Dilatant slurries

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 apparent viscosity, / app, is equal to the slope of a line from the origin to a point on the shear stress-shear rate curve it decreases or increases as the shear rate increases. Hence, the term viscosity for a non-Newtonian fluid has no meaning unless the shear rate is specified. In shear-thinning (or pseudoplastic) slurries, the apparent viscosity decreases as the shear rate increases and the value for n is less than one. In shear-thickening (or dilatant) slurries the apparent viscosity increases as the shear rate increases and the value of n is greater than 1 (Figure 4.2). 

When starch is added to cold water (below 29°C, 85°F), only negligible swelling will occur. However, the suspension volume expands, since the insoluble starch replaces water. Addition of starch to water at a concentration of 10% will increase the volume by 13%. The maximum in suspension solids is 40-45%. Various methods are used to determine the solids content of the starch slurry aerometer,92 density cells, densitometer, attenuation of vibration (Dynatrol) or a radiation-type density meter. Concentrated starch slurries have high viscosity and shear thickening (dilatent) rheology. Settling of starch from the slurry produces densely packed sediments that are difficult to disperse. 

Naphthali-Sandholm method, 404 dgorithm flowsketch, 411 Nitric acid reactor, 576 Nitrogen fixation, 574,578,588 Nitrotoluene isomers separation, 544 Noncatalytic reactions with solids, 595 Non-Newtonian liquids, 100, 103-109 Bineham. 104.105.107-109 dilatant, 103, 104 laminar flow, 108,109 pressure drop in lines, 106, 109 pseudoplaslic, 103, 104 rheopectic, 104,105 slurries, 71 thixotropic, 104-106 viscoelastic, 105, 106 Notation, 672 NPSH, pumps, 133,146 centrifugal pumps, 146 positive displacement pumps, 134, 135 various pumps, 144 NRTL equation, 475... 

Power characteristics for the mixing of non-Newtonian fluids have been determined for various impellers and other critical mixer design variables, using pseudoplastic, dilatant, and Bingham slurries, and polymeric solutions frequently... 

While many process fluids are Newtonian, some are non-Newtonian (as seen in Figure 9.7). For such cases, it is not sufQcient to use a single value for viscosity to determine the impeller Reynolds number. Concentrated slurries are typically non-Newtonian and particle-size dependent. They are frequently shear-thinning. Dilatant behavior seldom occurs. If the system is simply shear thinning, it is usually possible to describe its rheological behavior with a simple power-law relationship ... 

Numerous methods for measuring fluid viscosity exist, for example, capillary tube flow methods (Ostwald viscometer), Zahn cup method, falling sphere methods, vibrational methods, and rotational methods. Rotational viscometers measure the torque required to turn an object immersed or in contact with a fluid this torque is related to the fluid s viscosity. A well-known example of this type of system is the Couette viscometer. However, it should be noted that as some CMP slurries may be non-Newtonian fluids, the viscosity may be a function of the rotation rate (shear rate). An example of this is the dilatant behavior (increasing viscosity unda increasing shear) of precipitated slurries that have symmetrical particles [33]. Furthermore, the CMP polisher can be thought of as a large rotational plate viscometer where shear rates can exceed 10 s and possibly affect changes to the apparoit viscosity. The reader can refer to the comprehensive review of viscosity measurement techniques in the book by Viswanath et aL [34]. 

Lazy Slurry. A dilatant body which remains fluid when still or slowly stirred, but solidifies if stirred rapidly. It comprises about 100 parts of precipitated calcium carbonate (depending on the particle size) 10 parts of 5% ZnNOs 20 parts 5% Calgon 40 parts water. 

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. 

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... 

When that stress is exceeded, the shear rate grows. Further stress leads finally to linear (Newtonian) behaviour. Examples of plastic systems are chocolate, butter, cheese, various spreads and ice cream. In pseudoplastic systems the observed viscosity decreases with an increase in shear stress. An example of a pseudoplastic system is pudding. Dilatant systems resist deformation more than in proportion to the apphed force. The shear rate is growing much faster than that of Newtonian fluids and viscosity increases with an increase in shear stress. At low apphed forces, the system behaves as a Newtonian fluid. Examples of dilatants systems are honey with added dextran and a slurry of wet beach sand. Thixotropic systems become more fluid (they have lower viscosity) with increasing time of an apphed force. If the apphed force ceases to operate, the original viscosity of the system is restored due to a reversible transformation of the sol gel type. Examples of thixotropic systems are mayonnaise, ketchup, whipped and hardened fats, butter and processed cheeses. Rheopectic systems exhibit behaviour opposite to that of thixotropic systems. Their viscosity increases with increasing time of apphed force. An example is whipped egg white. 

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. 

Dilatant Refer to Fig. 4A and B. It is rarer than pseudoplasticity, but it may be observed in fluids containing high levels of deflocculated solids, such as clay slurries and sand/water mixtures we all have observed on the beach that if you press slowly your foot into the sand/water mix it will penetrate, but if you hit it strongly it will resist penetration. This may also be the case of sand/cement mortar. 

Unfortunately, many fluids do not obey Newton s hypothesis. Both dilatant (shearthickening) and pseudoplastic (shear-thinning) fluids have been observed (Figure 14.2). On log-log coordinates, dilatant flow curves have a slope greater than 1 and pseudoplastics have a slope less than 1. Dilatant behavior is somewhat uncommon but has been reported for certain slurries and imphes an increased resistance to flow with intensified shearing. Polymer melts and solutions are invariably pseudoplastic, that is, their resistance to flow decreases with the intensity of shearing. 

When slurries having particles that are either relatively large or have a high ionic charge on their surface (and hence have little tendency to flocculate) settle, the settled bed density approaches about 50 to 70% of the particle density. The bed resuspends only slowly and is not easily deformed rapidly. An example of such a bed is settled sand. In general, such beds may exhibit dilatancy, which means that the bed must expand to be deformed, and the apparent viscosity of the bed increases as the rate of shear increases. Th02 spheres of more than 5 to 10 microns settle to beds of this type. 

In UO3 H2O slurries of concentrations up to several hundred grams per liter, the yield stress is less than 0.1 Ib/ft and the slurries are almost of Newtonian character. A breeding blanket requires Th02 slurries containing 500 to 1500 grams of thorium per liter, and in these concentrations the yield stress varies from 0 to well over 1 Ib/ft, depending in part on the concentration, on the shape and form of the oxide particle, and on the presence or absence of certain additives. Settled beds of both Th02 and UO3 H2O may be either colloidal and plastic, or much more dense, non-colloidal, and apparently dilatant. 

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