Shear rate, slurry rheology

A study, relevant to recirculation behaviour in a RRIM machine, of polyol and polyol slurry rheology at shear rates in the range 0-103 s 1. This study is based on viscometry with modified cone and plate geometry. 

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.

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 power law model is very popular for representing the viscosity of a wide variety of non-Newtonian fluids because of its simplicity and versatility. However, care should be exercised in its application for reliable results, the range of shear stress (or shear rate) expected in the application should not extend beyond the range of the rheological data used to evaluate the model parameters. Both laminar and turbulent pipe flow of highly loaded slurries of line particles, for example, can often be adequately represented by either of these two models, as shown by Darby et al. (1992). 

Pipe Flow. The rheological properties of cement slurries have also been characterized using pipe viscometers (13,15-18). The experimental results show different flow patterns. In some circumstances, relatively large pipe diameters and high shear rates, the flow curves, and shear-stress at the wall versus Newtonian shear rate at the wall are independent of pipe diameter (16, 17). The reverse situation is observed when pipe diameters are relatively small, of the order of 5 mm (13, 15). The diameter dependency of the flow curves can be explained, as discussed... 

Comparison Between Different Viscometers. To validate their rheological measurements, several authors have tried to compare the results obtained using coaxial cylinder and pipe viscometers. Their findings are not necessarily in agreement. Bannister (15) was able to predict the frictional pressure drops of a cement slurry in a 1.815-in. ID pipe from pipe viscometer data corrected for wall slip. Mannheimer, who tried to reconcile coaxial cylinder and pipe viscometer data, both of them being corrected for wall slip was successful with one cement slurry formulation, but the approach failed with another one (13). Denis et al. (16) showed good agreement between coaxial cylinder and pipe viscometer data above a critical shear rate—or shear stress—that is pipe diameter dependent. 

Fluids that follow Newton s law of viscosity, Eqs. (2.4-l)- 2.4-3), are called Newtonian fluids. For a Newtonian fluid, there is a linear relation between the shear stress and the velocity gradient dvjdy (rate of shear). This means that the viscosity /r is a constant and independent of the rate of shear. For non-Newtonian fluids, the relation betweentj, and dvjdy is not linear i.e., the viscosity // does not remain constant but is a function of shear rate. Certain liquids do not obey this simple Newton s law. These are primarily pastes, slurries, high polymers, and emulsions. The science of the flow and deformation of fluids is often called rheology. A discussion of non-Newtonian fluids will not be given here but will be included in Section 3.5. 

At high particle concentrations, slurries are often non-Newtonian. For non-Newtonian fluids, the relationship between the shear stress and shear rate, which describes the rheology of the slurry, is not linear and/or a certain minimum stress is required before flow begins. The power-law, Bingham plastic and Herschel-Bulkley models are various models used to describe the flow behaviour of slurries in which these other types of relationships between the shear stress and shear rate exist. Although less common, some slurries also display time-dependent flow behaviour. In these cases, the shear stress can decrease with time when the shear rate is maintained constant (thixotropic fluid) or can increase with time when the shear rate is maintained constant (rheopectic fluid). Milk is an example of a non-settling slurry which behaves as a thixotropic liquid. 

Rheology in simple layman s terms is the relationship between the shear stress and the shear rate of the slurry under laminar flow conditions. Although this relationship extends to transitional and turbulent flows, most tests are conducted in a laminar regime, often in tubes or between parallel plates. 

Unfortunately, Equation 3-66 is of no value when n< 1.0, which is the case for many power law slurries. It would mean that as the shear rate increases, the effective viscosity decreases to zero. This is contradictory to nature. For power law exponents smaller than 1.0, alternative equipment should be used to measure rheology. 

The Metzner and Reed approach requires the engineer to assume a value of the shear stress at the waU to calculate x. Such assumptions are very difficult to make for engineers outside a research lab. It may be more practical to send samples of the slurry to a rheology lab and to go from plots of yield stress versus weight concentration, as well as from plots of viscosity versus weight concentration and shear rates to a more straightforward computation of friction factors (Figure 5-3). 

For dilutant fluids, n > 1. Rheological dilatancy refers to increasing viscosity with increasing shear rate. Therefore, these fluids are also called shear-thickening. Examples include whipped cream and starch slurries. They are rare in industrial practice. 

The effect of mixing (time and intensity) on the rheology of the pigment slurry is summarized by Robinson et al. (1997). Breakdown of the dispersion agglomerates requires imposition of shear on the slurry. Consequently, the impeller tip speed is critical for disperser operation and mixer design. As the maximum shear rate [ranging from 100 to 10" s in dispersion operations (Makinen, 1999)] determines the ultimate size of the particles, extending the dispersion time cannot compensate for an inadequate shear level. 

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