Steady-state shear viscosity versus

Steady-state shear viscosity versus shear rate for PBLG solutions (molecular weight = 238,000) in m-cresol for several concentrations. The 38 wt% and 40 wt% samples show Region I behavior. (From Walker et al. 1995, with permission of the Journal of Rheology.)... 

FIGURE 6.19 (Upper panel) Steady-state shear viscosity versus shear rate (soUd symbols), dynamic viscosity versus frequency (open symbols), and transient viscosity calculated from Eq. (6.65) versus the inverse of the time of shearing (solid line). (Lower panel) Dynamic storage and loss modulus master curve for the same entangled polybutadiene solution (Roland and Robertson, 2006). 

Steady state shear viscosity versus shear rate for a low density polyethylene melt (solid line) compared to predictions of the Cox-Merz rule, eq 4.2.6 (open points), and the Gleissle mirror rule, eq 4.2.7 (solid points). Replotted from Retting and Laun (1991). 

Fig. E3.5 Steady-state shear viscosity rj and first normal stress coefficient i, obtained from dynamic measurements versus shear rate for a low-density polyethylene melt, melt I. [H. M. Laun, Rheol. Ada, 17, 1 (1978).]...

In this chapter, we have presented the rheological behavior of homopolymers, placing emphasis on the relationships between the molecular parameters and rheological behavior. We have presented a temperature-independent correlation for steady-state shear viscosity, namely, plots of log ri T, Y) r](jiT) versus log or log j.y, where Tq is a temperature-dependent empirical constant appearing in the Cross equation and a-Y is a shift factor that can be determined from the Arrhenius relation for crystalline polymers in the molten state or from the WLF relation for glassy polymers at temperatures between and + 100 °C. 

Figure 10.21 gives plots of steady-state shear viscosity r] versus y for an injection-molded specimen of ether-based MDl/BDO/POTM TPU specimen at 170, 180, and 190 °C, which was obtained from a cone-and-plate rheometer at low shear rates and... 

Figure 1-7 shows schematic curves of the steady-state shear stress and shear viscosity versus shear rate for solid-like and liquid-like complex fluids. For a solid-like complex fluid, the steady-state shear stress is independent of shear rate (Fig. l-7a), and so the shear viscosity decreases with increasing shear rate asA ()>) oc y K A decreasing shear viscosity with inrreasing shear rate, is referred to as shear thinning. For the liqiiid-... 

Basically, a constant stress cr is applied on the system and the compliance J(Pa ) is plotted as a function of time (see Chapter 20). These experiments are repeated several times, increasing the stress in small increments from the smallest possible value that can be applied by the instrament). A set of creep curves is produced at various applied stresses, and from the slope of the linear portion of the creep curve (when the system has reached steady state) the viscosity at each applied stress, //, can be calculated. A plot of versus cr allows the limiting (or zero shear) viscosity /(o) and the critical stress cr (which may be identified with the true yield stress of the system) to be obtained (see also Chapter 4). The values of //(o) and <7 may be used to assess the flocculation of the dispersion on storage. 

It should be noted that the Doi and Ohta theory predicts only an enhancement of viscosity, the so-called emulsion-like behavior that results in the positive deviation from the log-additivity rule, PDB. However, the theory does not have a mechanism that may generate an opposite behavior that may result in a negative deviation from the log-additivity rule, NDB. The latter deviation has been reported for the viscosity versus concentration dependencies of PET/PA-66 blends (Utracki et al. 1982). The NDB deviation was introduced into the viscosity-concentratiOTi dependence of immiscible polymer blends in form of an interlayer slip caused by steady-state shearing at large strains that modify the morphology (Utracki 1991). 

Owing to experimental difficulties, steady-state shear measurements of Ni and 0 2 are relatively rare. Their rate of shear gradients, Ni/y,r] = 012/y usually show a similar dependence ]322]. The value of the complex viscosity ist] >t]. In the steady shear flow of a two-phase system, the stress is continuous across the interphase, but the rate of deformation is not. Thus, for polymer blends, plots of the rheological functions versus stress are more appropriate than those versus rate, that is, a Ni = Ni oi2) plot is similar to G = G (G"). 

From the slope of the linear portion of the creep curve (after the system reaches a steady state), the viscosity at each applied stress, is calculated. A plot of % versus (T (Figure 7.40) allows one to obtain the limiting (or zero shear) viscosity and the critical stress eta (which may be identified with the true yield stress of the system). 

Figure 1.5 Plots of shear viscosity (rj) versus shear rate (y) for (O) 4 wt% aqueous solution of polyacrylamide and (A) glycerin in steady-state shear flow at 25 °C.

Figure 14.4 gives plots of viscosity (log ri) versus cure time for different shear rates (y) when a general-purpose unsaturated polyester (Aropol 7030, Ashland Chemical Company) was subjected to steady-state shear flow in a cone-and-plate rheometer under an isothermal condition at 60 C. The resin had been prepared by the reaction of propylene glycol with a mixture of maleic anhydride and isophthalic anhydride. The resin system used in Figure 14.4 was cured with BPO as initiator and a solution of 5 wt % A,A-dimethylaniline, diluted in styrene, as accelerator. The following observations are worth noting in Figure 14.4. At an early stage of curing, the rj increased slowly, but then...

Figure 11.13 Steady-state uniaxial extensional viscosity normalized by the zero shear viscosity versus Weissenberg number Wi = re for nearly monodisperse polystyrene melts with molecular weights of 200,000 (-i-) and 390,000 ( ), where r is roughly the reptation time.The line is the prediction of the Doi-Edwards theory (from Bach etal. [56]).

Basic Protocol 2 is for time-dependent non-Newtonian fluids. This type of test is typically only compatible with rheometers that have steady-state conditions built into the control software. This test is known as an equilibrium flow test and may be performed as a function of shear rate or shear stress. If controlled shear stress is used, the zero-shear viscosity may be seen as a clear plateau in the data. If controlled shear rate is used, this zone may not be clearly delineated. Logarithmic plots of viscosity versus shear rate are typically presented, and the Cross or Carreau-Yasuda models are used to fit the data. If a partial flow curve is generated, then subset models such as the Williamson, Sisko, or Power Law models are used (unithi.i). 

Steady State Measurements Fig. 1 shows the shear rate-shear stress curves at various bentonite concentrations (calculated on the basis of the continuous phase) Hysteresis in the shear rate-shear stress curves was insignificant and the correlation between the ascending and descending curves was within experimental error. The results shown in Fig. 1 were therefore, the mean value of the ascending and descending curves. In the absence of any bentonite the suspension was Newtonian, whereas all suspensions containing bentonite at concentrations > 30 g dm were all pseudoplastic. This is illustrated from a plot of viscosity versus shear rate (Figure 2) which shows an exponential reduction of h with increase in shear rate. 

The generic flow properties of soft particle glasses are exemplified in Fig. 17, which shows the variations of the shear stress versus the shear rate measured at steady state for microgel pastes and compressed emulsions [187]. The flow curves in Fig. 17a obtained for microgel pastes with varying particle concentration, crosslink density, salt concentration, and solvent viscosity show the same qualitative behavior a minimum shear stress, the yield stress of the material, below which the... 

Figure 9.9 shows a classical data set by Meissner on the low-density polyethylene whose transient shear stress was shown in Figure 2.6. The tensile stress divided by the stretch rate is plotted versus time, together with three times the transient development of the zero-shear viscosity. The data deviate from a single curve at values of the strain (stretch rate multiplied by time) of about 2. There is a plateau at low stretch rates at a Trouton ratio of 3, but the plateau is followed by a sharp increase, and in general the tensile stress greatly exceeds three times the shear viscosity. (The shear viscosity for this polymer decreases with shear rate, so the deviation from three times the viscosity is greater than it would appear when the comparison is based only on the zero-shear viscosity.) The fact that the data lie above the band of three times the shear values at short times is probably an experimental artifact. A steady-state stress is not reached in these experiments, except perhaps at the highest and lowest stretch rates. An apparent steady state has been reported in other measurements.

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