Non-Newtonian behavior

The electroviscous effects and the other effects discussed in Sections 4.7a-c lead to what is called non-Newtonian behavior in the flow of dispersions. In the next section, we begin with a brief review of the basic concepts concerning deviations from Newtonian flow behavior and then move on to consider how high particle concentrations and electroviscous effects affect the flow and viscosity. 

We have already devoted a considerable amount of space to our discussion of viscosity without ever venturing beyond Newtonian systems. At least as much —probably more —could be said about non-Newtonian systems. 

The non-Newtonian fluids in shear flows may be classified broadly into three types  

Fluids with shear stresses that at any point depend on the shear rates only and are independent of time. These include (a) what are known as Bingham plastics, materials that require a minimum amount of stress known as yield stress before deformation, (b) pseudoplastic (or shear-thinning) fluids, namely, those in which the shear stress decreases with the shear rate (these are usually described by power-law expressions for the shear stress i.e., the rate of strain on the right-hand-side of Equation (1) is raised to a suitable power), and (c) dilatant (or shear-thickening) fluids, in which the stress increases with the shear rate (see Fig. 4.2). 

Viscoelastic materials, as mentioned in Section 4.1, display behavior somewhere between a solid and a liquid. 

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If our objective is to examine non-Newtonian behavior, we must design experiments which permit the relationship between and dv/dy to be studied over as wide a range as possible. This topic is taken up in the next section. 

If we wish to avoid the complication of non-Newtonian behavior, we must focus attention on a relatively narrow range of values for dv/dy. 

From plots of these data, estimate the Newtonian viscosity of each of the solutions and the approximate rate of shear at which non-Newtonian behavior sets in. Are these two quantities better correlated with the molecular weight of the polymer or the molecular weight of the arms ... 

Rheology. Both PB and PMP melts exhibit strong non-Newtonian behavior thek apparent melt viscosity decreases with an increase in shear stress (27,28). Melt viscosities of both resins depend on temperature (24,27). The activation energy for PB viscous flow is 46 kj /mol (11 kcal/mol) (39), and for PMP, 77 kJ/mol (18.4 kcal/mol) (28). Equipment used for PP processing is usually suitable for PB and PMP processing as well however, adjustments in the processing conditions must be made to account for the differences in melt temperatures and rheology. 

Gla.ss Ca.pilla.ry Viscometers. The glass capillary viscometer is widely used to measure the viscosity of Newtonian fluids. The driving force is usually the hydrostatic head of the test Hquid. Kinematic viscosity is measured directly, and most of the viscometers are limited to low viscosity fluids, ca 0.4—16,000 mm /s. However, external pressure can be appHed to many glass viscometers to increase the range of measurement and enable the study of non-Newtonian behavior. Glass capillary viscometers are low shear stress instmments 1—15 Pa or 10—150 dyn/cm if operated by gravity only. The rate of shear can be as high as 20,000 based on a 200—800 s efflux time. 

The increase in fuel viscosity with temperature decrease is shown for several fuels in Figure 9. The departure from linearity as temperatures approach the pour point illustrates the non-Newtonian behavior created by wax matrices. The freezing point appears before the curves depart from linearity. It is apparent that the low temperature properties of fuel are closely related to its distillation range as well as to hydrocarbon composition. Wide-cut fuels have lower viscosities and freezing points than kerosenes, whereas heavier fuels used in ground turbines exhibit much higher viscosities and freezing points. 

Chocolate does not behave as a tme Hquid owing to the presence of cocoa particles and the viscosity control of chocolate is quite compHcated. This non-Newtonian behavior has been described (28). When the square root of the rate of shear is plotted against the square root of shear stress for chocolate, a straight line is produced. With this Casson relationship method (29) two values are obtained, Casson viscosity and Casson yield value, which describe the flow of chocolate. The chocolate industry was slow in adopting the Casson relationship but this method now prevails over the simpler MacMichael viscometer. Instmments such as the Carri-Med Rheometer and the Brookfield and Haake Viscometers are now replacing the MacMichael. 

Elasticity is another manifestation of non-Newtonian behavior. Elastic Hquids resist stress and deform reversibly provided that the strain is not too large. The elastic modulus is the ratio of the stress to the strain. Elasticity can be characterized usiag transient measurements such as recoil when a spinning bob stops rotating, or by steady-state measurements such as normal stress ia rotating plates. 

The viscosity of a fluid arises from the internal friction of the fluid, and it manifests itself externally as the resistance of the fluid to flow. With respect to viscosity there are two broad classes of fluids Newtonian and non-Newtonian. Newtonian fluids have a constant viscosity regardless of strain rate. Low-molecular-weight pure liquids are examples of Newtonian fluids. Non-Newtonian fluids do not have a constant viscosity and will either thicken or thin when strain is applied. Polymers, colloidal suspensions, and emulsions are examples of non-Newtonian fluids [1]. To date, researchers have treated ionic liquids as Newtonian fluids, and no data indicating that there are non-Newtonian ionic liquids have so far been published. However, no research effort has yet been specifically directed towards investigation of potential non-Newtonian behavior in these systems. 

According to the structure of this equation the quantity cp indicates the influence of the filler on yield stress, and t r on Newtonian (more exactly, quasi-Newtonian due to yield stress) viscosity. Both these dependences Y(cp) andr r(cp) were discussed above. Non-Newtonian behavior of the dispersion medium in (10) is reflected through characteristic time of relaxation X, i.e. in the absence of a filler the flow curve of a melt is described by the formula ... 

Viscosity is usually understood to mean Newtonian viscosity in which case the ratio of shearing stress to the shearing strain is constant. In non-Newtonian behavior, which is the usual case for plastics, the ratio varies with the shearing stress (Fig. 8-5). Such ratios are often called the apparent viscosities at the corresponding shearing stresses. Viscosity is measured in terms of flow in Pa s, with water as the base standard (value of 1.0). The higher the number, the less flow. 

The non-Newtonian behavior of a plastic melt makes its flow through a die somewhat complicated. One characteristic of plastic is... 

Toothpaste flow is an extreme example of non-Newtonian flow. Problem 8.2 gives a more typical example. Molten polymers have velocity profiles that are flattened compared with the parabolic distribution. Calculations that assume a parabolic profile will be conservative in the sense that they will predict a lower conversion than would be predicted for the actual profile. The changes in velocity profile due to variations in temperature and composition are normally much more important than the fairly subtle effects due to non-Newtonian behavior. 

This method yields an absolute value. When a melt is near the melting point, the viscosity is so high that non-Newtonian behavior occurs. 

For many materials, the application of a stress creates a strain rate in a linear fashion, i.e., the rate of strain is proportional to the applied stress. This linear relationship, which defines a Newtonian fluid, does not hold true for polymers. Most molten polymers respond to stresses in a non-linear fashion, such that the greater the applied stress the more effective the stress is at inducing a strain rate. This non-Newtonian behavior is referred to as shear thinning ... 

In the molten state polymers are viscoelastic that is they exhibit properties that are a combination of viscous and elastic components. The viscoelastic properties of molten polymers are non-Newtonian, i.e., their measured properties change as a function of the rate at which they are probed. (We discussed the non-Newtonian behavior of molten polymers in Chapter 6.) Thus, if we wait long enough, a lump of molten polyethylene will spread out under its own weight, i.e., it behaves as a viscous liquid under conditions of slow flow. However, if we take the same lump of molten polymer and throw it against a solid surface it will bounce, i.e., it behaves as an elastic solid under conditions of high speed deformation. As a molten polymer cools, the thermal agitation of its molecules decreases, which reduces its free volume. The net result is an increase in its viscosity, while the elastic component of its behavior becomes more prominent. At some temperature it ceases to behave primarily as a viscous liquid and takes on the properties of a rubbery amorphous solid. There is no well defined demarcation between a polymer in its molten and rubbery amorphous states. 

It is also evident that this phenomenological approach to transport processes leads to the conclusion that fluids should behave in the fashion that we have called Newtonian, which does not account for the occurrence of non-Newtonian behavior, which is quite common. This is because the phenomenological laws inherently assume that the molecular transport coefficients depend only upon the thermodyamic state of the material (i.e., temperature, pressure, and density) but not upon its dynamic state, i.e., the state of stress or deformation. This assumption is not valid for fluids of complex structure, e.g., non-Newtonian fluids, as we shall illustrate in subsequent chapters. 

Nonnegative least squares (NNLS), 6 63 Non-Newtonian behavior of filled networks, 22 572 of silicone fluids, 22 575 versus Newtonian behavior,... 

Another feature of surfactant-water systems is that they can also aggregate into lyotropic liquid crystalline phases when Intermicellar interactions are significant. Typically, non-Newtonian behavior is usually found for these liquid crystalline phases. For the 3LDA0/ISDS mixed system, all evidence suggests that they do form liquid crystalline phase. 

The rheological properties change behavior, relative to more dilute solutions, above cp = 0.2, where non-Newtonian behavior is then exhibited. The power law dependence of rj on cp is in harmony with the Zimm rather than the Rouse model, which suggests that hydrodynamic interactions between these polymers, in a mean field sense, are important. Electrical properties also begin to deviate for Nafion solutions above cp = 0.2, and mechanical percolation is essentially the same for the sodium and acid forms. 

With this background of non-Newtonian behavior in hand, let us examine the viscous behavior of suspensions and slurries in ceramic systems. For dilute suspensions on noninteracting spheres in a Newtonian liquid, the viscosity of the suspension, r)s, is greater than the viscosity of the pure liquid medium, rjp. In such cases, a relative viscosity, rjr, is utilized, which is defined as rjs/rjL. For laminar flow, is given by the Einstein equation... 

This description of non-Newtonian behavior in ceramic slurries and snspensions leads us directly into a description of viscosity in polymeric materials, which are oftentimes highly non-Newtonian in their behavior. 

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