Yield Pseudoplastic Slurries

FIGURE 5-5 Values of the critical value of the Hanks and Ricks Reynolds number versus the flow index n for yield pseudoplastic slurries. 

Slatter [4] defined Rer as the roughness Reynolds number for yield pseudoplastic slurry... 

In most practical cases, oil field cement slurries contain several water-soluble organic additives. Therefore, cement interstitial liquid is an aqueous solution that is likely not to behave as a Newtonian fluid. Specifically, if the organic additives are long-chain polymers, the interstitial fluid will display a pseudoplastic behavior, as described, for instance, by the power law model. In turn, the slurry will display a yield pseudoplastic behavior as described for example by the Herschel-Bulkley model (see previous sections). 

Certain slurries require a minimum level of stress before they can flow. An example is fresh concrete that does not flow unless the angle of the chute exceeds a certain minimum. Such a mixture is said to posses a yield stress magnitude that must be exceeded before that flow can commence. A number of flows such as Bingham plastics, pseudoplastics, yield pseudoplastics, and dilatant are classified as time independent non Newtonian flu ids. The relationship of wall shear stress versus shear rate is of the type shown in Figure 3 9 (a), and the relationship between the apparent viscosity and the shear rate is shown in Figtne 3-9 (b). The apparent viscosity is defined as... 

Equation 3-5 i is known as the Herschel-Buckley equation of yield pseudoplastics and is accepted by most slurry experts to describe the rheology of yield pseudoplastics with... 

The Wilson-Thomas Method was developed in the 1980s for yield pseudoplastic and power law slurries. Wilson (1985) and Thomas and Wilson (1987) assumed that the fluid... 

A behaviour of the dense fine grained slurries in laminar flow regime can be described by Bingham fluid model or the yield pseudoplastic rheological model, respectively... 

For turbulent flow regime of power-law or yield pseudoplastic fluids several models were suggested (e.g. Metzner Reed, Torrance, Ryan Johnson, Hanks), Slatter [2]. Wilson and Thomas developed a new analysis for the turbulent flow of non-Newtonian fluids. They suggest for the mean velocity of the slurry the following expression, Wilson et al [3]... 

Fig. 1 Classes of rheological behavior that can be shown by coal slurries, as they appear when plotted on a shear rate/ shear stress graph. It is desirable for coal slurries to be Bingham plastic or pseudoplastic with yield, as such slurries flow readily at high shear rates (such as during pumping or atomization), while remaining stable against settling at low shear rates because of their yield stress. Dilatant slurries are completely unsuitable for coal slurry applications because they are extremely difficult to pump.

The size distribution of particles will control the amount of liquid needed to fluidize a given quantity of coal. In general, a fine size distribution will produce a more viscous slurry than a coarse size distribution at the same wt% solids, and the fine particles will produce a more non-Newtonian rheological curve. This can be seen in the laboratory results shown in Fig. 3, which compares a coarse coal slurry to a fine coal slurry. It is clearly seen that the fine slurry is much more viscous, its pseudoplastic character is very pronounced, and its yield value is high, while the coarse coal slurry is clearly a Bingham plastic. ... 

Fig. 3 Comparison of the rheological curves for a fine coal slurry (80% passing 34 gm, top size lOOgm, 52wt% solids) and for a coarse coal slurry (58wt% solids). Neither slurry used any additives. Because it is extremely difficult to measure the rheology of unstable slurries with conventional rheometers, these results were obtained using a continuous-pressure-vessel rheometer, which was specially designed for this purpose. The fine coal curve is the average of 10 measurements and the coarse coal curve is the average of 5 measurements, and the standard error of the shear rate measurements was approximately 1.0 Pa for these slurries. The fine coal slurry is clearly pseudoplastic with a yield value of approximately 18 Pa, while the coarse coal slurry is Bingham plastic with an estimated yield value of 4 Pa.

The behaviour of slurries which exhibit a yield stress can be represented by a model in which the relationship between the effective stress t — ty and the shear rate is either linear, as in Newtonian fluids (Bingham plastic model), or follows a power-law, as in pseudoplastic or dilatant fluids (Herschel-Bulkley model or yield power-law model). The shear stress-shear rate relationship for these models is shown in Figure 4.4. 

It is known, however, that settling is enhanced or initiated when the slurry is subjected to an externally imposed strain rate. Early experiments were performed by Highgate and Warlow [3] using spheres in a pseudoplastic fluid that was sheared in the space between coaxial cylinders. As the fluid had no yield stress, the particles settled slowly in the quiescent case. When shear was applied by rotating the outer cylinder, the settling velocity increased reaching five times the initial value at high strain rates. 

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