Constitutive law from the MRI measurements in the density-matched (closed symbols) suspension which shows a Newtonian behavior and in the mismatched suspension (open symbols) where a yield stress behavior is observed. The continuous line is a Bingham model σ = (3.2 + 5.1 )Pa. The line through the Newtonian behavior gives a slope of unity. Up to the highest strain rates shown here, no particle migration and no sedimentation are observed, i.e., the material remains homogeneous in both the vertical and the radial directions, and thus the volume fractions are the same in both cases, i.e., 60%. The system studied here is 40 μm polystyrene beads suspended in a mixture of water and NaI; the latter allows to tune the density difference.
(a) Shear rate vs time for different applied shear stresses in a mismatched suspension (Δρ = 150 kg/m3). (b) Critical shear rate as a function of the density difference [ Fall et al. (2009) ].
Filling height dependence of the rheological measurements obtained in a Couette geometry with 4.6 mm diameter PMMA beads. (a) Torque as a function of the rotation rate of the Couette cylinder. Different symbols (see the legend) correspond to different filling heights. Lines are fits to a Bingham model of the form T = T 0 + K Ω. (b) Variation of the critical rotation rate Ω c as a function of filling height—here Ω c = T 0/K. The solid line is a linear fit of the form Ω c = (0.12 ± 0.02) H/Rs .
(a) Height dependence of the yield torque T 0. The line is a parabolic fit of the data of the form, as expected from Eq. (7) . In good approximation, T 0 = (0.9 ± 0.1 × 10−3)Nm (H/Rs )2. (b) Effective viscosity of the suspension as a function of the filling height. The solid line is a linear fit of the data of the form K = (7.5 ± 1 × 10−3) Nm s (H/Rs ) as expected from Eq. (8) .
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