Pseudoplastic materials

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. 

Axial-flow turbines are often used in blendiug pseudoplastic materials, and they are often used at relatively large D/T ratios, from 0.5 to 0.7, to adequately provide shear rate in the majority of the batch particularly in pseudoplastic material. These impellers develop a flow pattern which may or may not encompass an entire tank, and these areas of motion are sometimes referred to as caverns. Several papers describe the size of these caverns relative to various types of mixing phenomena. An effec tive procedure for the blending of pseudoplastic fluids is given in Oldshue (op. cit.). 

The narrow molecular weight distribution means that the melts are more Newtonian (see Section 8.2.5) and therefore have a higher melt viscosity at high shear rates than a more pseudoplastic material of similar molecular dimensions. In turn this may require more powerful extruders. They are also more subject to melt irregularities such as sharkskin and melt fracture. This is one of the factors that has led to current interest in metallocene-polymerised polypropylenes with a bimodal molecular weight distribution. 

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. 

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)] ... 

Figure 6.1 Plot of shear stress versus shear rate for plastic and pseudoplastic materials. This is shown as (a) a linear-linear plot and (b) a log-log plot...

The application of a shear rate to a linear viscoelastic liquid will cause the material to flow. The same will happen to a pseudoplastic material and to a plastic material once the yield stress has been exceeded. The stress that would result from the application of the shear rate would not necessarily be achieved instantaneously. The molecules or particles will undergo spatial rearrangements in an attempt to follow the applied flow field. 

The non-linear response of plastic materials is more challenging in many respects than pseudoplastic materials. While some yield phenomena, such as that seen in clay dispersions of montmorillonite, can be catastrophic in nature and recover very rapidly, others such as polymer particle blends can yield slowly. Not all clay structures catastrophically thin. Clay platelets forming an elastic structure can be deformed by a finite strain such that they align with the deforming field. When the strain... 

Polymer rheology can respond nonllnearly to shear rates, as shown in Fig. 3.4. As discussed above, a Newtonian material has a linear relationship between shear stress and shear rate, and the slope of the response Is the shear viscosity. Many polymers at very low shear rates approach a Newtonian response. As the shear rate is increased most commercial polymers have a decrease in the rate of stress increase. That is, the extension of the shear stress function tends to have a lower local slope as the shear rate is increased. This Is an example of a pseudoplastic material, also known as a shear-thinning material. Pseudoplastic materials show a decrease in shear viscosity as the shear rate increases. Dilatant materials Increase in shear viscosity as the shear rate increases. Finally, a Bingham plastic requires an initial shear stress, to, before it will flow, and then it reacts to shear rate in the same manner as a Newtonian polymer. It thus appears as an elastic material until it begins to flow and then responds like a viscous fluid. All of these viscous responses may be observed when dealing with commercial and experimental polymers. 

The second model used to correct the shear rate for pseudoplastic materials is shown by Eq. 3.37 ... 

Since the shear-stress-shear-rate properties of pseudoplastic materials are defined as independent of time of shear (at constant temperature), the alignment or decrease in particle size occurring when the shear rate is increased must be instantaneous. However, perfect instantaneousness is not always likely if the foregoing causes of pseudoplastic behavior are correct, as they are believed to be. Pseudoplastic fluids are therefore sometimes considered to be those materials for which the time dependency of properties is very small and may be neglected in most applications. 

The opposite conclusion would presumably apply to dilatant fluids and for these the pressure drop in a rough pipe may perhaps exceed that for a Newtonian fluid. A similar situation might also arise for Bingham-plastic and pseudoplastic materials which exhibit elastic recovery to a high degree. 

Decreases in concentration or increases in temperature usually decrease the consistency indexes K and K but leave the flow-behavior indexes n and n relatively unaltered. The latter appear to be determined primarily by the components of the non-Newtonian fluid and increase only slightly with increases in temperatures or decreases in concentration for pseudoplastic materials. 

Probably the most widely used type of viscometer in the food industry is the Brookfield rotational viscometer. An example of this instrument s application to a non-Newtonian food product is given in the work of Sarava-cos and Moyer (1967) on fruit purees. Viscometer scale readings were plotted against rotational speed on a logarithmic scale, and the slope of the straight line obtained was taken as the exponent n in the following equation for pseudoplastic materials ... 

Axial-flow turbines are often used in blending pseudoplastic materials, and they are often used at relatively large D/T ratios, from 0.5 to 0.7, to adequately provide shear rate in the majority of the batch particularly in pseudoplastic material. These impellers develop a flow... 

To the same family of curves belong pseudoplastic materials. These fluids show a decrease in apparent viscosity with an increase in the rate of shear and are typical of the majority of non-Newtonian liquid food products. The way most often used to describe the properties of these materials is an empirical Ostwald-de Waele power law equation ... 

Figure 4-2. Flow curves for various ideal rheological bodies. A Newtonian liquid. B Pseudoplastic fluid. C Dilatant fluid. D Bingham plastic iii is the yield value). E Pseudoplastic material with a yield value. F Dilatant material with a yield value.

A fluid with a linear flow curve for Ty > ro is called a Bingham plastic fluid and is characterised by a constant plastic viscosity (the slope of the shear stress versus shear rate curve) and a yield stress. On the other hand, a substance possessing a yield stress as well as a non-linear flow curve on linear coordinates (for Xyx > ro ), is called a yield-pseudoplastic material. Figure 1.8 illustrates viscoplastic behaviour as observed in a meat extract and in a polymer solution. 

Some guidelines for the design and selection of valves for pseudoplastic materials have been developed by De Haven [1959] and Beasley [1992]. 

Owing to the inherently different flow fields produced by each class of agitators, it is convenient to consider separately the application of equation (8.24) to equipment of particular forms. Since most of the work related to heat transfer to pseudoplastic materials has been critically reviewed elsewhere [Gluz and Pavlushenko, 1966 Edwards and Wilkinson, 1972 Poggermann et al., 1980 Desplanches et al., 1980], only a selection of widely used correlations is given here. 

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