Figure 5.13 – Reproduced from Irani et al.(2014) [4]. Shear stressτ as a function of the strain rate ˙γ for a system size N = 103: (a) for different attraction strengths uatφ = 0.82; (b) for different packing fractions (from the bottom to the top)φ = 0.75, 0.78, 0.80, 0.82, 0.83, 0.84, 0.843, 0.85, 0.9, 0.95, 1.0 for the attraction strengthu= 2x10−4.
Finally, one perspective of our work would be to verify if the shear bands observed in the attractive system (pure calcite with NaOH) are stationary (i.e. permanent in time). To do so it is necessary to monitor the velocity profiles on much longer times. One difficulty encountered is that the mechanical properties of the calcite paste (with NaOH) start to change with large deformations. For example the storage modulus is multiplied by a factor 3 if sheared at ˙γ=400s−1 instead of ˙γ=100s−1, even for a few seconds. It is then difficult to separate the impact of interactions forces from that of flow history on the mechanical properties and the velocity profiles.
5.4 Other investigated systems
As mentioned at the beginning of this chapter, we have studied the effects of other additives on the local rheology of calcite paste. As specified in Table 5.1, we also add to calcite paste 100 mM of hydrochloric acid (HCl), or calcium hydroxide (Ca(OH)2) at two concentrations: 30 and 50 mM. These two systems present a strong evolution of their mechanical properties with time, as already shown for the calcium hydroxide in the previous chapter. The study of the temporal evolution of the elastic modulus for the sample containing HCl is described in the Annex B. In this section we show the preliminary results on flow for these two complex systems.
Concerning the calcite paste with HCl, Figure 5.14 displays the time averaged velocity map together with the velocity profiles for a sample atφ=10%. Both profiles are acquired at ˙γ=20 s−1: Figure 5.14 (a) during the increasing ramp and Figure 5.14 (b) in the decreasing ramp. The complete shear rate ramp imposed to this sample is ˙γ =10,20,50,100,200,400,200,100,50,20,10 s−1. Figure 5.14 (a) shows a homogeneous behavior, Figure 5.14 (b) instead displays shear banding with a high wall slip at the rotor (r=0). The evolution between the two profiles is very strong, even if they are acquired only 45 min apart. In this interval of time, the storage modulus strongly evolves too by almost one order of
(a) (b)
Figure 5.14 –Time-averaged velocity maps and the corresponding velocity profile (averaged overz) for a sample with 100 mM of HCl atφ=10%. The color bar represents the velocity in mm/s. Comparison between the ascending (a) and descending (b) shear rate ramps for ˙γ=20 s−1.
magnitude, i.e. from 3000 to 20000 Pa. Such a strong evolution was not observed for the pure calcite paste or the calcite paste with NaOH. The mechanical evolution of the sample is certainly due to the effects of chemical reactions, i.e. calcite dissolution and precipitation, as also shown in Annex B for the elasticity measurements.
Concerning calcite paste with calcium hydroxide, Figure 5.15 compares the flow curve of pure calcite and calcite with 30 or 50 mM of Ca(OH)2forφ=10%.
Figure 5.15 – Flow curve comparison for pure CaCO3, calcite with 30 and 50 mM of Ca(OH)2. All samples are atφ=10%.
All these flow curves are obtained on fresh pastes tested after the first pre-shear step (2 min). We can notice that, as for the viscoelastic properties, calcium hydroxide makes the samples more fluid (i.e. decreasing both the storage modulus and the viscosity). Moreover also here as in Chapter 4, the
5.4. OTHER INVESTIGATED SYSTEMS 137
30 mM of calcium hydroxide gives a stronger effect compared to the 50 mM for aφ =10% sample, confirming the DLVO calculation. Figure 5.16 shows the time evolution of the flow curves and of the elastic modulus of a calcite sample containing 30 mM of calcium hydroxide atφ =10%. The protocol used in this specific case is composed by two steps: flow measurements with a descending/ascending ramps from ˙γ=400−0.4 s−1 (≈20 min) and a measure of the storage modulus during 30 min. This two steps are repeated several times for ≈7 h. Figure 5.16 (a) shows the flow curvesτ(γ)˙ at different instant while Figure 5.16 (b) shows the storage modulus as a function of time. Due to the evolution of the storage modulus during the 30 min of testing, we plotG at the end of this step as Gend, so once a plateau value is reached. Both quantities, i.e. τ andGend, show a strong increase as a function of time, especially in the first hours.
(a) (b)
Figure 5.16 –(a) Evolution of flow curves in time for a calcite sample with 30 mM of Ca(OH)2 and φ =10%. Between two flow curves, the storage modulus is recorded during 30 min. The value at the end of this step versus time, is displayed in (b).
Moreover, Figure 5.17 shows the time averaged velocity maps and the corresponding velocity pro-files for a calcite sample with 30 mM of calcium hydroxide (φ =10%). The complete shear ramp is displayed (from (a) to (g)) as: ˙γ=10,50,100,400,100,50,10 s−1. During all the increasing ramp, i.e.
10 to 400 s−1, the suspension acts as a Newtonian liquid. The behavior in the decreasing ramp, i.e. 100 to 10 s−1, evolves strongly. The image (g), in fact, shows shear banding and is recorded only 40 min after the first velocity profile.
All the tests made for samples containing calcium hydroxide (both 30 and 50 mM) evidence a strong temporal evolution. This is certainly due to the reactivity of the systems in particular in presence of carbon dioxide, as already discussed in Chapter 4. Nevertheless, the limited quantities of carbon dioxide available in this geometry (Couette with a top lid) also suggests an evolution due to the imposed shear.
The complexity of these systems, more precisely the temporal evolution of their mechanical proper-ties, prompted us to only analyze the stable ones: pure calcite and calcite with NaOH, presented above.
An other perspective of this work would be to study more systematically these more complex system, in order to distinguish the contribution of the reactivity or aging from the contribution of the imposed shear. This could be done by testing a sample after 10-20 h in the geometry without any shear.
(a) (b) (c) (d)
(e) (f) (g)
Figure 5.17 –Time-averaged velocity maps and the correspondent spatio-temporal velocity profile for a φ=10% calcite sample with 30 mM of Ca(OH)2. The color bar represents the velocity in mm/s. (a)-(g) Complete shear rate ramp as ˙γ=10,50,100,400,100,50,10 s−1.