introduced with a relationship given by the Fröhlich–Kennelly equation [Jiles (1991)], with a relative initial magnetic permeability of 40 and a saturation magnetization of 1550 kA/m. The density of iron is assumed to be .
SEM photographs corresponding to (a) magnetite spheres, (b) hematite plates, (c) magnetite rods, (d) iron spheres, (e) iron plates, and (f) iron rods.
Histograms corresponding to spheres, plates, and rods. The solid lines represent a log-normal fit where the mean diameters of the magnetite and the iron particles are found to be and , respectively. stands for the number of particles used for the statistical analysis.
X-ray diffraction spectra of the metal iron particles. Characteristic peaks for pure iron are observed for the three different particles. Lattice planes of iron are indicated in parentheses.
(a) Magnetization curves after zero field cooled and field cooled corresponding to rod-like particles. Temperature: 5 K. Magnetic field: 5 T. (b) Room temperature magnetic hysteresis curve for iron spheres, plates, and rods.
Small-amplitude oscillatory shear magnetosweep curves corresponding to sphere (a) and rod-based (b) MR fluids. Particles with different magnetic properties were investigated at three different volume fractions. Due to lack of instrumental sensitivity, data below 1 Pa usually appeared scattered and as a consequence it is not shown in the figures.
Magnetic field dependence of storage and loss moduli for iron spheres, plates, and rods. (a) 0.5 vol %, (b) 1 vol %, and (c) 5 vol %; squares, ; circles, ; closed symbol, spheres; open symbol, plates; crossed symbol, rods.
Typical ramp-up shear flow curves for plate and rod-based MR fluids at 1 vol %. (a) Rheogram and (b) viscosity curve.
Shear viscosity as a function of Mason number for a wide range of magnetic fields and three different particle shapes. (a) Spheres, (b) plates, and (c) rods. The lines correspond to the theoretical models at low and moderate Mason numbers: black solid line, Martin and Anderson (1996); red dashed line, de Vicente et al. (2004); green dotted line, de Gans et al. (1999); blue dash-dotted line, Volkova et al. (2000).
Slope and intercept values for linear fits to the scaling curves shown in Fig. 9 in the interval range between and . The lines correspond to the theoretical models at low and moderate Mason numbers: black solid line, Martin and Anderson (1996); red dashed line, de Vicente et al. (2004); green dotted line, de Gans et al. (1999); blue dash-dotted line, Volkova et al. (2000).
Effect of particle shape in the static yield stress of MR fluids at different magnetic field strengths. Lines are plotted to guide the eyes.
Initial magnetic hysteresis curves for iron based MR suspensions at 1 vol % up to 1000 kA/m. Magnetization data are normalized by the saturation value for a comparative discussion. Lines are plotted to guide the eyes.
Force acting on a given particle due to particles above (or below), as a function of interparticle gap, for chains of spherical particles and chains of spherocylinders in a uniform external field. This force was calculated using the FEMM software and is presented for three values of the external field that correspond to data points shown in Fig. 11.
Dynamic yield stress as a function of magnetic field obtained by fitting the Bingham equation for low shear rates. Lines are plotted to guide the eyes.
Magnetic properties of synthesized iron particles. Assuming an iron density of , the averaged best fit curve to Fröhlich–Kennelly equation provides an initial relative magnetic permeability of 40 and a saturation magnetization of 1550 kA/m.
Onset of the viscosity increase at high shear observed in rheograms like those shown in Fig. 8.
Suspension relative magnetic permeability and magnetic contrast factor corresponding to the three samples investigated. These values are considered in the calculation of the Mason number for the scaling under steady shear flow.
Slopes corresponding to linear fits for static and dynamic yield stresses as a function of the magnetic field strength from Figs. 11 and 14, respectively.
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