True extensional viscosity

In these experiments, the tensile force is measured as a function of time, so that at a constant rate of deformation e it is possible to calculate the true tensile stress and the extensional viscosity r/c elastic properties of the deformation can be determined by measuring the elastic strain e. 

If we want to find out how a fluid behaves under extension, we have to somehow grip and stretch it. Experimentally, this is much more difficult than the shear arrangement, especially if the fluid has a low viscosity. Earlier (see Section 5) we saw that it is possible to classify steady extensional flows under the categories of uniaxial, biaxial and planar flows. We will now examine uniaxial testing, since this mode is more commonly employed as a routine characterization tool. Here we encounter two approaches the first seeks to impart a uniform extensional field and back out a true material function, while the second employs a mixed flow field that is rich in its extensional component (e.g. converging flows) and use it to back out a measured property of the fluid which is somehow related to its extensional viscosity. 

A typical example of extensional flow is the flow at the entrance of a capillary die. Cogswell [83] has shown that the pressure losses through sudi dies can be used as a measure of the extensional viscomty. This method has not lined popularity because of the skepticism in acc ting the complex converging-flow patterns at the die entrance as representative of true extensional flow with constant extensional rate. Cogswell [84] did suggest later that the die should be lubricated to reduce the shear flow and the profile of the die wall should vary at all cross sections in such a way as to ensure constant extensional rate along the die axis. Such a rheometer has been known to be developed and used for extensional viscosity data of polystyrene melt [85]. 

In the case of extensional viscosity, unified curves have been presented for a limited number of cases and the data used for coalescence are also-limited. Because of the difficulties in measurement of extensional viscosity, the reliability of the data is often questionable. Because the original data cannot be as trustworthy as in the case of shear viscosity or complex viscoaty data, the master curves of extensional data should be looked at in the same light. In the case dt shear viscosify, the master rheograms for the filled polymers have been shown to be the same as those for the unfilled system. is, of course, true in the medium to high shear-rate region. In the low-shear-rate region, however, the effects of yield stress would dominate and the uniqueness of the curve will be... 

Such an instrument could measure true viscosity, but one would need to use other dies and weights. With such a short die entrance, losses can consume up to half of ptot (recall Figure 6.2.9). Also the ratio of die to reservoir radius is rather large, R/Rr = 0.219, so reservoir losses are significant. Thus the melt index number is a combined measure of shear and extensional viscosity. 

These working equations, along with the limitations and utility of fiber spinning measurements, are summarized in Table 7.5.1. The major problem is that typically is not constant, so the force, which is measured over the entire fiber, is an integration of stresses due to various strain rates and even the upstream shear histmy in the die. For these reasons, the fiber spinning experiment is not a true rheometer, but gives only an iq>paient uniaxial extensional viscosity. 

For polymer melts, fiber spinning results can be compared to true uniaxial extensional viscosity data measured by rod pulling. Figure 7.5.7 shows such a comparison for a low density polyethylene. We see qualitative agreement between the methods but, a very strong effect of upstream history is evident in the fiber data. Both die extrusion velocity and residence time in the die exert a big influence. 

If aji tends to a constant value as stretching proceeds, will also approach a limiting value this is termed either the elongational, extensional, or tensile viscosity, The exten-sional viscosity is a true material property, and is independent both of the technique of measurement and of any assumptions concerning the constitutive behavior of the polymer. For homogeneous materials, its numerical value can be a function of the stretch rate and of the temperature at which the measurement is made. 

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