Rheological curve

Typical rheological curves obtained during a diepoxy-diamine reaction are shown in Fig. 6.3. The cure temperature (T = 90°C) is well above the glass transition temperature of the fully cured network (Tgoo 35°C), which means that only gelation occurs. Three typical regions are observed during cure (Matejka, 1991). 

For practical purposes, casting slips are often characterized by so-called apparent viscosity. This characteristic is defined for any point on the rheological curve (Fig. 155) as a ratio of shear stress to the deformation rate at the given point. The inadequacy of this characteristic is demonstrated by Fig. 155 a dilatant and a pseudoplastic mix have the same apparent viscosity at a stress corresponding to the intersection of their rheological curves, despite their quite diverse rheological behaviours. However, determination of apparent viscosity may be useful, for example in routine qualitative inspection. ... 

The size distribution of particles will control the amount of liquid needed to fluidize a given quantity of coal. In general, a fine size distribution will produce a more viscous slurry than a coarse size distribution at the same wt% solids, and the fine particles will produce a more non-Newtonian rheological curve. This can be seen in the laboratory results shown in Fig. 3, which compares a coarse coal slurry to a fine coal slurry. It is clearly seen that the fine slurry is much more viscous, its pseudoplastic character is very pronounced, and its yield value is high, while the coarse coal slurry is clearly a Bingham plastic. ... 

Fig. 3 Comparison of the rheological curves for a fine coal slurry (80% passing 34 gm, top size lOOgm, 52wt% solids) and for a coarse coal slurry (58wt% solids). Neither slurry used any additives. Because it is extremely difficult to measure the rheology of unstable slurries with conventional rheometers, these results were obtained using a continuous-pressure-vessel rheometer, which was specially designed for this purpose. The fine coal curve is the average of 10 measurements and the coarse coal curve is the average of 5 measurements, and the standard error of the shear rate measurements was approximately 1.0 Pa for these slurries. The fine coal slurry is clearly pseudoplastic with a yield value of approximately 18 Pa, while the coarse coal slurry is Bingham plastic with an estimated yield value of 4 Pa.

M. Chakraborty, C. Bhattacharya, and S. Datta (Chapter 4) review recent advances in the theory and applications of ELM systems. Several mathematical models for the rheological curves are considered, and regions of... 

The shape of the aqueous rheology curve also varies with the nature of the polymer. Both the carbomers and the cross-polymers show fairly similar behavior. Crosslinked ASE polymers, as shown in Figure 5.4, show a profile close to that of the carbomers, giving highly shear-thinning properties, although this is to some extent dependent on molecular weight. A noncrosslinked ASE polymer shows a more Newtonian profile. The HASE polymers tend to show a behavior between that of a noncrosslinked ASE thickener and the carbomers or crosslinked ASE polymers. 

Fig. IX-23. Rheological curve of a free disperse system containing anisometric particles cot...

Fig. IX-24. Full rheological curve of structured disperse system cot

The full rheological curve of such thixotropic system may be presented as a graph showing the effective viscosity, ry- = x/y, as a function of the shear stress, x, (Fig. IX-25). In this Figure r min corresponds to viscosity of the system with completely disintegrated structure. For the above mentioned bentonite... 

The analysis of full rheological curve illustrates how the complex mechanical behavior can be subdivided into several regions, and how within each of these regions it can be represented by a simple model that utilizes only one or two constant parameters. For this reason, such phenomena as Schwedov s creep and Bingham s viscoplastic flow, whose molecular mechanisms are so different, can be described by substantially different parameters within otherwise the same model. Such subdivision of complex behavior into a finite number of simpler constituents with particular quantitative characteristics illustrates the universal role of macrorheology. At the same time, detailed description of a mechanism involved in each of these elementary stages requires the use of molecular-kinetic concepts and may be characterized as a microrheological approach. 

Kiparissides C, Pladis P, Moen 0. From Polyethylene Rheology Curves to Molecular Weight Distributions. In Laso M, Perpete EA, editors. Multiscale Modelling of Polymer Properties, Computer-Aided Chemical Engineering. Volume... 

Fig. 2. Capillary rheological curves of base materials, (Extr. temper. = 200 C).

FIGURE 14 Rheological curves for Newtonian and pseudoplastic liquids. 

As the rheological curves for magnetite dense-medium show, for such systems the shear stress is not proportional to the shear rate therefore, such systems are not characterized by one simple value of viscosity, as in the case of Newtonian liquids. 

FIGURE 15 Rheological curves for magnetite dense media. Solid line, magnetite particle size 100% below 200 tm broken line, magnetite size 100% below 10 /xm. [Adapted from Berghbfer, W. (1959). Bergbauwissenschaften, 6(20), 493.]... 

Application of the two methods made it possible to plot the entire rheological curve, speed of deformation vs. equilibrium stress e = f(Pgg), as well as to determine rheological properties of interfacial layers. 

Figure 4. The rheological curves of the foam fracturing fluid.

The rheologic curves show that after a cycle of stressing at the shear stress the molten PET undergoes modifications at the supramolecular level of its structure. 

A comparison between the rheological curves of the PET curves and the curves provided by the mathematical model, for the polymer with and without inhibitor of carboxylic groups, was performed by monofactorial graphical processing. 

Figure 18.13 Rheological curves of HDPE, NR and their blends (data on the curves are NR contents in g/100 g HDPE).

Figure 18.54 Rheological curves (a) storage modulus and (b) tan 5 for the respective blends.

FIGURE 3.20 A complete rheological curve of structured disperse system tan 4> = qschw. tan c )ni = iIb-... 

As seen in Figure 3.21, a complete rheological curve contains four characteristic regions. Region I corresponds to low stresses under which the system may demonstrate a solid-like behavior with high viscosity (Kelvin model). This case is characteristic of the already mentioned bentonite clays. The studies of relaxation structures in moderately concentrated suspensions of bentonite clays indicated the appearance of elastic aftereffect at low shear stresses. This effect has an entropic nature, as it is associated with the... 

FIGURE 3.30 Description of a full rheological curve by the combination of quantitative two-parameter models. (From Shchukin, E.D. et al., Colloid and Surface Chemistry, Elsevier, Amsterdam, the Netherlands, 2001.)... 

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