Newtonian value

On the contrary, the swell decrease with the increase in filler content was attributed to the lesser amount of elastic polymer chains in the system to recover and swell at the exit. As the filler content was increased, the swell was approaching the Newtonian value of 13% [21]. 

The fully established friction factor for turbulent flow of a viscoelastic fluid in a rectangular channel is dependent on the aspect ratio, the Reynolds number, and the Weissenberg number. As in the case of the circular tube, at small values of Ws, the friction factor decreases from the newtonian value. It continues to decrease with increasing values of Ws, ultimately reaching a lower asymptotic limit. This limiting friction factor may be calculated from the following equation ... 

In this same spirit, it is proposed that the intermediate values of the heat transfer coefficient lying between the newtonian value and the lower asymptotic limit be estimated from the pipe flow correlation shown in Fig. 10.28 [114]. This approach should give reasonable estimates, at least for aqueous polyacrylamide and polyethylene oxide solutions. 

Newtonian value of 3.8) the dispersed phase could not be deformed. By contrast, lower bounds of A, were not established for polymer blends. 

It is usual, in practice, to ignore the Rabinowitsch equation and to assume that the velocity profile for the polymer liquid is parabolic to within the required error. With this assumption the wall shear rate is taken to be given by the Newtonian value, so that, from eqns 7.13 and 7.17, the apparent viscosity is... 

Fig. 82 will illustrate the conditions in this the coefficient of viscosity indicated by Poiseuille s law is plotted against shearing stress. A normal liquid is characterized by a constant rj and appears in the diagram as a horizontal line. Elastic fluids, or solutions, have a larger 77 at small t values, which decreases slowly to the Newtonian value. Super-fluid solutions, on the other hand, show normal behavior under the smallest shearing forces and progressively lower values for 77 with increasing r. 

Newtonian systems, an upper bound for the viscosity ratio, X, has also been reported for polymer blends - above certain value of X (which could be significantly larger than the Newtonian value of 3.8) the dispersed phase could not be deformed. By contrast, lower bounds of X were not estabhshed for polymer blends. 

Lumley kept the viscosity in the laminar sublayer at its Newtonian value, but he assumed an increased viscosity t/j in... 

Below a critical stress, eta, the viscosity reaches a limiting value, namely the residual (or zero shear) viscosity ctci may be denoted as the true yield stress of the emulsion, i.e. the stress above which the "structure of the system is broken down. Above o er, decreases rapidly with further increase of the shear stress (the shear thinning regime). It reaches another Newtonian value rj, which is the high shear limiting viscosity. 

For most practical suspensions (with > 0.1 and containing thickeners to reduce sedimentation) a plot of viscosity depends on the applied shear rate). The most common flow curve is shown in Figure 7.42 (usually described as a pseudo-plastic or shear thinning system). In this case, the viscosity decreases with increasing shear rate, reaching a Newtonian value above a critical shear rate. 

Viscosity, coefficient It is the shearing stress necessary to induce a unit velocity gradient in a material. In actual measurement, the viscosity coefficient of a material is obtained from the ratio of shearing stress to shearing rate. This assumes the ratio to be constant and independent of the shearing stress, a condition satisfied only by Newtonian fluids. Consequently, in all other cases that includes plastics non-Newtonian), values obtained are apparent and represent one point in the flow chart. Inherent viscosity refers to a dilute solution viscosity measurement where it is the ratio of the natural logarithm of the relative viscosity to the concentration of the plastic in grams per 100 ml of solvent. 

Numerical predictions of drag at Re = 40 and 100 Viscoelasticity reduces the drag below its Newtonian value Oseen-type linearization employed predicted upstream displacement and lowering of drag due to viscoelasticity (zero Reynolds number)... 

These expressions simplify to the correct Newtonian values when n is set to 1. We can invert these expressions so that given a known shear stress and a measured viscosity at that stress, the velocity can be calculated. 

Thus, one measures creep curves as a function of the applied stress (starting from a very small stress of the order of 0.01 Pa). This is illustrated in Fig. 3.45. The viscosity Pu (which is equal to the reciprocal of the slope of the straight portion of the creep curve) is plotted as a function of the applied stress. This is schematically shown in Fig. 3.46. Below a critical stress the viscosity reaches a limiting value, p(o) namely the residual (or zero shear) viscosity. Above a , p decreases rapidly with a further increase in the shear stress (the shear thinning regime). It reaches another Newtonian value Poo, which is the high shear limiting viscosity. 0, may be identified as the critical stress above which the structure of the suspension is broken down . Ucr is denoted as the true yield stress of the suspension. 

Note that substituting the Newtonian values of H and L from Eq. 133 into Eq. 135 yields... 

Furthermore, we observe that under vanishing stretch rates, the uniaxial extensional viscosity, rje ( ). tends to its Newtonian value given by... 

Therefore we can conclude that as long as -lAa.o/V i.o < 0.5, the first departures of from the Newtonian value will be positive. Hence fluid X will be extension thickening at low extension rates. A similar calculation for equal biaxial extension (Larson, 1988) shows that rn, = 6r] - 6(rjt + 2 2) ... 

The location of the shear thinning region on the reduced stress axis can be characterized by the value of a critical reduced stress Xc (i.e., the reduced stress for which the viscosity reaches the average value between the two Newtonian values). This critical stress increases with concentration up to volume fractions of 0.50 and then decreases to zero at maximum packing (Figure 10.5.2). 

Highly-branched, heterogeneous polymers such as LDPE have very broad relaxation time spectra, and this results in a very broad range of shear rates over which viscosity data make the transition from the Newtonian limiting value to a power-law region. In fact, it is often impossible to reach the Newtonian value using commercial rheometers, because the shear rate required is extremely low. The LDPE viscosity data shown in Fig. 10.10 were obtained using a specially modified rotational rheometer, the operation of which required exceptional skill. 

Figure 4 shows the transient evolution of the extensional viscosity at varying strain rates for PHA Sample I. The plots follow the start-up to reach a steady state plateau value. At short times, the curves fall on top of one another. At high strain rates, we observe a slight decrease in the steady state extensional viscosity for both PHA samples. This could indicate that the two PHA samples are strain-rate thinning, as predicted by the Doi-Edwards tube model [9]. The Trouton Ratio (Tr), defined as the ratio of the extensional viscosity to the zero-shear viscosity of the polymer, was also investigated for the two PHA samples. For both PHA samples, the Trouton Ratio maintained the Newtonian value of Tr=3 at low strain rates. 

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