Extensional rate biaxial

For an unvulcanized polydimethylsiloxane, the biaxial viscosity was approximately six times the shear viscosity over the biaxial extensional rates from 0.003 to 1.0 s (Chatraei et al., 1981), a result expected for Newtonian fluids, that is, the relationship between the limiting value of biaxial extensional viscosity (j, ) at zero strain rate and the steady zero-shear viscosity (i o) of a non-Newtonian food is ... 

Doughs with different protein contents (13.2, 16.0, and 18.8% based on 14%MB) showed different biaxial extensional viscosities (Huang and Kokini, 1993). Figure 31 shows that the biaxial extensional viscosity approached 6tj at an extensional rate of 7.3 x 10 sec . Strain thinning behavior was observed in dough during biaxial extension. 

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

Analyze lubricated squeezing flow to determine biaxial extensional viscosity (T)R), which is calculated from biaxial stress (cB) and biaxial extensional strain rate (eB). 

Dimensional Changes in Planar and Biaxial Extensional Flows Determine the rate of dimensional changes that have to be applied on a flat film in order to generate (a) planar extension, and (b) biaxial extension flows. 

Biaxial extensional flow is extensional flow in two directions with the same constant extensional strain rate qe. If the volume is constant then... 

M.Takahashi, T.Isaki, T.Takigawa, T.Masuda, Measurement of biaxial and uniaxial extensional flow of polymer melts at constant strain rates, J. Rheol. 31 (1993), 827-846. 

The biaxial extensional viscosity ( b) was defined as the ratio of the normal stress difference and the radial extension rate assumed to be half the strain rate ... 

Another axisymmetric extensional flow is biaxial extension. In this deformation, there is a compression along the axis of symmetry that stretches in the radial direction, as shown in Fig. 9. The principal strain rate is defined as... 

FIG. 31. Biaxial extensional viscosity and shear viscosity vs extension and shear for wheat flour dough with 16.0% protein content (Huang and Kokini, 1993). tjb is biaxial extensional viscosity, ij is shear viscosity. 6 ij superimposed with tjb indicate that the biaxial extensional viscosity are about five times larger than shear viscosity at the equivalent shear rate. 

Biaxial extensional viscosity Tbmperature, time, strain rate... 

The superposition argument outlined in Figure 5.12 shows that the energy release rate associated with advance of the delamination front due to this loading depends only on and on the extensional force reduction Ata = ta — t-m- The stress state in (B) is a uniform equi-biaxial stress of magnitude —tm the state (C) is the superposition of states (A) and... 

Figure 7.7.7 shows data collected in suction (uniaxial extension) and expulsion (biaxial or compression) plotted as apparent viscosity versus apparent extension rate. The liquid was Newtonian a glycerin-water mixture with shear viscosity of 1.6 poise. The dashed line gives Stjo, the value we would expect for pulling of the sample in air. We see that the values are closer to Ar)o because of the departure of the flow from ideal extensional flow. The solid lines represent calculations by Schunk et ai. (1990), who have carried out a fairly complete analysis of this flow, solving the Na-vier-Stokes equations via the finite element method. 

Melt behavior has been studied using uniaxial (also called simple or tensile), biaxial, and planar extensional flows [9, Ch. 6]. However, only the first two of these are in general use and will be discussed here. A uniaxial extensional rheometer is designed to generate a deformation in which either the net tensile stress Tg or the Hencky strain rate e (defined by Eq. 10.89) is maintained constant. The material functions that can, in principle, be determined are the tensile stress growth coefficient / (f, ), the tensile creep compliance, andthetensile... 

All aspects of crystallization dynamics of polymers, the strong dependence on the temperature, cooling rate, and the application of flow, are of relevance to highspeed FS (uniaxial extensional flow) [1-3,13] and during biaxial extensional flow, that is, flhn blowing [28,93-95]. 

Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity identified aind measured are uniaxial or simple, biaxial, and pure shear. Uniaxial viscosity is the only one used to characterize fluids. It has been employed mainly in the study of polymer melts, but also for other fluids. For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity ( fe)uni = 3/ . This is confirmed at very low shear rates in Figure 13, which provides a typical example of the extensional viscosity behavior of a polymer (129). The two other extensional viscosities are used to study elastomers in the form of films or sheets. Uniaxial and biaxial extensions are important in industry (118,125-128,130,132), the former for the spinning of textile fibers and roller spattering of paints, and the latter for blow molding, vacuum forming, film blowing, and foam processes. 

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