Transient extensional viscosities

In Fig. 15.26 an example is given of Eq. (15.97) for a Maxwell element with G = 1000 N/m2 and t = 1 s. For small extensional rates of strain, the extensional viscosity is constant and equal to 3000 N s/m2. For higher extensional rates of strain, the viscosity increases. At the extensional rate of strain of 0.5 s-1 there is a transition to infinite extensional viscosities. The dotted line is the transient shear viscosity r)+(t) at low shear rates and equal to 14 of the transient extensional viscosity r)+ (f) at low extensional rates of strain. 

In Fig. 15.27, the transient extensional viscosity of a low-density polyethylene, measured at 150 °C for various extensional rates of strain, is plotted against time (Munstedt and Laun, 1979). Qualitatively this figure resembles the results of the Lodge model for a Maxwell model in Fig. 15.26. For small extensional rates of strain (qe < 0.001 s ) 77+(f) is almost three times rj+ t). For qe > 0. 01 s 1 r/+ (f) increases fast, but not to infinite values, as is the case in the Lodge model. The drawn line was estimated by substitution of a spectrum of relaxation times of the polymer (calculated from the dynamic shear moduli, G and G") in Lodge s constitutive equation. The resulting viscosities are shown in Fig. 15.28 after a constant value at small extensional rates of strain the viscosity increases to a maximum value, followed by a decrease to values below the zero extension viscosity. 

FIG. 15.26 Transient extensional viscosity, (t), vs. time, calculated with Lodges constitutive equation for a Maxwell element with G = 1000 N/m2 and r = 1 s. 

FIG. 15.27 Transient extensional viscosity, r/+ (f)of low-density polyethylene LDPEIUPAC A at 150 °C, vs. time, for various extensional rates of strain. From Munstedt and Laun (1979). Courtesy Springer Verlag. 

In the same way, but much more complicated, with a damping function depending on the Hencky strain, it proved to be possible to calculate the transient extensional viscosity as a function of qe. The result is illustrated in Fig. 15.30 for the same polymer. It shows that extensional viscosity remains finite and increases with increasing strain rate up to a maximum at qe = 2 s, after which it decreases again. The calculated lines coincide quite well with the experiments, but the calculated viscosities are somewhat too high. 

FIG. 15.30 Transient extensional viscosity of LDPE Melt I for extensional rates of strain varying from 0.001 to 1 s-1, at 150 °C. From Wagner and Meissner (1980). Courtesy John Wiley 8t Sons, Inc. 

FIG. 16.21 Apparent or transient extensional viscosity of the round robin test fluid Ml as a function of Hencky strain, measured in many different devices (lames and Walters, 1993). The various instruments are spin line Binding et al. Ferguson and Hudson Ngyuen et al. horizontal spin line Oliver open siphon Binding et al. stagnation flow. Laun and Hingmann Schweitzer et al. contraction flow. Binding et al. ... 

Often, it is not possible to reach a steady state in extension and it is convenient to define a transient extensional viscosity, tje, that is a function of time, t, and the extensional strain rate, e, (Barnes et al., 1989). 

Transient extensional viscosity (t j+) of PE-2, PE-2 embedded with polybutylene terephthalate (PBT) drops, and PE-2 embedded with PBT fibrils at extension rate of 0.05 [1/sec] and 150°C. 

The morphology may affect the rheological properties under shear and extension in different manners. If the dispersed phase is rigid but deformable, it more effectively contributes to the rheological properhes of the blend. In Section 8.3.2, the transient extensional viscosity was measured at a lower temperature than the melting temperature of the dispersed phase. Rigid fibrils enhance extensional viscosity even with a small amount of the dispersed phase (1 wt%). Nevertheless, the morphological effect under shear flow is not... 

The fibre-windup technique [Padmanabhan et al., 1996] can provide transient extensional-viscosity data using modified rotational shear rheometers. One end of the sample is clamped while the other end is wound around a drum at a constant rotational speed to achieve a given extension rate, with the rheometer s torque transducers being used to obtain the extensional viscosity. The technique is claimed to provide valuable extensional viscosity data for high viscosity liqmds. 

As indicated in Figure 7.1.2, there are several types of extensional deformation all can be described using the convention given in Chapter 4, which defines two transient extensional viscosities (Meissner, 1985)... 

For mobile liquids, the use of this kind of controllable instruments is practically impossible. For these liquids, the non-controllable measurement techniques are available only and in general an apparent transient viscosity will be obtained. Nevertheless these measurements are still of great value, because in many cases they approximate industrial process conditions. Mostly used is the spinning line rheometer, where an elastic liquid is pressed through a spinneret and the liquid is pulled from the die by winding the filament around a rotating drum or by sucking the tread into a capillary tube. This is schematically shown in Fig. 15.25. A serious problem is the translation of the obtained data to the extensional viscosity. Many other non-controllable devices are discussed by,... 

The FENE-P model is able to prediet qualitatively many effects in dilute polymer solutions sueh as shear thinning, first normal stress difference, and a stififer response in extensional viscosity. The model is an improvement on the Maxwell model, but it does not always behave well in transient flows. 

Phan-Thien and Tanner used data of Meissner for the low-density polyethylene in Figure 9.9 to test the model, with = 0.2 and s = 0.01. The fit to steady shear viscosity and normal stresses is good, and the transients are fit reasonably well the shear data are insensitive to the value of s as expected. The fit to the extensional data at three stretch rates is shown in Figure 9.13. The agreement is quite good, especially when it is recalled that there is probably an experimental artifact at short times that causes the data to be high. The model predicts an approach to a steady extensional viscosity that scales as 1/e, but the data do not extend sufficiently far to test the prediction. 

Figures 6a-b show the extensional viscosity of the branched samples at 180°C. The measurements were conducted at different extension rates and compared to the linear viscoelastic (LVE) envelope determined by a step strain experiment at the same temperature. The two samples show strain hardening characterized by a deviation of the transient viscosity from the LVE envelope. The deviation at all extension rates confirms the presence of chain branching but more importantly shows a relationship between the extension rate and the extent of hardening. This correlation is considered crucial during parison inflation as it allows better control during the inflation of the parison.

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