Pseudoplasticity curve

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. 

Reiner-Philippoff s model (6) is normally used to fit the entire pseudoplastic curve ... 

If the decrease in viscosity is very large at small shear rates, the system is sometimes called pseudoplastic (curves 4 and 5). Commonly, concentrated suspensions show a plastic behavior, that is, there is no response until a limiting yield stress oy has been exceeded. If the flow is linear above oy, the system is called Bingham plastic (curve 4) and can be expressed by the Bingham model (5) ... 

To provide the corneal endothelium with good protection, viscoelastic agents should ideally have high viscosity and elasticity at rest (zero shear rate). Such viscoelastic substances could protect the corneal endothelium from compression forces (Fig. 52). Additionally, the viscoelastic should have a steep pseudoplasticity curve, i.e., a quick viscosity reduction with increasing movement. Shear forces conducted to the corneal endothelium would, in this way, be minimized (Hammer 8c Burch, 1984). 

FIGURE 3.7 The viscosities of simple liquids do not change on increasing the rate of stirring (shear rate), i.e. Newtonian. The viscosities of some polymer solutions decrease when stirred rapidly (pseudoplastic). The pseudoplastic curve is typical of carboxymethyl cellulose solutions (Blanose Hercules) in water. The shear rate is a measure of how fast a force is applied. 

Shear stress-shear rate curves of the latex dispersions (which were fully coated with PVA, i.e. at concentrations corresponding to the plateau of the isotherm) showed Newtonian behaviour below a critical electrolyte concentration, above which the flow curves became pseudoplastic, with some hysteresis (indicating thixotropy). From these pseudoplastic curves, the yield value, xg, was obtained by extrapolating the ascending curve to zero shear rate. 

Since common processing techniques for polymers involve shear rates of about 100-100 000 s there is no substitute for the comprehensive study of shear-stress versus shear rate over the typical processing windows of shear rate and temperature. Clearly, one-point tests such as melt flow index cannot be used as a guide to processability since the shapes of pseudoplastic curves are not identical (Figure 9.9). 

For a non-Newtonian system, as is the case with most food colloids, the stress-shear rate gives a pseudoplastic curve and the system is shear thinning, i.e. the viscosity decreases with increasing sheeu rate. In most cases the shear stress-shear rate curve can be fitted with the Herschel-Bulkley equation. 

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). 

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) ... 

Figure 8.5. Apparent viscosity-shear rate curves for dilatant fluid, a Newtonian fluid and pseudoplastic fluid which have the same apparent viscosity at zero shear rate...

Figure 7.8. Power curve for pseudoplastic fluids agitated by different types of impeller...

The applied force is linearly increased and the results are plotted in a flow-curve. This is a test to attain the yield point of pseudoplastic material. 

Pectins in aqueous solutions show pseudoplastic non-thixotropic behaviour, independent of their degree of methoxylation. Figure 1 shows the viscosity curve of a 2,5 % pectin solution, sheared the preselected shear rate-time function. The viscosity curves for the increasing and decreasing shear rate are superimposed. The pseudoplasticity of pectin solutions decreases with decreasing concentration. 

Many fluids show a decrease in viscosity with increasing shear rate. This behavior is referred to as shear thinning, which means that the resistance of the material to flow decreases and the energy required to sustain flow at high shear rates is reduced. These materials are called pseudoplastic (Fig. 3a and b, curves B). At rest the material forms a network structure, which may be an agglomerate of many molecules attracted to each other or an entangled network of polymer chains. Under shear this structure is broken down, resulting in a shear... 

Plastic fluids are Newtonian or pseudoplastic liquids that exhibit a yield value (Fig. 3a and b, curves C). At rest they behave like a solid due to their interparticle association. The external force has to overcome these attractive forces between the particles and disrupt the structure. Beyond this point, the material changes its behavior from that of a solid to that of a liquid. The viscosity can then either be a constant (ideal Bingham liquid) or a function of the shear rate. In the latter case, the viscosity can initially decrease and then become a constant (real Bingham liquid) or continuously decrease, as in the case of a pseudoplastic liquid (Casson liquid). Plastic flow is often observed in flocculated suspensions. 

The typical viscous behavior for many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels) is illustrated by the curves labeled structural in Figs. 3-5 and 3-6. These fluids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. In some materials this can be attributed to a reversible structure or network that forms in the rest or equilibrium state. When the material is sheared, the structure breaks down, resulting in a shear-dependent (shear thinning) behavior. Some real examples of this type of behavior are shown in Fig. 3-7. These show that structural viscosity behavior is exhibited by fluids as diverse as polymer solutions, blood, latex emulsions, and mud (sediment). Equations (i.e., models) that represent this type of behavior are described below. 

Figure 3 shows plots of p versus shear rate at three different temperatures for the same latex (20% w/w latex A) at full coverage with PVA. These curves are typical of a pseudoplastic system showing a reduction of n with increasing shear rate, 7 p reaches a limiting value at If > 50 s l. It is also clear from fig. 3 that at 7 < 10 s-- -, n increases rapidly with reduction in 7. Comparison with nQ values obtained from the creep curves would indicate the p should increase very steeply with reduction of 7, in the low shear rate region (p is the limit of p as Y+0). °... 

Under conditions of steady fully developed flow, molten polymers are shear thinning over many orders of magnitude of the shear rate. Like many other materials, they exhibit Newtonian behaviour at very low shear rates however, they also have Newtonian behaviour at very high shear rates as shown in Figure 1.20. The term pseudoplastic is used to describe this type of behaviour. Unfortunately, the same term is frequently used for shear thinning behaviour, that is the falling viscosity part of the full curve for a pseudoplastic material. The whole flow curve can be represented by the Cross model [Cross (1965)] ... 

The extrapolated yield stress gives 0.06 Pa and a plastic viscosity of 3.88 mPas. We can use this to estimate the force between the particles, which gives 425kBT/a, in fair agreement with the value determined using pair potential curves. Here the Casson model has been used to partially linearise a pseudoplastic system rather than a system with a true yield stress. 

PPG (at higher temperatures) behaves like a typical pseudoplastic non-Newtonian fluid. The activation energy of the viscosity in dependence of shear rate (284-2846 Hz) and Mn was detected using a capillary rheometer in the temperature range of 150-180°C at 3.0-5.5 kJ/mol (28,900 Da) and 12-13 kJ/mol (117,700 Da) [15]. The temperature-dependent viscosity for a PPG of 46 kDa between 70 and 170°G was also determined by DMA (torsion mode). A master curve was constructed using the time-temperature superposition principle [62] at a reference temperature of 150°G (Fig. 5) (Borchardt and Luinstra, unpublished data). A plateau for G was not observed for this molecular weight. The temperature-dependent shift factors ax were used to determine the Arrhenius activation energy of about 25 kJ/mol (Borchardt and Luinstra, unpublished data). 

An extensive class of non-Newtonian fluids is formed by pseudoplastic fluids whose flow curves obey the so-called power law ... 

These liquids are known as Ostwald-de Waele fluids. Figure 5 depicts a typical course of such a flow curve. Figure 6 shows a dimensionless standardized material function of two pseudoplastic fluids often used in biotechnology. It proves that they behave similarly with respect to viscosity behavior under shear stress. 

Thixotropic Time-dependent pseudoplastic flow. At constant applied shear rate, viscosity decreases. In a flow curve, hysteresis occurs. Paint, quicksand. In bentonite clay gels which liquefy on shaking and solidify on standing, there is a time-dependent aligning to match the induced flow. After the shear rate is reduced it takes some time for the original alignments to be restored. 

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