Viscosity changes with shear rate

Viscous Hquids are classified based on their rheological behavior characterized by the relationship of shear stress with shear rate. Eor Newtonian Hquids, the viscosity represented by the ratio of shear stress to shear rate is independent of shear rate, whereas non-Newtonian Hquid viscosity changes with shear rate. Non-Newtonian Hquids are further divided into three categories time-independent, time-dependent, and viscoelastic. A detailed discussion of these rheologically complex Hquids is given elsewhere (see Rheological measurements). 

The 17, 170, A, and n are all parameters that are used to fit data, taken here as 17 = 0.05, 170 = 0.492, A = 0.1, and n = 0.4. A plot of the viscosity vs shear rate is given in Figure 10.8. For small shear rates, the viscosity is essentially constant, as it is for a Newtonian fluid. For extremely large shear rates, the same is true. For moderate shear rates, though, the viscosity changes with shear rate. In pipe flow, or channel flow, the shear rate is zero at the centerline and reaches a maximum at the wall. Thus, the viscosity varies greatly from the centerline to the wall. This complication is easily handled in FEMLAB. 

The viscosity change with shear rate can be scaled by the Peclet number, which is defined by... 

The mechanism(s) of a particulate fluid electroviscous effect is still not fully resolved and quantified. It is not strictly relevant to this work and is therefore not dealt with in detail. At this stage it can only be said that it is a very multi-parameter and multidisciplinary event and, secondly, it should be understood that there is little change in the viscosity p of the fluid as it is normally defined in its continuum context save for a derived effective or non Newtonian viscosity sense. The term electroviscous, which has often been used to describe the present class of fluids, is misleading in this case. Rather, the held imposes a yield stress type of property on the fluid which is similar to, but not the same as, that which is a feature of the ideal Bingham plastic. This can readily be seen by referring to Figs. 6.63 to 6.66 inclusive. It is alternatively possible to claim that either the plastic viscosity changes with shear rate or the electrode surface yield stress does. 

Molten polymers are viscoelastic materials, and so study of their behaviour can be complex. Polymers are also non-ideal in behaviour, i.e. they do not follow the Newtonian liquid relationship of simple liquids like water, where shear-stress is proportional to shear strain rate. Unlike Newtonian liquids, polymers show viscosity changes with shear rate, mainly in a pseudoplastic manner. As shear rate increases there is a reduction in melt viscosity. This is true of both heat-softened plastics and rubbers. Other time-dependent effects will also arise with polymer compounds to complicate the rheological process behaviour. These may be viscosity reductions due to molecular-mass breakdown or physical effects due to thixotropic behaviour, or viscosity increases due to crosslinking/branching reactions or degradation. Generally these effects will be studied in rotational-type rheometers and the extrusion-type capillary rheometer. 

Figure 10.8 Viscosity changes with shear rate. Note that the affect of temperature is much less than that of shear rate.

Although shear rate effects are more pronounced in good solvents, the intrinsic viscosity decreases with shear rate even in 0-solvents, where excluded volume is zero (317,318). The Zimm model employs the hydrodynamic interaction coefficients in the mean equilibrium configuration for all shear rates, despite the fact that the mean segment spacings change with coil deformation. Fixman has allowed the interaction matrix to vary in an appropriate way with coil deformation (334). The initial departure from [ ]0 was calculated by a perturbation scheme, and a decrease with increasing shear rate in 0-systems was predicted to take place in the vicinity of / = 1. 

Non-Newtonian viscosity is sometimes called apparent viscosity, presumably because it changes with shear rate. In this book we call it non-Newtonian viscosity. 

Flowability of plastics is largely determined by the dependence of viscosity on shear rate. Viscosity of water, for example, does not change with shear rate. When water moves through a capillary, fast or slow, its viscosity is same. In a forced oscillation rheometer, parallel plates immersed in water can move fast or slow, but the viscosity of water remains still the same. Therefore, a plot of viscosity against shear rate looks as a flat straight line, parallel to the horizontal axis (Fig. 17.1). 

The shear stresses and the shear rates in Fig. 8 were computed by the appropriate formula for Newtonian flow at the capillary wall. But if the results of such a computation indicate that the viscosity varies with shear rate, then the Rabinowitsch analysis is applied to determine the correct shear rate at the wall for non-Newtonian behavior (c. References 2 and 3). Figure 4-9 illustrates how the addition of a polymeric viscosity modifier to a paraffinic petroleum base oil changes the viscosity behavior from Newtonian (Fluid B) to non-Newtonian (Fluids C, D and E). The shear rates and the shear stresses have a hundred-fold range. 

Equation (6.70) indicates that the viscosity is independent of the shear rate Aq. However, it is well known that the polymeric liquid exhibits non-Newtonian behavior, namely, that the viscosity value decreases with increasing shear rate after the rate reaches a certain value. This discrepancy is a weak point of the elastic dumbbell model and arises from an inherent weakness in the Gaussian distribution assumed for the connector vector. We can see the cause of this deficiency from the following analysis of how the dumbbell configuration changes with shear rate. 

Fig. 7.7 (a) Viscosity versus shear rate curve of polypropylene (melting index 8 g/10 min imder 2.16 Kg and 230 °C) at 230 °C, and the applieable methods in various regitms (Gahleitner 2001) (Reprinted with permission) (b) Illustration of polymta- melt viseosity changing with shear rates and various influence factors (see the text for the details)... 

To adequately describe the settling of particles in non-Newtonian fluids one needs to know how the viscosity of the medium changes with shear rate or shear stress. 

A typical viscosity versus shear rate curve would be like the one shown in Fig. 1.6. There is a Newtonian region in the low shear where the viscosity does not change with shear rate. At some critical shear rate, there is a continuous drop off of viscosity with shear rate. The drop-off of viscosity wifli shear rate would occur sooner if the molecular-weight distribution is widened. This is because the shorter molecular chains are of lower viscosity and cause the vis-... 

Viscosity, rate of change with shear rate +... 

Next, determine the viscosity of the chemical slug. For this example, assume the chemical slug is a Newtonian fluid so that variations of viscosity with frontal-advance rate do not have to be considered. That is, the viscosity is a function of composition but does not change with shear rate. The viscosity of the chemical slug is obtained from the definition of mobility. It is first necessary to determine the relative permeability of the chemical slug in the presence of residual oil. The ROS to chemical flooding is 0.2. From... 

Variation of melt viscosity for both the preblends and preheated blends with the blend ratio are shown in Fig. 19. There are two distinct regions in viscosity change with the addition of polyacrylic rubber (ACM) in the blends. First, in the higher shear rate region, the viscosity increases with the addition of the ACM (up to 40% ACM) in the blend and then it decreases. In the lower... 

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 ... 

For a Newtonian fluid, the shear stress is proportional to the shear rate, the constant of proportionality being the coefficient of viscosity. The viscosity is a property of the material and, at a given temperature and pressure, is constant. Non-Newtonian fluids exhibit departures from this type of behaviour. The relationship between the shear stress and the shear rate can be determined using a viscometer as described in Chapter 3. There are three main categories of departure from Newtonian behaviour behaviour that is independent of time but the fluid exhibits an apparent viscosity that varies as the shear rate is changed behaviour in which the apparent viscosity changes with time even if the shear rate is kept constant and a type of behaviour that is intermediate between purely liquid-like and purely solid-like. These are known as time-independent, time-dependent, and viscoelastic behaviour respectively. Many materials display a combination of these types of behaviour. 

Among other characteristics, non-Newtonian fluids exhibit an apparent viscosity that varies with shear rate. Consequently, the determination of the shear stress-shear rate curve must be an initial consideration. Although the apparent viscosity of a thixotropic or a rheopectic fluid changes with the duration of shearing, meaningful measurements may be made if the change is relatively slow. Viscoelastic fluids also exhibit behaviour that is a function of time but their apparent viscosities can be measured provided conditions of steady shearing are obtained. 

This expression can describe the viscosity change with time at a fixed rate and in the limit of long times provides the steady state viscosity at a of shear rate. The term fi(y) is an integral function of the strain. Approximate forms are available, for example ... 

In addition to temperature, the viscosity of these mixtures can change dramatically over time, or even with applied shear. Liquids or solutions whose viscosity changes with time or shear rate are said to be non-Newtonian, that is, viscosity can no longer be considered a proportionality constant between the shear stress and the shear rate. In solutions containing large molecules and suspensions contain nonattracting aniso-metric particles, flow can orient the molecules or particles. This orientation reduces the resistance to shear, and the stress required to increase the shear rate diminishes with increasing shear rate. This behavior is often described by an empirical power law equation that is simply a variation of Eq. (4.3), and the fluid is said to be a power law fluid ... 

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