Pseudoplastic region

Continuing in the pseudoplastic region it is often found that an upper threshold can be reached beyond which no further reduction in viscosity occurs. The curve then enters a second linear region of proportionality the slope of which is the second Newtonian viscosity. 

Figure 7-5. Generalized flow curve with the first Newtonian region (N), pseudoplastic region (st), second Newtonian region (N2), dilatant region (d), and onset of turbulence or melt break (t).

Without doubt, the most commonly encountered analytical form of the viscosity-shear rate relationship is the power law model (Bird et al, 1960), which describes the pseudoplastic region. The power law model is sometimes called the law of Ostwald and de Waele (Bird et u/., 1960 Reiner, 1960) and is given by the expression ... 

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... 

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. 

Suspensions of fine sohds may have pseudoplastic or plastic-flow properties. When they are in laminar flow in a stirred vessel, motion in remote parts of the vessel where shear rates are low may become negligible or cease completely. To compensate for this behavior of slurries, large-diameter impellers or paddles are used, with (D /Df) > 0.6, where Df is the tank diameter. In some cases, for example, with some anchors, > 0.95 Df. Two or more paddles may be used in deep tanks to avoid stagnant regions in slurries. 

For suspension of rapidly setthng particles, the impeller turbine diameter should be Df/3 to Dfl2. A clearance of less than one-seventh of the fluid depth in the vessel should be used between the lower edge of the turbine blade tips and the vessel bottom. As the viscosity of a suspension increases, the impeller diameter should be increased. This diameter may be increased to 0.6 Df and a second impeller added to avoid stagnant regions in pseudoplastic slurries. Moving the baffles halfway between the impeller periphery and the vessel wall will also help avoid stagnant fluid near the baffles. 

A simple relationship has been shown to exist, however, between much of the data on power consumption with time-independent non-Newtonian liquids and Newtonian liquids in the laminar region. This link, which was first established by Metzner and Otto 1 2 for pseudoplastic liquids, depends on the fact that there appears to be an average angular shear rate y mt, for a mixer which characterises power consumption, and which is directly proportional to the rotational speed of impeller ... 

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). °... 

Measurements of the zero shear viscosity (20 °C) were made with a Bohlin VOR rheometer in the viscometry mode. If a Newtonian region was not found at the lowest measurable shear rates, the samples were characterized with a Bohlin-CS constant stress rheometer, with which it was possible to obtain extremely low shear rates. This approach was especially needed for highly viscous samples exhibiting pseudoplastic behavior on the VOR rheometer. Newtonian regions were found for each sample in this manner, yielding the zero shear viscosities reported. 

Figure 7.14 The change in critical HLB values as a function of added salt concentration, where the salt is either NaCl or Nal. Results were obtained from measurements of particle size, stability, viscosity and emulsion type as a function of HLB for liquid paraffin-in-water emulsions stabilised by Brij 92-Brij 96 mixtures. Data from different experiments showed different critical values hence, on each diagram hatching represents the critical regions while data points actually recorded are shown. Results in (a) show particle size and stability data those in (b) show the HLB at transition from pseudoplastic to Newtonian flow properties (see section 7.3.10) and emulsion type (o/w— w/o) transitions.

Generally large yield stress effects were dominant in the nematic melts, but they were strongly pre-history dependent. A three region flow curve for 15 mol % modified poly(pheny1-1,4-phenylene terephthalate) was probably due to a not completely molten system. Dynamic viscosity measurements showed strong pseudoplastic behaviour. Strain and time dependence phenomena were not observed. 

High-Viscosity Systems All axial-flow impellers become radial flow as Reynolds numbers approach the viscous region. Blending in the transition and low-viscosity system is largely a measure of fluid motion throughout the tank. For close-clearance impellers, the anchor and helical impellers provide blending by having an effective action at the tank wall, which is particularly suitable for pseudoplastic fluids. 

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