Extensional thinning

The origin of the Byrd Subglacial Basin is still uncertain because it has also been attributed to extensional thinning of continental crust in the back-arc associated... 

The extensional viscosity functions of emulsions were characterized using a Capillary Breakup Extensional Rheometry (CaBER). The apparent extensional viscosities ) of SE-la emulsions as a function of strain rate e are given in Fig. 23.5 for the different mean emulsion drop sizes of 2,4, and 10 pm. From this, an extensional viscosity characteristics for the emulsion with a drop size of 10 pm was derived close to constant and rather low (ca. 0.2 Pas, Newtonian-like). For emulsion drop sizes of 2 and 4 pm, pronounced extensional thinning was observed in the low elongation rate domain, whereas some pronounced extensional thickening behavior was monitored in the higher elongation rate domain. 

Suppose that for viscoelastic fluid X we measure the ratio as -0.2 at low shear rates. In a slow steady uniaxial extensional flow, should we expect fluid X to show extensional thickening or extensional thinning ... 

This work shows that high shear rates are required before viscous effects make a significant contribution to the shear stress at low rates of shear the effects are minimal. However, Princen claims that, experimentally, this does not apply. Shear stress was observed to increase at moderate rates of shear [64]. This difference was attributed to the use of the dubious model of all continuous phase liquid being present in the thin films between the cells, with Plateau borders of no, or negligible, liquid content [65]. The opposite is more realistic i.e. most of the liquid continuous phase is confined to the Plateau borders. Princen used this model to determine the viscous contribution to the overall foam or emulsion viscosity, for extensional strain up to the elastic limit. The results indicate that significant contributions to the effective viscosity were observed at moderate strain, and that the foam viscosity could be several orders of magnitude higher than the continuous phase viscosity. 

Figure 3.2 (Case 1) shows a simple uniaxial extensional flow created by the uniform stretching of a rectangular or a thin filament in the 1 direction. For this flow, 22 = - n /2, and because of the incompressibility assumption, 22 = 33. Thus, in Eq. 3.1-1, m = —0.5, giving the following rate of deformation matrix...

Thus, in order to create a steady simple uniaxial extensional flow, the rheometer must cause the thin filament length to increase exponentially in time. 

Figure 3.2 shows planar extensional flow generated by the uniform stretching of a thin wide sheet or film in one direction only, while allowing the thickness in the perpendicular direction to decrease. Thus, / 11 = —e33 and 22 = 0. Therefore, m = 0 in Eq. 3.1-1, giving... 

Since homogenous melts are covered in a later account of pressure build-up and power input in the extruder (Chapter 7), this chapter confines itself to the flow behavior of homogenous unfilled polymer melts and on the introduction of the most important rheological parameters such as viscosity, shear thinning, elasticity, and extensional viscosity. The influence of these rheological properties on simple pressure- and drag flows is demonstrated, while the influence of rheological parameters on pressure build-up and power input in the extruder is described in more detail in Chapter 7. 

In Sect. 15.4 it was shown how the shear thinning behaviour of the viscosity could be described empirically with the aid of many suggestions found in literature. It was not mentioned there that the first normal stress coefficient also shows shear thinning behaviour. In this Sect. 15.5 it became clear that also the extensional viscosity is not a constant, but depending on the strain rate upon increasing the strain rate qe the extensional viscosity depart from the Trouton behaviour and increases (called strain hardening) to a maximum value, followed by a decrease to values below the zero extensional viscosity. It has to be emphasised that results in literature may show different behaviour for the extensional behaviour, but in many cases this is due to the limited extensions used,... 

Figure 1-14 compares the time-dependent extensional viscosity to the time-dependent shear viscosity, after onset of flow, at various shear and extension rates, for the same molten polyethylene described in Figs. 1-9 to 9-11 (Meissner 1972). This figure shows that the behavior of the extensional viscosity can be very different from that of the shear viscosity the former increases while the latter decreases with increasing strain rate at a fixed time after inception of steady flow. Thus, while the shear viscosity is shear thinning, the extensional viscosity is extension thickening. 

The uniaxial extensional viscosity rj(s) and the viscometric functions rj(y) and ki(y), predicted by the Doi-Edwards model for monodisperse melts, are shown in Fig. 3-32. The Doi-Edwards model predicts extreme thinning in these functions the high-shear-rate asymptotes scale as 17 oc oc y , and4 i oc The second normal... 

As discussed in Section 12.3.3, unusual time- and shear-rate-dependencies have been reported for some wormy micellar solutions at dilute concentrations—for example, 1-5 mTAB/NaSal. At higher concentrations, 7-250 mM, of a similar surfactant, tetrade-cyltrimethyammonium bromide in NaSal, the extensional viscosity increases with in-creasing extension rate until a maximum is reached, and extension thinning then follows Thomme and Warr 1994). Prud homme and Warr interpret the maximum as the critical... 

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