Extensional viscosity uniaxial

Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity identified and 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 ... 

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). 

The ratio of extensional viscosity r e to shear viscosity r s is known as the Trouton ratio, which is three for Newtonian fluids in uniaxial extension and larger than three for non-Newtonian fluids. For a viscoelastic fluid such as a polymer in solution, the uniaxial extensional viscosity characterizes the resistance of the fluid... 

Underwriters Laboratory UL 94 Standard for Safety, 11 457-458 Undifferentiated chemicals, 20 712 Undiscovered petroleum resources, 18 595 Unfilled tooth restorative resins, 8 333 Uniaxial extensional viscosity, measuring, 21 740... 

Figure 1.14 Uniaxial extensional viscosity rj (open symbols) and shear viscosity r] (closed and half-closed symbols) as functions of time after start-up of steady uniaxial extension or steady shearing for Melt I. (From Meissner, J. Appl. Polym. Sci. 16 2877, Copyright 1972. Reprinted by permission...

A solution or melt composed of such stretchable molecules can be highly springy, especially in extensional flows (Tirtaatmadja and Sridhar 1993). The kinematics of an extensional flow are described in Section 1.4.1.2. From Eqs. (1-6) and (1-9), one can show that for a Newtonian fluid (for which a = 2rjD) the Trouton ratio Tr = f)u/hQ the uniaxial extensional viscosity to the zero-shear viscosity /jo is numerically equal to 3. For polymers, Tr can be much higher than this. Figure 3-2, for example, shows Tr for a... 

Figure 3.2 Trouton ratio, Tr, of uniaxial extensional viscosity to zero-shear viscosity jq after start-up of steady uniaxial extension at a rate of 1 sec i for a Boger fluid consisting of a 0.185 wt% solution of flexible polyisobutylene (Mu, = 2.11 x 10 ) in a solvent composed mostly of viscous polybutene with some added kerosene (solid line). The dashed line is a fit of a multimode FENE dumbbell model, where each mode is represented by a FENE dumbbell model, with a spring law given by Eq. (3-56), without preaveraging, as described in Section 3.6.2.2.I. The relaxation times were obtained by fitting the linear viscoelastic data, G (co) and G"(cu). The slowest mode, with ri = 5 sec, dominates the behavior at large strains the best fit is obtained by choosing for it an extensibility parameter of = 40,000. The value of S — = 3(0.82) n/C(x, predicted from the...

Figure 3.19 The polymer contribution to the steady-state uniaxial extensional viscosity r divided by the polymer contribution to the zero-shear viscosity rjp = r/o — fjj for the dumbbell model with a nonlinear FENE spring and various values of B = ipL. (From Bird et al. Dynamics of Polymeric Liquids, Vol. 2, Copyright 1987. Reprinted by permission of John Wiley Sons, Inc.)...

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... 

Figure 3.39 Uniaxial extensional viscosity rj as a function of time following start-up of steady uniaxial extension at the extension rates e indicated. Data are shown for an unbranched polystyrene (PS I), a high-density polyethylene with short, unentangled side branches (HOPE I), and two low-density polyethylenes (LDPE III and lUPAC A), with long side branches. (From Laun 1984, with permission from the Universidad Nacional Autonoma de Mexico.)------------------------------...

The steady-state uniaxial extensional viscosity rj is given by ([Pg.181]

While the fiber contribution to the steady-state stress tensor at steady-state is modest for shearing flow, its contribution to the stress in extensional flow is large at steady state. In a uniaxial extensional flow, the fibers orient in such a way that the viscous dissipation is maximized. Large values of the extensional viscosity are the result from Batchelor s (1971) theory the uniaxial extensional viscosity is... 

Senouci and Smith (1988) used a simplified analysis for converging flow in a piston-driving capillary rheometer at 120-130°C and obtained ratios of uniaxial extensional viscosities to shear viscosities of maize grits and potato powder in the range of 60-3900. 

Table I. Dynamic Uniaxial Extensional Viscosities and Shear Viscosities...

Figure 6. Dynamic uniaxial extensional viscosities of coal-water fuels formulated with different stabilizers.

Uniaxial extensional viscosity Crystallization temperature Tfemperature, time, strain rate... 

Reactive viscosity of thermosets Uniaxial extensional viscosity Biaxial extensional viscosity First normal stress difference 6721-10 6721-10 A slit die rheometer according to ISO 11443 can also be used. 

DYNAMIC UNIAXIAL EXTENSIONAL VISCOSITIES AND THEIR IMPORTANCE IN THE MECHANICAL STABILITY OF WATER-SOLUBLE CARBOHYDRATE POLYMER SOLUTIONS... 

In mechanical degradation, chain scission does not occur from individual attack on a specific atom of the macromolecular chain, but from the application of a critical stress. The extensional viscosities of high-molecular-weight, synthetic polymers have been studied for the past two decades, in attempts to relate the values with drag reduction behavior. To date the dynamic uniaxial extensional viscosities of aqueous carbohydrate solutions have not been reported. 

S. Soyles, D.A. Dinga, G.P. Glass, J.E. Dynamic Uniaxial Extensional Viscosity. Response in Spray Applications, Polymers as Rheology Modifiers, ACS 462 (1991)... 

In extensional flow, the diagonal components of are non-zero (i.e. T,y = 0 for i j). In the case of uniaxial extension, Th is the primary stress that can be measured, while T22 and T33 are generally equal to the pressiure of the environment. Thus, the uniaxial extensional viscosity rj is defined by. 

Figures 11 - 13 (see [4] and [5]) show examples of the different kinds of uniaxial extensional viscosities as a function of extension rate, in some cases compared to the equivalent shear viscosities.

Furthermore, we observe that under vanishing stretch rates, the uniaxial extensional viscosity, rje ( ). tends to its Newtonian value given by... 

Although in a shear flow the viscosity of a polymeric fluid usually decreases with increasing deformation rate, in an extensional flow the viscosity frequently increases with increasing extension rate that is, the fluid is extensional thickening (recall Figure 2.1.3). Figure 4.2.5 shows the time-dependent uniaxial extensional viscosity... 

---