Viscosity shear behaviour

In concentrated suspensions, the particles touch each other. If there is also an attraction between the particles, the suspension may not flow when the shear stress is small it is a solid (Figure C4-14). The stress at which the liquid starts moving is known as the yield stress. Once the liquid yields, it often behaves like a Newtonian liquid with a constant differential viscosity. The behaviour of such Bingham fluids is similar to that of shear thinning fluids ... 

It shoiild be noted that this is the exact derivation of equation (3). These models are usually referred to quasi-linear models and display qualitatively correct predictions of typical phenomena of elongational flows such as the occurrence of the strain-hardening effect in transient extension. Nevertheless the predicted elongational viscosity is never boimded in the long time range and a steady state value can only be expected for small elongation rates. Moreover, the shear behaviour remains unrealistic as compared to the experiment, especially because of constant predicted viscosity and first normal... 

Primary polymer structure may account for some of the viscosity loss behaviour, but VI improvers which function as associative thickeners are a major confounding factor. When the physically associated multi-polymer structures enter a shear field, they can dissociate into their separate molecular species. These smaller individual polymers are low enough in molecular weight that they degrade either slowly or not at all. When the molecules leave the shear field, they associate again so that there is little or no permanent loss of viscosity. However, when in the shear field, the contribution to viscosity is from the smaller, distorted individual molecules. The net result is a system which exhibits a high temporary viscosity loss relative to its low permanent viscosity loss. 

Capillaries of different L/D ratios are employed. Figure 2 and Figure 1 of (13) give -for a synthetic lubricant of the same type and basic viscosity - Newtonian behaviour at about 0.1 MPa. Deviation from constant, shear Independent viscosity Is caused by dissipation In the capillary (7) and yields the experimental thermal correction for the test oil. 

The majority of published work on extrusion behaviour deals with compounded stock. Those papers reporting work on raw rubbers have usually been on the use of capillary rheometers to determine extrusion properties at higher shear rates than are possible with Mooney viscometers. Capillary rheometers are, in principle, quite simple to use, and the application of electronic, minicomputer and laser technology has reduced the operation and data analysis to a routine task. There are no standard ASTM or other test procedures, but under a specific set of conditions, once a material is characterized, the data can be used as standard for comparison of all subsequent batches. It is readily possible to characterize a raw rubber by an extrusion experiment to determine the viscosity/shear rate curve, extrudate swell, and stress relaxation.Both Sezna and Karg have shown how the Monsanto Processability Tester (MPT), a modified, computerized extrusion rheometer, can be used in predicting mixing behaviour. The MPT (shown schematically in Fig. 7) is a most versatile instrument. It has a larger than conventional barrel for minimal pressure drop in the barrel, a pressure transducer at the entrance to the orifice, a microprocessor system, and a laser device for... 

There are a munber of popular viscometer geometries where the shear rate is not the same everywhere. In order to convert the basic experimental data into unambiguous viscosity/shear-rate data, an intermediate calculation step is needed. This uses an assumption about the liquid, usually that at any particular value of shear rate, the local viscosity/shear-rate data can be described by a power-law-type behaviour, where the slope of the log/log curve is given by n. (For true power-law Uquids, this is the same as n, the power-law index.) The following are the necessary equations for wide-gap concentric cylinders the paraUel-plate geometry and tubes used as viscometers, hi each case the viscosity data is related to a certain shear rate calculated at some fixed point in the geometry, and n is related to the basic measured parameters. 

Figure 3.8 shows the improved behaviour of the Carreau model compared with the power law model. Several workers have reported that the Carreau model gives a much improved fit to their viscosity/shear rate data (Abdel-Khalik et al, 1974 Bird et al, 1974 Chauveteau and Zaitoun, 1981). 

The capillary viscometer can only provide the viscosity-shear rate relationship for a polymer. It cannot give other viscometric functions. Viscometric functions associated with normal stress behaviour in steady shear... 

Fig. 7.7 Comparison of viscosity-shear-rate behaviour of conventional and anisotropic melts.

The reasons why rheology is selected as a separate chapter is as follows the capillary rheometer and the rotational rheometer, which had originally been designed for the rheological measurements of liquids have been used for the observation of gum rubber and compound behaviour. The question is what these measurements really mean, because gum rubbers as well as compounds are not liquids but they are in the rubbery state. However, in this chapter, the conventional practice of treating the material as if it were liquid is followed. Not only is the viscosity-shear rate relationship discussed but also the melt fracture, extrudate swell and slip. Shown in Figure 8.1 are flow curves of NBR samples. A, B, C, and D at 100 °C [1]. 

Polymers owe much of their attractiveness to their ease of processing. In many important teclmiques, such as injection moulding, fibre spinning and film fonnation, polymers are processed in the melt, so that their flow behaviour is of paramount importance. Because of the viscoelastic properties of polymers, their flow behaviour is much more complex than that of Newtonian liquids for which the viscosity is the only essential parameter. In polymer melts, the recoverable shear compliance, which relates to the elastic forces, is used in addition to the viscosity in the description of flow [48]. 

Flow behaviour of polymer melts is still difficult to predict in detail. Here, we only mention two aspects. The viscosity of a polymer melt decreases with increasing shear rate. This phenomenon is called shear thinning [48]. Another particularity of the flow of non-Newtonian liquids is the appearance of stress nonnal to the shear direction [48]. This type of stress is responsible for the expansion of a polymer melt at the exit of a tube that it was forced tlirough. Shear thinning and nonnal stress are both due to the change of the chain confonnation under large shear. On the one hand, the compressed coil cross section leads to a smaller viscosity. On the other hand, when the stress is released, as for example at the exit of a tube, the coils fold back to their isotropic confonnation and, thus, give rise to the lateral expansion of the melt. 

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. 

Effect of increase of On viscosity On flow behaviour index On critical shear rate On sharkskin... 

In practice there are a number of other factors to be taken into account. For example, the above analysis assumes that this plastic is Newtonian, ie that it has a constant viscosity, r). In reality the plastic melt is non-Newtonian so that the viscosity will change with the different shear rates in each of the three runner sections analysed. In addition, the melt flow into the mould will not be isothermal - the plastic melt immediately in contact with the mould will solidify. This will continuously reduce the effective runner cross-section for the melt coming along behind. The effects of non-Newtonian and non-isothermal behaviour are dealt with in Chapter 5. 

When a fluid is flowing along a channel which has a uniform cross-section then the fluid will be subjected to shear stresses only. To define the flow behaviour we may express the fluid viscosity, rj, as the ratio of shear stress, r. 

Many microbial polysaccharides show pseudoplastic flow, also known as shear thinning. When solutions of these polysaccharides are sheared, the molecules align in the shear field and the effective viscosity is reduced. This reduction of viscosity is not a consequence of degradation (unless the shear rate exceeds 105 s 1) since the viscosity recovers immediately when die shear rate is decreased. This combination of viscous and elastic behaviour, known as viscoelasticity, distinguishes microbial viscosifiers from solutions of other thickeners. Examples of microbial viscosifiers are ... 

Liquids of complex structure, such a polymer solutions and melts, and pseudo-homogeneous suspensions of fine particles, will generally exhibit non-Newtonian behaviour, with their apparent viscosities depending on the rate at which they are sheared, and the time for which they have been subjected to shear. They may also exhibit significant elastic... 

Many fluids, including some that are encountered very widely both industrially and domestically, exhibit non-Newtonian behaviour and their apparent viscosities may depend on the rate at which they are sheared and on their previous shear history. At any position and time in the fluid, the apparent viscosity pa which is defined as the ratio of the shear stress to the shear rate at that point is given by ... 

When the apparent viscosity is a function of the shear rate, the behaviour is said to he shear-dependenf, when it is a function of the duration of shearing at a particular rate, it is referred to as time-dependent. Any shear-dependent fluid must to some extent be time-dependent because, if the shear rate is suddenly changed, the apparent viscosity does not alter instantaneously, but gradually moves towards its new value. In many eases, however, the time-scale for the flow process may be sufficiently long for the effects of time-dependence to be negligible. 

The relation between shear stress and shear rate for the Newtonian fluid is defined by a single parameter /z, the viscosity of the fluid. No single parameter model will describe non-Newtonian behaviour and models involving two or even more parameters only approximate to the characteristics of real fluids, and can be used only over a limited range of shear rates. 

When the fluid behaviour can be described by a power-law, the apparent viscosity for a shear-thinning fluid will be a minimum at the wall where the shear stress is a maximum, and will rise to a theoretical value of infinity at the pipe axis where the shear stress is zero. On the other hand, for a shear-thickening fluid the apparent viscosity will fall to zero at the pipe axis. It is apparent, therefore, that there will be some error in applying the power-law near the pipe axis since all real fluids have a limiting viscosity po at zero shear stress. The procedure is exactly analogous to that used for the Newtonian fluid, except that the power-law relation is used to relate shear stress to shear rate, as opposed to the simple Newtonian equation. 

The rheological properties of a particular suspension may be approximated reasonably well by either a power-law or a Bingham-plastic model over the shear rate range of 10 to 50 s. If the consistency coefficient k is 10 N s, /m-2 and the flow behaviour index n is 0.2 in the power law model, what will be the approximate values of the yield stress and of the plastic viscosity in the Bingham-plastic model ... 

Because concentrated flocculated suspensions generally have high apparent viscosities at the shear rates existing in pipelines, they are frequently transported under laminar flow conditions. Pressure drops are then readily calculated from their rheology, as described in Chapter 3. When the flow is turbulent, the pressure drop is difficult to predict accurately and will generally be somewhat less than that calculated assuming Newtonian behaviour. As the Reynolds number becomes greater, the effects of non-Newtonian behaviour become... 

What is a non-Newtonian fluid Describe the principal types of behaviour exhibited by these fluids. The viscosity of a non-Newtonian fluid changes with the rate of shear according to the approximate relationship ... 

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