Basic operational modes for controllable MR fluid devices. Adapted from A. G. Olabi and A. Grunwald, Mater. Des. 28, 2658 (2007). Copyright ©2007, with permission from Elsevier.
Schematic diagram of the constant volume squeeze flow experiment (not to scale). For simplicity the free surface profile is represented as a vertical line. In a typical experiment and . The largest compressive strain was .
Schematic representation illustrating the standard micromechanical model consisting in a cubic network of single chains.
Schematic representation of the coordinate reference system used in particle-level simulations.
Normal force versus gap distance at various approaching speeds for two Newtonian silicone oils.
Compressive force from Fig. 5 divided by the viscosity and approaching speed as a function of gap distance . Lines correspond to Stefan’s model predictions under no-slip and perfect slip conditions. The experimental error is contained within the symbol size.
Typical normal force versus compressive strain curves of MR fluids at different magnetic field strengths ( MR fluid, ).
Comparison between yield compressive stresses and yield shear stresses for MR fluids. For the calculation of the compressive stress we have assumed an initial radius of . For completeness we also show results for dynamic yield shear stresses obtained by extrapolation in lin-lin representations of shear stress versus shear rate at large deformations (Bossis et al., 2002).
Dimensionless normal force as a function of compressive strain for different magnetic fields. Blue dashed line corresponds to Eq. (14); . Black solid line corresponds to Eq. (9); . Red dotted line corresponds to the expression . Red stars represent particle-level simulation results.
Strain dependence of the shear viscoelastic moduli for different magnetic field strengths. (a) Storage and loss moduli as functions of compressive strain. Closed symbol, ; open symbol, . (b) Normalized storage and loss moduli as functions of strain. Dashed line corresponds to .
Evolution of the magnetic energy normalized with the number of particles in the absence of flow for five different replicates; .
Side view snapshots of 3D simulations squeezed at (a) , (b) , (c) , and (d) ; , .
Average magnetic energy normalized with the number of particles as function of the compressive strain. The periodic fluctuation of the normal force shown in the inset is associated to macroscopic rearrangements.
Evolution of the number of percolating clusters, , as a function of the compressive strain. The number of percolating clusters is strongly dependent on the connectivity criterion employed and roughly increases linearly with the strain. The red solid line is a linear fit with slope and correlation coefficient .
parameter as a function of the normalized normal force. The red solid line is a linear fit with slope and correlation coefficient . Inset corresponds to the correlation between (black squares) and (red open circles) versus the compressive strain dependence.
Fitting parameter for normal force-compressive strain curves reported in Fig. 7 according to . corresponds to macroscopic model predictions [Eq. (9)] using the static yield shear stress as an input. In these calculations we assumed as visually determined. corresponds to the indentation depth calculated by fitting Eq. (14) to the experimental values. In these calculations we have taken and which correspond to typical values for pure iron.
Suspension relative magnetic permeability and magnetic contrast factor calculated using Maxwell–Garnett and Fröhlich–Kennelly equations (Jiles, 1991).
Fitting parameters and for normal force-compressive strain curves reported in Fig. 7 in accordance with . The approaching speed is . The strain fitting range is .
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