Figure 1

(Color online) Shear stress vs apparent deformation in Couette flows under constant apparent shear rate $\left(1.5{\text{s}}^{-1}\right)$ with the bentonite suspension after different times of rest: (from bottom to top) 3, 10, 20, 30, and 60 min. The Couette geometry and the rheometer were described in [5, 17]. The apparent deformation and shear rate were computed from the ratio of the relative motion of the tools to the gap. Inset: same data scaled by a stress factor (see values in Fig. 8) depending on the time of rest.Reuse & Permissions

Figure 2

$T_2$ as a function of solid volume fraction for a bentonite suspension (different from that used for all the other tests in this paper). The continuous line is a fit of Eq. (6).Reuse & Permissions

Figure 3

Benchmark test for NMR CPMG measurements of spin-spin relaxation. Relaxation curves obtained on the same bentonite sample for refocusing times of 1, 2, 4, and 8 ms, respectively.Reuse & Permissions

Figure 4

(Color online) Typical velocity fields (given as the magnitude) during steady-state extrusion flows with different fluid types, with the velocity scaled by the piston velocity (0.2 mm/s). MRI measurements: (a) bentonite suspension, just after mixing; (b) bentonite suspension, after a long time of rest (18 h); (c) a Carbopol gel (see [28]), simple yield stress fluid; (d) a kaolin (clay) suspension in water, simple yield stress with possible solid migration leading to increase in the solid fraction in the dead zones. Our focus on the moderate velocities of the upper zone leads to signal loss in the high velocity regions near the die entrance, making the velocities measured inside the die, if present, irrelevant. Commercial software flow-3D simulations (see [28]): (e) simple yield stress fluid represented by a “biviscous” model (high viscosity below a critical shear rate), (f) simple yield stress fluid represented by a model including a true viscoelastic solid regime up to a critical deformation and a liquid regime behavior beyond this deformation, and (g) Newtonian fluid. Note that for the Newtonian fluid, in this dimensionless representation the velocity field is independent of the fluid viscosity. For the yield stress fluids the velocity field is almost constant for a Bingham number in the range 0.1–10 (the Bingham number is the ratio of the yield stress to the additional viscous part of the shear stress).Reuse & Permissions

Figure 5

(Color online) $T_2$-weighted images: (a) when the piston is far from the die and (b) when the piston is close to the die and after a flow following a rest of 18 h. The echo time allows optimal observation of $T_2$ variations. Dark (pink online) regions and image distortion at the very top and bottom of the pictures correspond to the edge of the imaging zone and should be disregarded. The image contrast here has been enhanced to highlight the 10% signal difference between the corners and the rest of the sample. Note that these are typical images extracted from a series of experiments with a similar procedure for setup and flow but with different timings for getting the MRI data and different sets of NMR coefficients but leading to consistent data. We finally obtained a quite consistent series of pictures from which we chose to present two typical ones. (c) Quantitative display of the evolution of signal intensity in the lower left corner of (b), as averaged along the indicated thick beam. Labels 1, 2, and 3 on the graphic correspond to labels 1, 2, and 3 on the beam. The vertical dashed line in the graphic corresponds to the dotted line drawn inside the beam and approximately indicates the boundary between dark (pink online) and light (yellow online) zones in (b). Horizontal dashed lines are a guide for the eyes and show a $10–15\mathrm{\%}$ relative step in signal intensity at the boundary.Reuse & Permissions

Figure 6

Average flow profile of the vertical $\left(z\right)$ velocity component vs the radial direction $\left(x\right)$ in the two top centimeters of the flow data displayed in Figs. 4a, 4b. Velocity values were scaled by their average value. For each curve, oscillations are on the same order of magnitude as those expected from the limited signal-to-noise ratio: (dotted line) just after mixing; (continuous line) after a 18 h rest.Reuse & Permissions

Figure 7

(Color online) $T_2$ CPMG NMR signal decay (scaled by the value measured at the initial time) of a bentonite suspension $\left(\varphi =5\mathrm{\%}\right)$ as a function of time. The curves are obtained for different times of rest after premixing. From bottom to top: from 0 to 1 h (black squares) and after 72 h at rest followed by a strong mixing (stars), after 8 h rest without mixing (light squares, green online), 16 h (light, blue online), 72 h (light squares, pink online). The continuous line shows an example of model fitting [Eq. (9)Reuse & Permissions

Figure 8

Two scenarios possibly explaining the long relaxing tail in CPMG experiments: (a) spontaneous pore opening in the paste (unlikely) and (b) creation of cages between clay platelets, free of any paramagnetic impurity.Reuse & Permissions

Figure 9

(Color online) The experimental steady-state flow field in the upper zone and left side of an 8:1 contraction with an imposed piston velocity of $200\mu \text{m}/\text{s}$ displaying the corresponding vector field of the lower left corner: (a) for a simple yield stress fluid (Carbopol gel [28]) and (b) for a bentonite suspension. The dotted elliptical line focuses on the same specific zone.Reuse & Permissions

Figure 10

(Color online) Force vs apparent deformation (see text) for squeeze flows (at a velocity of mm/s) with the bentonite suspension after different times of rest: (from bottom to top) 0, 3, 10, 20, 30, 60, 90, and 180 min. Inset: same data with the force scaled by a factor (see values in the main panel) depending on the time of rest.Reuse & Permissions

Figure 11

Scaling factors as a function of time of rest. Squeeze flow: factor used to rescale the curves of Fig. 10 and obtain the master curve in the inset (using a factor of 1 for 3 min of rest). Simple shear: same approach for obtaining the master curve in the inset of Fig. 1. Elastic modulus: ratio of the elastic modulus to its value after 3 min of rest.Reuse & Permissions

Figure 12

(Color online) Shear stress vs apparent deformation for creep tests described in Fig. 1, but for different apparent shear rates (after a time of rest of 10 min following preshear): (from bottom to top) 0.045, 0.15, 0.45, 1.5, and 4.5 1/s. Insets: (top right) same data scaled vertically and horizontally by the same factor depending on the time of rest; (top left) force factor as a function of the shear rate (squares), as a function of the vertical velocity (in mm) for the squeeze tests shown in Fig. 11 (circles); (bottom) conceptual view of the destructuration process, depending only on the imposed deformation and relying on breakage and deformation of flocs.Reuse & Permissions

Figure 13

(Color online) Apparent shear stress vs apparent deformation for squeeze tests described in Fig. 4 for a time of rest of 10 min, but for different vertical velocities: (from bottom to top) 0.01, 0.1, and 1 mm/s. Insets: (top) same data scaled vertically and horizontally by the same factor depending on the time of rest. Here, we computed the apparent shear stress from the vertical force via $\tau =3Fh/2\pi R^3$, in which $R$ is the current radius of the squeezed layer; this relation is derived from the usual expression for the critical squeezing force under the lubrication assumption [2].Reuse & Permissions

Figure 14

1D model for localized relaxation eigenmodes in a water layer surrounding the bentonite clay. The bold curve shows the approximate shape of the fundamental relaxation mode involved in CPMG measurements.Reuse & Permissions