Pseudoplastic fluid with yield stress

Two of the most common empirical models used to describe the behaviour of pseudoplastic fluids with yield stresses are the Bingham plastic [377] model ... 

Hanks, R. W. and Ricks, B. L. 1974. Laminar-turbulent transition in flow of pseudoplastic fluids with yield stress. 7. Hydronautics 8 163-166. 

In a more phenomenologically oriented study [396], Newtonian liquids (p < 19 mPa s), non-Newtonian liquids (pseudoplastic e.g. CMC), several high viscosity liquids with viscoelastic properties and Carbopol and xanthane as fluids with yield stress were used. In gassed conditions three flow ranges could be distinguished ... 

Pseudomonas fluorescens, 1 732 11 4 Pseudomonas putida, 11 4 Pseudomonas testosteroni alcohol dehydrogenase, 3 672 Pseudopelletierine, 2 81-82 Pseudoplastic flow, 7 280t Pseudoplastic fluids, 11 768 Pseudoplasticity, 10 679 Pseudoplastic with yield stress flow, 7 280t Pseudopolymorphism, 8 69... 

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). 

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). 

It has been found that in the case of viscometers with co-axial cylinders, the flow is not homogenous if the distance between cylinders is too wide [1, 18]. The maximum distance should be not higher than 1 mm [ 1]. At higher distance the flow curves correspond to the pseudoplastic fluids with no clearly marked yield stress value. For low shear rate the flow of paste in the gap between the cylinders is not uniform as long as the stress does not exceed the yield stress value this can be derived from the Reiner-Rivhn equation ... 

For pseudoplastic fluids, the shear rate at any given point is solely dependent upon the instantaneous shear stress, and the duration of shear does not play any role so far as the viscosity is concerned. The shear stress vs. shear rate pattern for a pseudoplastic fluid with and without yield stress is shown in Figure 2.5. 

Basic description of non-Newtoruan fluids is provided so that concepts of shear rate dependent viscosities with or without elastic behavior, yield stress with or without shear rate dependent viscosities and time dependent viscosities at fixed shear rates get classified. The filled polymer systems fall into the category of pseudoplastic fluids with or without yield stress and also often depict the behavior of thixotropic fluids. Their viscoelasticity may give rise to various anamolous effects that are discussed in Chapter 2, such as the Weissenberg effect, extrudate swell, drawn resonance, melt fracture and so on. 

Figure 2.5 Variation of shear stress versus shear rate for pseudoplastic fluids with and without yield stress.

From Table 2.1, it can be seen that polymer melts fall within the non-Newtonian category of pseudoplastic fluids and viscoelastic fluids. In the case that polymer melts are loaded with fillers, their flow behavior would depict pseudoplastidty with yield stress, thixotropy, and viscoelasticity. 

Pseudoplastic fluids have no yield stress threshold and in these fluids the ratio of shear stress to the rate of shear generally falls continuously and rapidly with increase in the shear rate. Very low and very high shear regions are the exceptions, where the flow curve is almost horizontal (Figure 1.1). 

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 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 ... 

A grafted layer of polymer of thickness L increases the effective size of a colloidal particle. In general, dispersions of these particles in good solvents behave as non-Newtonian fluids with low and high shear limiting relative viscosities (fj0 and rj ), and a dimensionless critical stress (a3aJkT) that depends on the effective volume fraction = (1 + L/a)3. The viscosities diverge at volume fractions m0 < for mo < fan < 4>moo> the dispersions yield and flow as pseudoplastic solids. 

These examples serve to illustrate the ability of soluble polymer, interacting in a controlled fashion with colloidal particles, to transform both the equilibrium state and the mechanical properties of dispersions. All states are possible, from low viscosity fluids to pseudoplastic pastes with high yield stresses. 

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... 

The pseudoplastic fluids do not show yield stress value. Their apparent viscosity decreases with the shear rate. The flow curve reveals linear character at very high shear rate. The logarithmic plot of shear rate as a function of shear stress of these fluids is often a straight line with the slope between 0 and 1. For the pseudoplastic behaviour description is hence frequently used the power-law equation ... 

The pseudoplastic fluids can be consider as the Bingham fluid with the yield stress value and plastic viscosity equal to tg a and it is the reason of their name (see Fig. 5.4). 

A fluid with a linear flow curve for Ty > ro is called a Bingham plastic fluid and is characterised by a constant plastic viscosity (the slope of the shear stress versus shear rate curve) and a yield stress. On the other hand, a substance possessing a yield stress as well as a non-linear flow curve on linear coordinates (for Xyx > ro ), is called a yield-pseudoplastic material. Figure 1.8 illustrates viscoplastic behaviour as observed in a meat extract and in a polymer solution. 

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