Rheology viscosity shear dependence

Frequently used single-point viscosity tests in the starch plant are orifice pipettes,56 orifice funnels,57 the Hot Scott viscometer, and various methods to determine alkaline fluidity.58 For absolute measurements of the rheological properties, rotating viscometers with coaxial cylinders are used.59 The paper industry uses mainly the Brookfield viscometer and the Hercules viscometer for determining shear-dependent viscosity, pseudoplasticity, and thixotropy. Oscillatory and capillary viscometers are used for more detailed viscosity characterization, such as yield value, elastic properties, and viscoelasticity.60... 

The major characteristic of a polymeric reactor that is different from most other types of reactors discussed earlier is the viscous and often non-Newtonian behavior of the fluid. Shear-dependent rheological properties cause difficulties in the estimation of the design parameters, particularly when the viscosity is also time-dependent. While significant literature on the design parameters for a mechanically agitated vessel containing power-law fluid is available, similar information for viscoelastic fluid is lacking. 

However, they may not indicate the true bulk viscosity of a suspension that forms a thin layer of the continuous phase (e.g., serum of tomato juice) around the immersed probe or when the probe is covered by a higher viscosity gel due to fouling. Vibrational viscometers are suitable for measuring viscosities of Newtonian fluids, but not the shear-dependent rheological behavior of a non-Newtonian fluid (e.g., to calculate values of the power law parameters). 

Stable particle suspensions exhibit an extraordinarily broad range of rheological behavior. which depends on particle concentration, size, and shape, as well as on the presence and type of stabilizing surface layers or surface charges, and possible viscoelastic properties of the suspending fluid. Some of the properties of suspensions of spheres are now reasonably well understood, such as (a) the concentration-dependence of the zero-shear viscosity of hard-sphere suspensions and (b) the effects of deformability of the steric-stabilization layers on the particles. In addition, qualitative understanding and quantitative empirical equations... 

Lepez et al. (1990) examined the rheology of glass-bead-filled HOPE and PS. They found that a Cross model describes the viscosity-shear-rate relationship, a Quemada model describes the concentration dependence of the viscosity, and a compensation model applies for the tempemture dependence of the viscosity. This model is expressed as... 

Even the measurement of the steady-state characteristics of shear-dependent fluids is more complex than the determination of viscosities for Newtonian fluids. In simple geometries, such as capillary tubes, the shear stress and shear rate vary over the cross-section and consequently, at a given operating condition, the apparent viscosity will vary with location. Rheological measurements are therefore usually made with instraments in which the sample to be sheared is subjected to the same rate of shear throughout its whole mass. This condition is achieved in concentric cylinder geometry (Fi re 3.37) where the fluid is sheared in the annular space between a fixed and a rotating cylinder if the gap is small compared with the dimneters of the cylinders, the shear rate is approximately... 

PVC pastes exhibit complex rheological behavior with the viscosities showing dependence on the shear rate and on the time of shear. A paste viscosity may increase with shear rate (dilatancy) or decrease shear thinning or pseudoplasticity). Some pastes may show dilatant tendencies over one range of shear rates but... 

Often latexes are used in formulations containing pigments, fillers, other additives and water-soluble polymers to achieve the desired end-use properties. One of the requirements for these formulations is some specific viscosity at a given shear rate, as in carpet backing formulations, or some shear-dependent viscosity or rheological behaviour, as in paints. 

Since the power-law and the Bingham plastic fluid models are usually adequate for modelling the shear dependence of viscosity in most engineering design calculations, the following discussion will therefore be restricted to cover just these two models where appropriate, reference, however, will also be made to the applications of other rheological models. Theoretical and experimental results will be presented separately. For more detailed accounts of work on heat transfer in non-Newtonian fluids in both circular and non-circular ducts, reference should be made to one of the detailed surveys [Cho and Hartnett, 1982 Irvine, Jr. and Kami, 1987 Shah and Joshi, 1987 Hartnett and Kostic, 1989 Hartnett and Cho, 1998]. 

While Eq. (2.33) is valid for monodispersedathermal polymers, in reality polymers are polydispersed and do interact with each other. Consequently, application of the model to a real system requires that the influence of individual molecular weight fractions on the rheological functions is taken into account. For example, in the simplest case of the zero-shear viscosity-composition dependence for entangled systems [194, 195] the prediction is ... 

It is well known that the rheological properties of partially hydrolyzed polyacrylamide depend on the stresses associated with a given flow field. In a simple shear flow, the apparent viscosity is constant at low shear rates (Newtonian behavior). At a critical shear rate, the apparent viscosity decreases as the shear rate is increased, i.e., a shear thinning behavior [48]. The viscosity shear-rate data of water soluble-polymers are commonly fitted using the Carreau viscosity model [49]. According to this model, the apparent viscosity, p, is a function of the shear rate, Y, as follows ... 

Figure 24 Shear-dependent viscosity of polyacrylamide solutions. (From KC Tam and C Tiu, Water-soluble polymers (rheological properties) in Polymeric Materials Encyclopedia, JC Salamone, ed. Boca Raton, FL CRC Press, 1996, p. 8655.)...

The rheology of blends of linear and branched PLA architectures has also been comprehensively investigated [42, 44]. For linear architectures, the Cox-Merz rule relating complex viscosity to shear viscosity is valid for a large range of shear rates and frequencies. The branched architecture deviates from the Cox-Merz equality and blends show intermediate behavior. Both the zero shear viscosity and the elasticity (as measured by the recoverable shear compliance) increase with increasing branched content. For the linear chain, the compliance is independent of temperature, but this behavior is apparently lost for the branched and blended materials. These authors use the Carreau-Ya-suda model. Equation 10.29, to describe the viscosity shear rate dependence of both linear and branched PLAs and their blends ... 

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