Pseudoplastics

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (02.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation (02.6.2) can be used to define an apparent viscosity, happ, at a given shear rate. If q pp decreases witli increasing shear rate, tire dispersion is called shear tliinning (pseudoplastic) if it increases, tliis is known as shear tliickening (dilatant). The latter behaviour is typical of concentrated suspensions. If a finite shear stress has to be applied before tire suspension begins to flow, tliis is known as tire yield stress. The apparent viscosity may also change as a function of time, upon application of a fixed shear rate, related to tire fonnation or breakup of particle networks. Thixotropic dispersions show a decrease in q, pp with time, whereas an increase witli time is called rheopexy. 

Numerous examples of polymer flow models based on generalized Newtonian behaviour are found in non-Newtonian fluid mechanics literature. Using experimental evidence the time-independent generalized Newtonian fluids are divided into three groups. These are Bingham plastics, pseudoplastic fluids and dilatant fluids. 

Pseudoplastic fluids have no yield stress threshold and in these fluids the ratio of shear stress to the rate of shear generally falls continuously and rapidly with increase in the shear rate. Very low and very high shear regions are the exceptions, where the flow curve is almost horizontal (Figure 1.1). 

A common choice of functional relationship between shear viscosity and shear rate, that u.sually gives a good prediction for the shear thinning region in pseudoplastic fluids, is the power law model proposed by de Waele (1923) and Ostwald (1925). This model is written as the following equation... 

Figure l.l Shear thinning behaviour of pseudoplastic fluids... 

Which range should be considered The answer is the region near the origin of a plot like Fig. 2.2 for pseudoplastic materials. The slope of the tangent to a pseudoplastic curve at the origin is called the viscosity at zero rate of shear. Note that this is an extrapolation to a limit rather than an observation at zero shear (which corresponds to no flow). We shall use the symbol to indicate the viscosity of a polymer in the limit of zero shear, since the behavior is Newtonian (subscript N)in this region. 

The design permits different velocity gradients to be considered, so that pseudoplasticity can be investigated if desired. 

Figure 2.5 shows some actual experimental data for versus 7, measured on a sample of polyethylene at 126°C. Note that the data are plotted on log-log coordinates. In spite of the different coordinates. Fig. 2.5 is clearly an example of pseudoplastic behavior as defined in Fig. 2.2. In this and the next several sections, we discuss shear-dependent viscosity. In this section the approach is strictly empirical, and its main application is in correcting viscosities measured...

Polymers display pseudoplasticity, with apparent viscosity decreasing as 7 increases [Eq. (2.30) and Fig. 2.2]. 

The phenomenon under consideration is complicated and the theory developed in the last section is fairly simple-involved, but not really difficult. We have successfully discovered that the transition from Newtonian to pseudoplastic behavior is governed by the product 77, or the relative values of the shear rate and the rate of molecular response. 

Fig. 10. Fluid behavior in simple shear flow where A is Bingham B, pseudoplastic C, Newtonian and D, dilatant.

Pseudoplastic fluids are the most commonly encountered non-Newtonian fluids. Examples are polymeric solutions, some polymer melts, and suspensions of paper pulps. In simple shear flow, the constitutive relation for such fluids is... 

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

The pressure drop accompanying pipe flow of such fluids can be described in terms of a generalized Reynolds number, which for pseudoplastic or dilatant fluids takes the form ... 

The flow properties of sodium alginate solutions depend on concentration. A 2.5% medium viscosity sodium alginate solution is pseudoplastic, especially at the higher shear rates in the range of 10—10,000/s. 

Properties. Xanthan gum is a cream-colored powder that dissolves in either hot or cold water to produce solutions with high viscosity at low concentration. These solutions exhibit pseudoplasticity, ie, the viscosity decreases as the shear rate increases. This decrease is instantaneous and reversible. Solutions, particularly in the presence of small amounts of electrolyte, have exceUent thermal stabiHty, and their viscosity is essentially constant over the range 0 to 80°C. They are not affected by changes in pH ranging from 2 to 10. 

Slurry Viscosity. Viscosities of magnesium hydroxide slurries are determined by the Brookfield Viscometer in which viscosity is measured using various combinations of spindles and spindle speeds, or other common methods of viscometry. Viscosity decreases with increasing rate of shear. Fluids, such as magnesium hydroxide slurry, that exhibit this type of rheological behavior are termed pseudoplastic. The viscosities obtained can be correlated with product or process parameters. Details of viscosity deterrnination for slurries are well covered in the Hterature (85,86). 

Solutions of welan are very viscous and pseudoplastic, ie, shear results in a dramatic reduction in viscosity that immediately returns when shearing is stopped, even at low polymer concentrations (230). They maintain viscosity at elevated temperatures better than xanthan gum at 135°C the viscosity half-life of a 0.4% xanthan gum solution is essentially zero, whereas a welan gum solution has a viscosity half-life of 900 minutes (230). The addition of salt to welan solutions slightly reduces viscosity, but not significantly. It has excellent stabiUty and theological properties in seawater, brine, or 3% KCl solutions... 

Effect of Shear. Concentrated aqueous solutions of poly(ethylene oxide) are pseudoplastic. The degree of pseudoplasticity increases as the molecular weight increases. Therefore, the viscosity of a given aqueous solution is a function of the shear rate used for the measurement. This relationship between viscosity and shear rate for solutions of various molecular weight poly(ethylene oxide) resins is presented in Figure 8. 

Com and rice starches have been oxidized and subsequently cyanoethylated (97). As molecular size decreases due to degradation during oxidation, the degree of cyanoethylation increases. The derivatized starch shows pseudoplastic flow in water dispersion at higher levels of cyanoethylation the flow is thixotropic. Com and rice starches have been oxidized and subsequently carboxymethylated (98). Such derivatives are superior in the production of textile sizes. Potato starch has been oxidized with neutral aqueous bromine and fully chemically (99) and physically (100) characterized. Amylose is more sensitive to bromine oxidation than amylopectin and oxidation causes a decrease in both gelatinization temperature range and gelatinization enthalpy. 

CMC hydrates rapidly and forms clear solutions. Viscosity buUding is the single most important property of CMC. DUute solutions of CMC exhibit stable viscosity because each polymer chain is hydrated, extended, and independent. The sodium carboxylate groups are highly hydrated, and the ceUulose molecule itself is hydrated. The ceUulose molecule is linear, and conversion of it into a polyanion (polycarboxylate) tends to keep it in an extended form by reason of coulombic repulsion. This same coulombic repulsion between the carboxylate anions prevents aggregation of the polymer chains. Solutions of CMC are either pseudoplastic or thixotropic, depending on the type. 

As substituent uniformity is increased, either by choosing appropriate reaction conditions or by reaction to high degrees of substitution, thixotropic behavior decreases. CMCs of DS >1.0 generally exhibit pseudoplastic rather than thixotropic rheology. Pseudoplastic solutions also decrease in viscosity under shear but recover instantaneously after the shear stress is removed. A plot of shear rate versus shear stress does not show a hysteresis loop. 

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