Dilatation, yield stresses

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. 

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

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). 

Fluids that show viscosity variations with shear rates are called non-Newtonian fluids. Depending on how the shear stress varies with the shear rate, they are categorized into pseudoplastic, dilatant, and Bingham plastic fluids (Figure 2.2). The viscosity of pseudoplastic fluids decreases with increasing shear rate, whereas dilatant fluids show an increase in viscosity with shear rate. Bingham plastic fluids do not flow until a threshold stress called the yield stress is applied, after which the shear stress increases linearly with the shear rate. In general, the shear stress r can be represented by Equation 2.6 ... 

In the case of fluids without yield stress, viscous and viscoelastic fluids can be distinguished. The properties of viscoelastic fluids lie between those of elastic solids and those of Newtonian fluids. There are some viscous fluids whose viscosity does not change in relation to the stress (Newtonian fluids) and some whose shear viscosity T] depends on the shear rate y (non-Newtonian fluids). If the viscosity increases when a deformation is imposed, we define the material as a shear-thickening (dilatant) fluid. If viscosity decreases, we define it as a shear-thinning fluid. 

Fig. 34. Yield stress and critical dilatational stress required for crack nucleation in PEEK...

Yield-dilatant (n > 1) materials are rare but several cases of yield-pseudoplastics exist. For instance, data from the literature of a 20% clay in water suspension are represented by the numbers To = 7.3dyn/cm, K = 1.296dyn(sec)"/cm and n = 0.483 (Govier and Aziz, 1972, p. 40). Solutions of 0.5-5.0% carboxypolymethy-lene also exhibit this kind of behavior, but at lower concentrations the yield stress is zero. 

Fluids with a Yield Stress. Both pseudoplastic and dilatant fluids are characterized by the fact that no finite shear stress is required to make the fluids flow. A fluid with a yield stress is characterized by the property that a finite shear stress, To, is required to make the fluid flow. A fluid obeying... 

Fig. 1 Classes of rheological behavior that can be shown by coal slurries, as they appear when plotted on a shear rate/ shear stress graph. It is desirable for coal slurries to be Bingham plastic or pseudoplastic with yield, as such slurries flow readily at high shear rates (such as during pumping or atomization), while remaining stable against settling at low shear rates because of their yield stress. Dilatant slurries are completely unsuitable for coal slurry applications because they are extremely difficult to pump.

Simple classifications of fluids can be made on the basis of their rheological profiles. Figure 3.78 shows the (a) shear stress and (b) viscosity profiles for various systems. From Figure 3.78 one may define the following systems. Newtonian systems have a constant viscosity with respect to shear rate. Dilatant (or shear-thickening) systems have a viscosity that increases with respect to shear rate. Pseudo-plastic (or shear-thinning) systems have a viscosity that decreases with respect to shear rate. Yield-stress materials are materials that have an initial structure that requires a finite stress before deformation can occur. The stress that initiates deformation is defined as the yield stress. 

Utracki and Fisa (1982) and Metzner (1985) review the rheology of (asymmetric) fibre-and flake-filled plastics, noting the importance of the filler-polymer interface, filler-filler interactions, filler concentration and filler-particle properties in determining rheological phenomena such as yield-stress, normal-stress and viscosity profiles (thixotropy and rheo-pexy, dilatancy and shear thinning). 

Experience has shown structured fluids to be more difficult to manufacture, due to the complexity of their rheological profiles. In addition to elasticity, dilatancy, and rheopexy, certain structured fluid compositions may exhibit solid-like properties in the quiescent state and other flow anomalies under specific flow conditions. For emulsions and solid particulate dispersions, near the maximum packing volume fraction of the dispersed phase, for example, yield stresses may be excessive, severely limiting or prohibiting flow under gravity, demanding special consideration in nearly all unit operations. Such fluids pose problems in... 

Below this yield stress, no continued shear strain can occur, only a small elastic (dilational) strain that corresponds to the distortion of the... 

The fundamental assumption of the classical rheological theories is that the liquid stmcture is either stable (Newtonian behavior) or its changes are well dehned (non-Newtonian behavior). This is rarely the case for flow of multiphase systems. For example, orientation of sheared layers may be responsible for either dilatant or pseudoplastic behavior, while strong interparticle interactions may lead to yield stress or transient behaviors. Liquids with yield stress show a plug flow. As a result, these liquids have drastically reduced extrudate swell, B = d/d (d is diameter of the extrudate, d that of the die) [Utracki et al, 1984]. Since there is no deformation within the plug volume, the molecular theories of elasticity and the relations they provide to correlate, for example either the entrance pressure drop or the extmdate swell, are not applicable. 

Dilatant Flows Krieger and Choi [1984] smdied the viscosity behavior of sterically stabilized PMMA spheres in silicone oil. In high viscosity oils, thixotropy and yield stress was observed. The former was well described by Eq 7.41. The magnimde of Oy was found to depend on ( ), the oil viscosity, and temperature. In most systems, the lower Newtonian plateau was observed for the reduced shear stress value = Oj d / RT > 3 (d is the... 

Based on the magnitude of n and to, the non-Newtonian behavior can be classified as shear thinning, shear thickening, Bingham plastic, pseudoplastic with yield stress, or dilatant with yield stress (see Fig. 2 and Table I). The Herschel-Bulkley model is able to describe the general flow properties of fluid foods within a certain shear range. The discussion on this classiflcation and examples of food materials has been reviewed by Sherman (1970), DeMan (1976), Barbosa-Canovas and Peleg (1983), and Barbosa-Canovas et al. (1993). 

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