Viscosity steady elongational

The normal stress difference, elongation rate (e) are here the only measurable quantities. The steady elongational viscosity fj) is defined as... 

Develop expressions for the elongational viscosities fji and fj2 for steady shearfree flows of a convected Jeffreys model. Comment how this expression compares with experiments. 

Godunov SK, Romenskii El (1972) Non-steady state equation of non-linear theory of elasticity in Euler co-ordinates. Zh Prikl Mech Technich Phys 6 124-144 (in Russian) Golovicheva IE, Sinovich SA, Pyshnograi GV (2000) Effect of molecular weight on shear and elongational viscosity of linear polymers. Prikl Mech Tekhnich Fiz 41(2) 154-160 (in Russian)... 

Though a simple Maxwell model in the form of equations (1) and (2) is powerful to describe the linear viscoelastic behaviour of polymer melts, it can do nothing more than what it is made for, that is to describe mechanical deformations involving only infinitesimal deformations or small perturbations of molecules towards their equilibrium state. But, as soon as finite deformations are concerned, which are typically those encountered in processing operations on pol rmers, these equations fail. For example, the steady state shear and elongational viscosities remain constant throughout the entire rate of strain range, normal stresses are not predicted. 

It shoiild be noted that this is the exact derivation of equation (3). These models are usually referred to quasi-linear models and display qualitatively correct predictions of typical phenomena of elongational flows such as the occurrence of the strain-hardening effect in transient extension. Nevertheless the predicted elongational viscosity is never boimded in the long time range and a steady state value can only be expected for small elongation rates. Moreover, the shear behaviour remains unrealistic as compared to the experiment, especially because of constant predicted viscosity and first normal... 

Figure 6 Steady state functions for LD at 160°C (experimental and calculated), (o) elongational viscosity, ( ) shear viscosity, (A) first normal stress difference.

Figure 13 Steady state elongational viscosity for LD at 160°C (experimental data and fit using (—) linear form and (-) exponential form of Y).

In Fig. 19 the steady state uniaxial elongational viscosity, ng/3. Is conqiared with the steady state shear, n> as well as dynamic, n , end complex, n, viscosities. It Is evident that some strain hardening, evident In I.100 (LLDPE-10) Is systematically diluted by the Increasing amount of LPX-30. Thus, Series 1 behaves as a truly miscible system. By contrast, addition of LDPE (11.100) to LPX-30 (1.0) Is generating more a complex variation of properties. The strain hardening, already visible at lOX of LDPE, reaches Its maximum not at lOOX LDPE but rather at 50 50 composition. Note that at e 0.1 (s" ) the maximum strain at break for 11.50 Is ejj > eg 3.2. The blends behave as Immiscible. 

The second Interesting observation based on ICR and RMS results Is related to the need for pressure correction In capillary flow. Already In Fig. 19 an agreement between the dynamic viscosity, n, and corrected for pressure effect capillary shear viscosity, n, was shown. In Fig. 22 five different measures of viscosity are shown for LLDPE-A (four for the other samples) steady state elongational viscosity, nE/3 conqplex and dynamic viscosity, n and n > as well as the steady state capillary viscosity corrected and uncorrected for the pressure effects, hcorr n(lCR), respectively. There Is a... 

The Trouton ratio (Tr) may also be defined as the ratio of the elongation viscosity (rj ) to the steady-shear viscosity (rj),... 

While dynamic mechanical and steady shear measurements are frequently used in rheology studies of surfactant systems, extensional viscosity measurements are lacking. This can be attributed to the difficulties associated with such measurements and the lack of commercial laboratory instrumentation since the discontinuance of the Rheometric Scientific RFX rheometer. For many detergent compositions, the relatively low viscosity further complicates such measurements. There appear to be very few data on extensional or elongation viscosity for detergent consumer products and actives in the technical literature at this time. 

For steady elongational flow (ic = constant) it is conventional to define a quantity tf, called the elongational viscosity (or Trouton viscosity ), as... 

FIGURE 3.8 Reduced steady-state elongational viscosity as a function of elongational rate for pol5rpro-pylene at 180°C. (From Minoshima, W. White, J.L. Spruiell, J.E. J. Appl. Polym. Sci., 1980, 25, 287. With permission.)... 

When the flow of constant elongational rate e is started, the tensile stress Ozz < xx increases with time and reaches the steady state. The steady state elongational viscosity is defined by... 

Fig. 7.20. Shear viscosity ( ) and elongational viscosity t e(e) in a steady flow of monodisperse polystyrene = 2.54 x lO ). Reproduced from ref. 85.

In polymer blends, both the morphology and flow behavior depend on the deformation field. Under different flow conditions the blend may adopt different structures, hence behave as different materials. Note that in multiphase systems, the relationships between the steady state, dynamic and elongational viscosities (known for simple fluids) are not observed. Similarly, the time-temperature (t-D superposition principle that has been a cornerstone of viscoelastometry is not valid. 

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