Apparent extensional viscosity

Accordingly, the measurements of both F and Q and the experimental determination of the values of v versus z permit us to determine the apparent extensional viscosity. This parameter can alternatively be obtained from the total strain, which, according to Eq. (13.117), is given by... 

At the entrance of a die, there is a converging field which produces a strong extensional flow. Cogswell (24) has suggested a procedure for calculating an apparent extensional viscosity, from... 

Using experimental results obtained with the three Santoprene grades studied, the entrance pressure drop and the apparent extensional viscosity were calculated according to equations (18) and and (19). Results are given in graphical terms in Figures 11 and 12 respectively. 

The Apparent Extensional Viscosity The evolution of filament diameter is driven by the capillary pressure and resisted by the extensional stress in the fluid. Thus, measurements can also be represented in terms of an apparent extensional viscosity, defined as... 

Fig. 3 12 Melt spinning measurement for apparent extensional viscosity [14].

If and are known, one can calculate an apparent extensional viscosity as the ratio... 

Figure 9.9 Variation of apparent extensional viscosity with extensional rate for caicium carbonate fiiied polypropyiene at 200°C with different levels of filler loading as indicated. (Reprinted from Ref. 86 with kind permission from John Wiley Sons, Inc., New York, USA.)...

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. 

Fig. 23.6 Apparent extensional viscosity r as a fimcti4 pm, for C, D ca. <2 pm...

Uniaxial exensional viscosity by rod pulling (o) compared to apparent extensional viscosity by bubble collapse (A). From Munstedt and Middleman (1981). 

We will see that these are usually limited to use at strain rates well below 10 s . In order to reach higher rates, the drawdown of an extruded filament (melt spinning) and the converging flow at the entrance to a capillary have been used to determine apparent extensional viscosities. 

We have seen that rheometers capable of accurate measiuements of extensional flow properties are limited to use at low Hencky strain rates, usually well below 10 s . In order to reach higher strain rates, the drawdown of an extruded filament ( melt spinning ) and the converging flow into an orifice die or capillary have been used to determine an apparent extensional viscosity . Since the stress and strain are not imiform in these flows, it is necessary to model the flow in order to interpret data in terms of material functions or constants. And such a simulation must incorporate a rheological model for the melt under study, but if a reliable rheological model were available, the experiment would not be necessary. This is the basic problem with techniques in which the kinematics is neither controlled nor known with precision. It is necessary to make a rather drastically simplified flow analysis to interpret the data in terms of some approximate material function. 

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