*3.3.2 Quantification of static and dynamic yield stress*

The static yield stress is retrieved from CSS tests in the VC configuration: the shear stress at the point where the linear part of the ramp-up curve leaves the vertical axis and deflects to the non-linear part (at 45 Pa, **Figure 4b**). At this point, the pronounced wall slip also stops (**Figure 4a**): the shear stress has reached the yield stress of the unsheared material in the middle of the gap. The dynamic yield stress can be obtained from both CSR and CSS methods in the VC configuration: the intercept of the ramp-down curve and the vertical axis. In the BC configuration, the dynamic yield stress is underestimated by a factor 3 (comparing **Figure 4a** and **b**) and the static yield stress by a factor 5.

Here, we see that viscosity plots on the log-log scale are magnifying yielding at low shear rates but are also magnifying artefacts when the material transitions from an elastic state to plastic. Other utilised elements such as grooved bob or parallel plate elements may reveal more.

#### *3.3.3 Slippage with rough/profiled elements*

Utilising rough measuring elements is a well-known remedy to reduce wall slip, but it may not solve the wall slip problem entirely. We experienced that a rough element may only shift the wall slip problem to lower shear rates, as shown in **Figure 5**. Further roughening measures might be necessary to fully eliminate the wall slip.

**Figure 5** shows the rheometry results of three different elements/protocols on the same mud. CSR ramping mode is applied. We see that the BC (blue) starts slipping at about 10 Pa, reaching a maximum shear stress at 40 Pa (end of steep slippage branch), completing a loop and returning finally back to 10 Pa, paralleling with the wall slip of the ramp-up. The vane performs differently; it peaks at 55 Pa and merges

#### **Figure 5.**

*Grooved bob (GBC) rheometry results compared to smooth bob-cup (BC) and vane-in-cup (VC), fluid mud from Beerkanaal, the port of Rotterdam, The Netherlands.*

with the up-ramp of the BC. Upon return, it only bends down a little before cessation of shear. The grooved bob (green) slips at 15 Pa and follows a course between the CSR bob and the CSR vane results. This grooved bob result is positioned similarly with respect to BC in CSS measurements conducted by [11].

#### *3.3.4 Gap variation parallel plate (PP) elements*

A way to investigate wall slip and enable correction (e.g. Mooney transformation) is by conducting a rheometry method using a series of different gaps. This is easily done with a parallel plate (PP) measuring element. **Figure 6** includes such exercise.

This figure illustrates a combination of rheometry data of Shakeel et al. [11] that contributed to their rejection of wall slip, while in contrary revealing wall slip upon closer inspection of the data from the PP element. These data are very similar to a PP measurement presented in Ewoldt et al. (2015) [38] on Nivea lotion. When repeated with sandpaper glued to the plates, their result was similar to our vane result for >1 [1/s].

The PP outputs higher shear stress, calculated at the rim of the element utilising Newtonian fluid theory, than the other elements. In reality, with non-Newtonian shear-thinning fluids, a higher torque is measured for the same shear stress at the rim: the stresses in the centre part of the plates are comparably higher; hence, the

#### **Figure 6.**

*From viscosity plot to flow curve, fluid mud from the port of Hamburg, Germany: a): Data presentation after [11] and b): Transformed into flow curve, including Mooney wall slip correction and comparison with BC and VC.*

#### *Rheology, Rheometry and Wall Slip DOI: http://dx.doi.org/10.5772/intechopen.108048*

outputted calculated shear stress is higher than the true shear stress at the rim, hence a tendency for higher shear stresses.

The shear rate of the vane is calculated as described in Section 3.3.2 and is hence comparable to the BC element: an associated shear rate in a Newtonian fluid. Despite the virtual wider annular gap of the vane, no Couette inverse method has been applied to convert to the actual shear rate in the non-Newtonian fluid. If such correction would have been applied, the steep branch of the vane would have shifted somewhat to the right, in other words to higher shear rates.

Usage of a too small gap size may also play a role, increasing shear stresses because of confinement. Yan et al. (2009) [39] show rheometry results where the yield stress increases for axial gaps smaller than 0.2 mm. It is conjectured that this occurs when the plate distance becomes smaller than the correlation distance of the structure of the fluid. Hence, jamming effects emerge. So, the higher shear stresses for the 1 mm gap, for shear rates <5 [1/s], indicate that the unsheared clay aggregates have a size of 1 to 2 mm.

**Figure 6** shows that the commencement of wall slip with a parallel plate system is postponed with respect to a concentric cylinder. This could be due to non-uniform conditions over the plate's surface, and hence total slip commences when yield stresses are exceeded at most of its surface.

Perfect alignment should not be expected. We applied the Mooney wall slip correction procedure to the PP result of [11], despite that shear stress and slippage velocities are not uniform in a PP element, compromising the basic assumption of the Mooney transformation. Also, the bottom clearance of the vane is smaller than its virtual annular gap. Hence, it is conceivable that data for <0.6 [1/s] is influenced by local failure here.

As we see in **Figure 6**, the Mooney wall slip correction procedure projects data back to lower shear rates, close to vane results. This implies that, practically speaking, a vane is a better element to address the internal strength properties of mixtures in rheometry.
