Pseudoplastic fluids shear thinning

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). 

Most fluids exhibit non-Newtonian behavior—blood, household products like toothpaste, mayonnaise, ketchup, paint, and molten polymers. As shown in Figure 7.9, shear stress, t, increases linearly with strain rate, y, for Newtonian fluids. Non-Newtonian fluids may be classified into those that are time dependent or time independent and include viscoelastic fluids. Shear thinning (pseudoplastic) and shear thickening (dilatant) fluids are time independent while rheopectic and thixotropic are time dependent. The shear stress (viscosity) of shear thinning fluids decreases with increasing shear rate and examples include blood and syrup. The viscosity of dilatant fluids increases with shear rate. The viscosity of rheopectic fluids—whipping cream, egg whites—increases with time while thixotropic fluids— paints (other than latex) and drilling muds— decrease their viscosity with the duration of the shear. 

The most common type of time-independent non-Newtonian fluid behavioiu observed is pseudoplasticity or shear-thinning, characterised by an apparent viscosity which decreases with increasing shear rate. Both at very low and at very high shear rates, most shear-thinning polymer solutions and melts exhibit Newtonian behaviour, i.e. shear stress-shear rate plots become straight lines. 

Laboratory testing shows that visual examination and viscosity measurements are not sufficient to fully define polymer solvation. In this work, the solvation of hydroxyethyl cellulose (HEC) and xanthan has been studied. These polymers are both widely used in various petroleum applications. HEC is used in many workover and completion applications, while xanthan has its most wide spread uses in drilling and enhanced oil recovery (EOR) applications. Solublization of both polymers results in fluids with pseudoplastic (or shear thinning properties). Even though the polymers both exhibit pseudoplastic behivior, the polymers vary considerably as to their molecular size and physical properties. 

With a power law index, = 1, the fluid behaves Newtonian. If 0 < < 1, the viscosity decreases when shear rates increase. This behavior, which applies to virtually all polymers, is called pseudoplasticity or shear thinning behavior. If > 1, the liquid is called dilatant or shear thickening. This behavior, in which viscosity increases when the shear rate increases, has only been observed in materials with a very high concentration of fillers and has no relevance to reactive extrusion. 

Fig. 5 shows the relation of shear stress and shear rate of silver paste with different wt % of thinner. The trend of non-Newtonian behavior is consistent with the results found by Chhabra Richardson, (1999) for the types of time-independent flow behavior. The time-independent non-Newtonian fluid behavior observed is pseudoplasticity or shear-thinning characterized by an apparent viscosity which decreases with increasing shear rate. Evidently, these suspensions exhibit both shear-thinning and shear thickening behavior over different range of shear rate and different wt% of thinner. The viscosity and shear stress relationship with increasing percentage of thinner is plotted in Fig 6. It is clearly observed that both viscosity and shear stress decreases resp>ectively. 

The basic rheological properties of low concentration AA-Na dispersions have been extensively studied. They exhibit non-Newtonian pseudoplastic behavior (shear thinning) at concentrations between 0.125 and 1.5 % w/v, while at lower concentrations they behave as low viscosity Newtonian fluids [37]. 

FIGURE 7.2 Newtonian and non-Newtonian fluids (a) Shear stress versus shear rate (b) apparent viscosity versus shear rate. B-P, Bingham plastic N, Newtonian P, pseudoplastic or shear thinning S-T, shear thickening. 

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... 

Figure l.l Shear thinning behaviour of pseudoplastic fluids... 

This equation is based on the assumption that pseudoplastic (shear-thinning) behaviour is associated with the formation and rupture of structural linkages. It is based on an experimental study of a wide range of fluids-including aqueous suspensions of flocculated inorganic particles, aqueous polymer solutions and non-aqueous suspensions and solutions-over a wide range of shear rates (y) ( 10 to 104 s 1). 

In general, for shear-thinning pseudoplastic fluids the apparent viscosity will gradually decrease with time if there is a step increase in its rate of shear. This phenomenon is known as thixotropy. Similarly, with a shear-thickening fluid the apparent viscosity increases under these circumstances and the fluid exhibits rheopexy or negative-thixotropy. 

Many fluids show a decrease in viscosity with increasing shear rate. This behavior is referred to as shear thinning, which means that the resistance of the material to flow decreases and the energy required to sustain flow at high shear rates is reduced. These materials are called pseudoplastic (Fig. 3a and b, curves B). At rest the material forms a network structure, which may be an agglomerate of many molecules attracted to each other or an entangled network of polymer chains. Under shear this structure is broken down, resulting in a shear... 

The typical viscous behavior for many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels) is illustrated by the curves labeled structural in Figs. 3-5 and 3-6. These fluids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. In some materials this can be attributed to a reversible structure or network that forms in the rest or equilibrium state. When the material is sheared, the structure breaks down, resulting in a shear-dependent (shear thinning) behavior. Some real examples of this type of behavior are shown in Fig. 3-7. These show that structural viscosity behavior is exhibited by fluids as diverse as polymer solutions, blood, latex emulsions, and mud (sediment). Equations (i.e., models) that represent this type of behavior are described below. 

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. 

Non-Newtonian Viscosity In the cone-and-plate and parallel-disk torsional flow rheometer shown in Fig. 3.1, parts la and 2a, the experimentally obtained torque, and thus the % 2 component of the shear stress, are related to the shear rate y = y12 as follows for Newtonian fluids T12 oc y, implying a constant viscosity, and in fact we know from Newton s law that T12 = —/ . For polymer melts, however, T12 oc yn, where n < 1, which implies a decreasing shear viscosity with increasing shear rate. Such materials are called pseudoplastic, or more descriptively, shear thinning Defining a non-Newtonian viscosity,2 t],... 

M. M. Cross, Rheology of Non-Newtonian Fluids a New Flow Equation for Pseudoplastic Systems, J. Colloids Sci., 20, 417 137 (1965) also M. M. Cross, Relation Between Viscoe-lasiticity and Shear-thinning Behaviour in Liquids, Rheological Acta, 18, 609-614 (1979). 

FIGURE 11.12 Viscous behavior of complex fluids (i) shear stress vs. shear rate and (ii) viscosity vs. shear rate. The notation for the curves is (a) Newtonian, (b) shear thinning, (c) shear thickening, (d) Bingham plastic, and (e) pseudoplastic. 

Pseudoplastic Fluids, A pseudoplastic or a shear-thinning fluid is one of the most commonly encountered non-Newtonian fluids. The variation of the shear stress, t, versus the shear rate, 7, for a pseudoplastic fluid is shown in Figure 2. A plot of t versus 7 is characterized by linearity at very low and very high shear rates. The slope at very low shear rate gives the... 

Dilatant Fluids. Dilatant fluids or shear-thickening fluids are less commonly encountered than pseudoplastic (shear-thinning) fluids. Rheological dilatancy refers to an increase in the apparent viscosity with increasing shear rate (3). In many cases, viscometric data for a shear-thickening fluid can be fit by using the power law model with n > 1. Examples of fluids that are shear-thickening are concentrated solids suspensions. 

For a Newtonian fluid, the power law index n = 1, and k is the fluid viscosity. Also, for shear-thinning (pseudoplastic) fluids, n < 1. 

Pseudoplastic A fluid whose viscosity decreases as the applied shear rate increases. Also termed shear thinning. 

The shearing characteristics of non-Newtonian fluids are illustrated in Fig. 7. Curves A and B represent viscoelastic behavior. Curve C illustrates the behavior if the fluid thins with increasing shear, generally referred to as shear thinning or pseudoplasticity. The opposite effect of shear thickening or dilatancy is shown as curve D. 

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