Yield stress in magnetorheological suspensions near the limit of maximum-packing fraction
Different model geometries used for stress calculations in MR fluids. The microscopic affine model [Ginder et al. (1996)] supposes affine displacement of particles with shear (a). Arrows denote displacement vectors of particles. The stress arises from the restoring interparticle force Fx . If a given particle leaves its equilibrium position [dashed sphere in (a)], it will be immediately stacked on top of the closest particle, showing that the structure is mechanically unstable. The macroscopic thermodynamic model [Bossis et al. (1997)] assumes formation of thick columns and ignores arrangement of particles within them (b). The stress comes from the restoring magnetic torque denoted by a bold arrow. A more realistic structure combines the features of both previous ones. Under strain, some particles experience affine motion, creating gaps between them, and the others are drawn into these gaps, maintaining the mechanical contacts with neighboring particles. One of the simplest structures corresponding to this picture is the BCT cluster shown in (c), which is found to be the most favorable for the energetic point of view [Tao and Sun (1991); Clercx and Bossis (1993); Tao and Jiang (1998)]. The stress response of such structure arises from both the longitudinal striction (due to the formation of gaps) and the restoring magnetic torque.
Longitudinal, , and transverse, , components of the magnetic permeability tensor of a suspension consisting of Fe-CC particles dispersed in mineral oil (volume concentration 50%) as function of the applied shear strain.
Theoretical stress-strain curve for a suspension consisting of Fe-CC particles dispersed in mineral oil (volume concentration 50%). The applied magnetic field is H 0 = 18.5 kA/m.
Experimental and theoretical dependencies of the yield stress increment, , on the magnetic field intensity, H 0, for a suspension containing 50 vol.% of Fe-CC in mineral oil. The inset shows the field dependency of the yield stress, , without subtraction of the value at zero field, . Full squares stand for the experimental data and the solid curve for the theoretical prediction—Eq. (10), replacing γ by γ cr ≈ 0.115. The dashed line represents the best fit of the experimental data to a power law ()—the exponent of this best fit is 1.91 ± 0.07.
Elementary cell of the MR suspension used for the calculation of the longitudinal magnetic permeability, . The surface plot of the magnetic flux density and the magnetic field lines are shown. The red (darkest in the printed version) spots near the contacts between particles correspond to the regions of high magnetic flux density in the vicinity of the contact points between spheres.
Elementary cell of the MR suspension used for the calculation of the transverse magnetic permeability, . The surface plot of the magnetic flux density and the magnetic field lines are shown.
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