Low shear Newtonian viscosity

Figure 8 illustrates the influence of NaCl on the low-shear Newtonian viscosity at polymer concentration of 1,000 ppm. The polymer solution viscosity dropped as the salt concentration was increased up to 8 wt%, then it slightly increased. The initial drop in viscosity is due to charge screening effects. However, the slight increase in viscosity at sodium chloride concentrations > 8 wt% is due to the increase in the solvent viscosity because of the presence of salts. 

Figure 8. Effect of sodium chloride on the low-shear Newtonian viscosity at polymer concentration of 1,000 ppm.

Figure 16. Effect of alkali type on the evolution of the low-shear Newtonian viscosity of 1,000 ppm polymer solution.

Solvent viscosity, mPa s [Tj] Intrinsic viscosity, dL/g Ll Low-shear Newtonian viscosity, mPa s... 

Dutta [27] has shown that for most thermoplastic melts lossessing a low-shear Newtonian viscosity plateau), a reasonably good estimate of zero-shear viscosity can be obtained from the knowledge of MFI using Eq. (4.12). 

There is a well-established relation ip for polymer melts between the low shear Newtonian viscosity and MW, rjo = k (Equation 5.6), where X is a constant and n is 3.4 or a very similar number [6]. 

For a given polymer molecule, its motion may be divided into relatively fast motions of the segments which are smaller than Me and relatively slower motions of the whole chain, which is larger than Me. This interpretation may be expanded to include polymers having MW distribution. Considering the whole polymer there must be a relationship between the longest relaxation time (terminal relaxation time) and its MW. An example is the relationship between low shear Newtonian viscosity, rjg, and MW. With commercial gum rubbers, rjg is observed only with low MW polymer or a polymer whose MW distribution lacks the high MW tail. Nevertheless, rjg will be considered for a moment. 

The other models can be appHed to non-Newtonian materials where time-dependent effects are absent. This situation encompasses many technically important materials from polymer solutions to latices, pigment slurries, and polymer melts. At high shear rates most of these materials tend to a Newtonian viscosity limit. At low shear rates they tend either to a yield point or to a low shear Newtonian limiting viscosity. At intermediate shear rates, the power law or the Casson model is a useful approximation. 

The Williamson equation is useful for modeling shear-thinning fluids over a wide range of shear rates (15). It makes provision for limiting low and high shear Newtonian viscosity behavior (eq. 3), where T is the absolute value of the shear stress and is the shear stress at which the viscosity is the mean of the viscosity limits TIq and, ie, at r = -H... 

The experimental evidence concerning the effects of LCB on the non-Newtonian behaviour of polyethylene melts is not as extensive as might be wished. Guillet and co-workers (167) studied fractions of both linear and branched polyethylenes and found that, for a given low shear-rate viscosity. 

Mendelson (169) studied the effect of LCB on the flow properties of polyethylene melts, using two LDPE samples of closely similar M and Mw plus two blends of these. Both zero-shear viscosity and melt elasticity (elastic storage modulus and recoverable shear strain) decreased with increasing LCB, in this series. Non-Newtonian behaviour was studied and the shear rate at which the viscosity falls to 95% of the zero shear-rate value is given this increases with LCB from 0.3 sec"1 for the least branched to 20 sec"1 for the most branched (the text says that shear sensitivity increases with branching, but the numerical data show that it is this shear rate that increases). This comparison, unlike that made by Guillet, is at constant Mw, not at constant low shear-rate viscosity. 

Melt Viscosity. Low shear melt viscosities were measured by Kepes cone-plate viscometer (7) at 150°, 170°, and 190°C. No stabilizer was added to the sample. The flow curves are shown in Figure 6. The viscosities of NMWD are in good agreement with those observed by others (8) the viscosities of BMWD by our measurements are somewhat lower. The Newtonian viscosities, y0, were observed with NMWD sample. With BMWD sample, vo was estimated by extrapolation shown in the figure. The extrapolated values are uncertain they may have been underestimated. The Newtonian viscosities are listed in Table III. 

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. 

At the percolation limit, the rheological behavior of the suspension changes from Newtonian to either the Cross equation with a low shear limit viscosity or the Bingham plastic equation with an apparent yield... 

For Colloid this low-shear Newtonian zone can be observed since the viscosity of these solutions does not change appreciably up to about 100 sec l. From hereon the-viscosity decreases as the shear rate is increased. It has been noted by Mungan (18) and... 

Is such a deformable chain model inconsistent with the non-Newtonian intrinsic viscosity Finding an answer to this question is the goal of this paper. To this end, the viscosity of xanthan solutions was measured over a broad range of shear stress, including especially the low-shear Newtonian limit which has not been measured by Whitcomb and Macosko. The intrinsic viscosity at various shear stresses was then determined and the resultant experimental curve was compared to theoretical expectations for a flexible chain (bead-and-spring) model. 

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. 

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. 

Furthermore, the behavior observed in Figure 10.32 is fairly typical - i.e. at low shear, the viscosity evolves little with the shear, and can therefore be qualified as Newtonian, whereas beyond a critical value of the shear rate, it decreases... 

Figures shows the variation of the apparent viscosity of Alcoflood II75L in deionized water with the shear rate for various polymer concentrations at 30°C. For all polymer concentrations examined, the apparent viscosity decreased with increasing the shear rate. This trend is due to uncoiling and aligning of polymer chains when exposed to shear forces. At shear rates >0.1 s", the viscosity-shear rate relationship was fitted with the power-law model. At shear rates < 0.1 s", the experimental data deviate from the power-law behavior. However, no low-shear Newtonian behavior was observed within the range of shear rates examined.

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