Newtonian plateau

In the case of AD17, only decrease of viscosity is observed while for cp>cp, the viscosity of AD27 and AD37 solutions measured at the newtonian plateau is an increasing function of ca. pH 7 in pure water... 

Figure 3.33 Shear stress as a function of shear rate for a typical polymer. The polymer has a zero-shear Newtonian plateau, a power law intermediate region, and an infinite-shear...

A Tacussel TAT-5 pH-meter was used with a glass-calomel unitubular electrode. Both a Ubbelohde type viscometer and a "Low-Shear 30" apparatus (Contraves) were used to obtain viscosity values in the Newtonian plateau. A Fica 55-MK II spectrofluorimeter was used with excitation and emission wave lengths of 351nm and 410nm respectively. 

Williamson (predicts first Newtonian plateau and power law region) q=il0-/ryn-1... 

Sisko (predicts power law region and second Newtonian plateau) Tl=TL+k yn"1... 

The Power Law Model. The power law model proposed by Ostwald [57] and de Waale [15] is a simple model that accurately represents the shear thinning region in the viscosity versus strain rate curve but neglects the Newtonian plateau present at small strain rates. The power law model can be written as follows ... 

Figure 2.36 [53] shows shear and elongational viscosities for two types of polystyrene. In the region of the Newtonian plateau, the limit of 3, shown in eqn. (2.66), is quite clear. 

Fig. 3.5 Logarithmic plot of the shear rate-dependent viscosity of a narrow molecular weight distribution PS (A) at 180°C, showing the Newtonian plateau and the Power Law regions and a broad distribution PS( ). [Reprinted with permission from W. W. Graessley et al., Trans. Soc. Rheol., 14, 519 (1970).]...

The upper limit of the Newtonian plateau is dependent on Mw and the melt temperature. Commonly, it is roughly in the region y = 10 2s 1. Low viscosity fiber-forming Nylon and polyethylene terephthalate (PET) are important exceptions, as their Newtonian plateau extends to higher shear rates. 

The transition from the Newtonian plateau to the Power Law region is sharp for monodispersed polymer melts and broad for polydispersed melts (see Fig. 3.5). 

The three parameters are a, which is the slope of the curve log(/y/— 1) vs. log(r/Tj /2 ) ii/2, which is the shear stress value, where r = t 0/2 and t]0, which is the zero shear viscosity. Thus the Ellis model matches the low shear Newtonian plateau and the shearthinning region. 

These equations are solved numerically under the assumptions of velocity, shear stress, and temperature continuity at all interfaces. They use the Sabia 4-parameter viscosity model (69), because of its ability to include the Newtonian plateau viscosity, which is important for multilayer extrusion, because of the existence of low shear-rate viscosities at the interfaces. 

The advantage of these models is that they predict a Newtonian plateau at low shear rates and thus at low shear stresses. We will see back these models in Chap. 16 where an extra term 7700 is added to the equations to account for the viscosity of polymer solutions at high shear rates. At high shear rates the limiting slopes at high shear rates in log r) vs. log y curves are for the Cross, the Carreau and the Yasuda et al. models —m, (n-1) and (n-1), respectively. 

Polyester BB1 was run twice in steady mode at 290°C (Figure 10), and shows that the orientational effect of the first run has a drastic effect on steady shear viscosity. In the first run the log viscosity vs. log shear rate had a slope of -0.92 (solid like behaviour, yield stress), but in the second run a pseudo-Newtonian plateau was reached from approx. 1 sec 1. Capillary viscosity values corresponded reasonably well with the second run steady shear data. The slope at high shear rates was close to -0.91 which corresponds nicely to the first-run steady shear run. All this could suggest, that this system is not completely melted, but still has some solid like regions incorporated. At 300°C capillary viscosity data showed an almost pseudo-Newtonian plateau. This corresponds quite well to the fact that fiber spinning as mentioned earlier was difficult and almost impossible below 290°C, but easy at 300°C. At an apparent shear rate of 100 sec 1, a die-swell was found to be approximately 0.95. 

Aqueous pectin dispersions show flow behavior similar to many other polysaccharide solutions. Flow curves of specific viscosity rpp vs. shear rate have a Newtonian plateau (constant r sp) at low shear rates, followed by a shear thinning region at moderate shear rates (Morris et al., 1981). Most pectin solutions have relatively low viscosity compared to some other commercial polysaccharides, such as guar gum, mainly because of the lower MW. Consequently, pectin has limited use as a thickener. 

The Dynamic flow. The flow curves, n vs. u In Fig. 22, were not corrected for the apparent yield stress. For PP and LLDPE-A the curves nearly reached the Newtonian plateau and the Cole-Cole plots were found to be seml-clrcular Indicating that Oy = 0, However, for blends the situation Is less clear. Judging by the flow curves for BL, BL-1 and BL-2 at low deformation rates, the Newtonian plateau seems to be far away. This may Indicate the Incipient yield stress. To clarify this point n" vs. n was plotted In Fig. 23. An onset of the second relaxation mechanism Is visible. The long relaxation times In BL may only originate In the Interphase Interactions. These usually lead to the presence of the apparent yield stress. 

Viscosity and the Power-Law Index of Wood-Plastic Composite Materials Let us consider in more detail how fillers tend to make the system more shear thinning, that is, to decrease the power-law index. At lower shear rates or frequencies, neat plastics often exhibit a Newtonian plateau, that is, a higher apparent power-law index, and in the presence of fillers, the plateau often turns upward or even disappears. In other words, the addition of filler often makes the power-law plot more steep, that is, shifts it to a more uniform straight line dependence of viscosity verses shear rate (or frequency). 

Figure 17.7 shows that shear rate and frequency are almost identical for neat polymers that is, the Cox-Merz rule (see above) is valid for these systems. The power-law index n, calculated from the slope of the two viscosity curves in Figure 17.7, would be the same (excluding data at very low frequencies, at so-called Newtonian plateau). But for filled plastics this rule is not applicable, and one will get different values of the power-law index from the two viscosity curves. In other words, one will obtain much higher viscosity data from a parallel plate rheometer. 

Pseudoplastic Flows For suspensions, the most common type is a pseudoplastic flow curve with the so called upper, and lower, r, Newtonian plateau [Cross, 1965, 1970, 1973] °°... 

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... 

Theoretically and experimentally, p vs. shear stress show a sharp peak at the stresses corresponding to a transition from the Newtonian plateau to the power-law flow, i.e., to the onset of the elastic behavior (see Figure 9.9). 

When assessing the rheological behavior of PA/PO blends, a strong effect of shear forces upon should be considered. The reason is a qualitative difference between the flow curves for PO and PA. Aliphatic PAs show an extended Newtonian plateau typical of polymers with a narrow MWD (71). PA6, for instance, can retain the Newtonian pattern of flow (72) up to a shear rate of 10 s . The curve describing the relationship of rj versus y for PO is typical of polymers with a wide MWD the anomaly in viscosity ( j decreases with increase in the shear rate) was observed at a much lower shear rate of < 10 s . That is why the effects of viscosity s growth—in the case of PA6/PO compatibilized blends—manifest themselves to the utmost at relatively low shear rates, upto 10 s . Such shear rates are typical of extrusion of polymer materials (72). 

The rheological behavior of these materials is still far from being fully understood but relationships between their rheology and the degree of exfoliation of the nanoparticles have been reported [73]. An increase in the steady shear flow viscosity with the clay content has been reported for most systems [62, 74], while in some cases, viscosity decreases with low clay loading [46, 75]. Another important characteristic of exfoliated nanocomposites is the loss of the complex viscosity Newtonian plateau in oscillatory shear flow [76-80]. Transient experiments have also been used to study the rheological response of polymer nanocomposites. The degree of exfoliation is associated with the amplitude of stress overshoots in start-up experiment [81]. Two main modes of relaxation have been observed in the stress relaxation (step shear) test, namely, a fast mode associated with the polymer matrix and a slow mode associated with the polymer-clay network [60]. The presence of a clay-polymer network has also been evidenced by Cole-Cole plots [82]. 

Results. In Figure 1 are shown the viscosity versus shear stress data for xanthan solutions (.1 to 1 mg/ml) in 0.5M NaCl, 0.04M phosphate buffer, pH 7, containing 0.02% NaN3 as a preservative. The data show a Newtonian plateau between 0.001 and 0.08 dyne/cm for 0.1, 0.2, and 0.3 mg/ml. As the shear stress increases beyond 0.1 dyne/cm, a sharp drop occurs in the viscosity. The viscosity decreases until a second Newtonian plateau is reached at 2-20 dyne/cm. For higher xanthan concentrations the low-shear stress Newtonian plateau occurs at lower shear stresses and the transition between the two plateaus is broadened. Whitcomb and Macosko (2) have reported similar data except that their data did not extend into the low-shear Newtonian range at low concentrations. 

The question now arises, what model(s) make these data understandable in molecular terms In Figure 2 is shown the non-Newtonian intrinsic viscos- ity for the rigid rod model, with length 1.5 m and midpoint diameter 1.9 nm, as calculated by Whitcomb and Macosko (2)- The model gives a satisfactory fit to the experimental data, including the new data for the first Newtonian plateau. 

Only recently has the theory of chain dynamics been extended by Peterlin (J [) and by Fixman (12) to encompass the known non-Newtonian intrinsic viscosity ofTlexible polymers. This theory, which is an extension of the Rouse-Zimm bead-and-spring model but which includes excluded volume effects, is much more complex than that for undeformable ellipsoids, and approximations are needed to make the problem tractable. Nevertheless, this theory agrees remarkably well (J2) with observations on polystyrene, which is surely a flexible chain. In particular, the theory predicts quite well the characteristic shear stress at which the intrinsic viscosity of polystyrene begins to drop from its low-shear Newtonian plateau. 

Figure 13.2 Generalized flow curve for non-Newtonian behaviour. (A) shear-thinning (pseudoplastic) behaviour with low shear Newtonian plateau (B) shear-thinniiig behaviour with high shear Newtonian plateau i oo (C) dilatant (shear thidceniiig) behaviour...

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