Viscosity at zero shear rate

Figure 8.5. Apparent viscosity-shear rate curves for dilatant fluid, a Newtonian fluid and pseudoplastic fluid which have the same apparent viscosity at zero shear rate...

Intrinsic viscosity at zero shear rate (Part 8). 

The enzymic activity was proportional to the change of the inverse of the numerical average molecular weight per time unit. The linear relationship between Mv and Mn allowed a simple calculation of the activity from the knowledge of the intrinsic viscosity at zero shear rate as a function of the reaction time. A practical example is given. 

Hydrogenated SBCs are often used to modify polyolefins such as polypropylene, polybutylene and polyethylene. One of the unique characteristics of strongly phase-separated block copolymers such as high molecular weight (>50 000) SEBS and SEPS is their response to shear in the melt. These polymers retain their phase-separated structure well above the Tg of the polystyrene because their order-disorder transition temperatures are above processing temperatures. This phase separation strongly inhibits flow in the absence of shear resulting in infinite viscosity at zero shear rates. The application of shear... 

This expression allows the determination of the viscosity at zero shear rate from the time dependence of the relaxation modulus. 

According to Eq. (5.55), the viscosity at zero shear rate is given by... 

The viscosity at zero shear rate is strongly dependent on molecular weight for long chains (q = M > 2Mg), while remains nearly constant... 

The viscosity data of Figure 5 can be reduced to a single curve by replotting nr as a function of /o indicating that the relative viscosity at zero shear rate is a unique function of /0 A relation between dispersion viscosity and

0, derived by Mooney (5) and modified, by Krieger and Dougherty (6), gives... 

The dependence of polymer solution viscosity at zero shear rate (Pp) on the polymer concentration and on salinity may be described by the Flory-Huggins equation (Flory, 1953),... 

Figure 5.20 is an example of the polymer viscosity at different shear rates. The laboratory data were used for fitting in Eq. 5.4. In this case, the water viscosity at zero shear rate was 6 mPa s, and the two fitting parameters, p and y,/2, were 1.8 and 450 s, respectively. Note that according to Eq. 5.4, the calculated 0p at any shear rate can never be higher than j,p at zero shear rate. 

An example is shown in Figure 6.6, lower curve. At very low shear rate, the solution shows Newtonian behavior (no dependence of r] on shear rate), and this is also the case at very high shear rate, but in the intermediate range a marked strain rate thinning is observed. The viscosity is thus an apparent one (/ ,), depending on shear rate (or shear stress). It is common practice to give the (extrapolated) intrinsic viscosity at zero shear rate, hence the symbol [ri]0 in Eq. (6.6). The dependence of t] on shear rate may have two causes. 

The four parameters of this model, namely, rjo, 7oo, 2, and n, are the apparent viscosity at zero shear rate, apparent viscosity at infinite shear rate, time shear relaxation constant, and the exponential index, respectively. The parameter 1 has a unit of time and can assume any value in the range (0, oo). The index n is dimensionless, with 0 < n < 1. Equation 8 is graphically represented in Fig. 1 for illustration. Various parameters assumed for obtaining the plots appearing in Fig. 1 are as follows rjo = 900, rj o = 0.1, and the nondimensional time shear relaxation... 

In the behavior of polymeric liquids two quantities are important. These are steady-state recoverable shear compliance, (as shown above) and steady-state viscosity at zero shear rate, r o- These quantities are related ... 

Fig. lA, Reduced plot of the non-Newtonian viscosity shown in Fig. 1.3, where is the viscosity at zero shear rate, and the time constant is chosen empirically for each solution. Reproduced from W. W. Graessley Adv. Pofym. 

Fig. 5.5. Steady state viscosity at zero shear rate of polystyrene in toluene is plotted against (a) concentration and (b) molecular weight. Reproduced from...

Limiting viscosity at zero shear rate, i.e., at the upper Newtonian plateau... 

Fig. 14. Relative viscosity at zero shear rate as a function of fiber volume fraction. Composites i -C/PE + - C/TPE - TC/PE -TC/TPE. (After ref 65).

Zero shear rate viscosity (the steady-state viscosity at zero shear rate) is influenced by the type of polymer, MW, MWD, and additives. To calculate the increase of zero shear rate viscosity with increasing MW [3], use... 

Figure 4.13 Dependence of viscosity at zero shear rate on the rod-likeness parsuneter for solutions of bacterial HA in NaCI at the biopolymer concentrations ofC=0.5mg/ml (diluted solution) and C= lOmg/ml (semi-dilutedsolution) T,°C=25°C(from the data of Fouissacet al. [39]). Reproduced with permission from [39], Copyright 1993, American Chemical Society...

The empirical equation relating viscosity at zero-shear rate (t]o) to molecular weight for linear amorphous polymers is used to compare PLLA melts with those of conventional polymers. The form of this equation has been applied to the elasticity coefficient, Aq, to further quantify the effect of molecular weight on the elasticity (Cooper-White and Mackay 1999) ... 

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