Extensional rate planar

Figure 5.9 Transient uniaxial extensional (A), planar extensional ( ), and shear viscosity ( ) of an 11-mode pom-pom melt in start-up compared with measurement results for LDPE (shear/ elongation rate, 0.01/s temperature, 140 °C) [5]...

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. 

Winter et al. [119, 120] studied phase changes in the system PS/PVME under planar extensional as well as shear flow. They developed a lubrieated stagnation flow by the impingement of two rectangular jets in a specially built die having hyperbolic walls. Change of the turbidity of the blend was monitored at constant temperature. It has been found that flow-induced miscibility occurred after a duration of the order of seconds or minutes [119]. Miscibility was observed not only in planar extensional flow, but also near the die walls where the blend was subjected to shear flow. Moreover, the period of time required to induce miscibility was found to decrease with increasing flow rate. The LCST of PS/PVME was elevated in extensional flow as much as 12 K [120]. The shift depends on the extension rate, the strain and the blend composition. Flow-induced miscibility has been also found under shear flow between parallel plates when the samples were sheared near the equilibrium coexistence temperature. However, the effect of shear on polymer miscibility turned out to be less dramatic than the effect of extensional flow. The cloud point increased by 6 K at a shear rate of 2.9 s. ... 

Planar extensional flow or pure shear flow is extensional flow with the same but opposite rates of strain in two directions in the third direction, there is no flow ... 

MIXED FLOW. Other flows with extensional components also have coil-stretch transitions. The smaller the extensional component is relative to the overall strain rate, the higher the overall strain rate at which the transition takes place (Giesekus 1962, 1966) A steady planar flow, for example, can be considered to be a mixture of a shearing and an extensional flow in such a mixed flow, the velocity gradient tensor, Vv, can be expressed as (Fuller and Leal 1980, 1981)... 

This formula applies to planar extensional flow as well as to shear, if the shear rate y in Eq. (9-11) is replaced by 2e, where is the extension rate. Taylor predicted that droplet breakup should occur when the viscous stresses that deform the droplet overwhelm the surface tension forces that resist deformation this occurs when D reaches a value Db given approximately by... 

Drop Deformability When a neutrally buoyant, initially spherical droplet is suspended in another liquid and subjected to shear or extensional stress, it deforms and then breaks up into smaller droplets. Taylor [1932,1934] extended the work of Einstein [1906, 1911] on dilute suspension of solid spheres in a Newtonian liquid to dispersion of single Newtonian liquid droplet in another Newtonian liquid, subjected to a well-defined deformational field. Taylor noted that at low deformation rates in both uniform shear and planar hyperbolic fields, the sphere deforms into a spheroid (Figure 7.9). 

In the inflation stage, the molten or thermally softened polymer is subjected to the action of the gas pressure. One analysis [13] that involved minimal strain rates showed that a planar extensional viscosity y pe (kg/ms) could be correlated with strain rate ( pe). The relationship between these quantities was... 

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... 

The above expression can be applied to idealized systems with three types of deformation planar (plel), uniaxial (unel) extensional, and simple shear (ss) mixers. For a mixing device dominated by planar elongational flow, the distances along the X axis are related to strain or strain rate by... 

Figure 6 shows a direct comparison of the experimentally determined vortex shapes and the corresponding predictions for different mass flow rates at a temperature of 180 C (the contraction ratio is 1 19 in this case). In Figure 6a, the experimental vortex shape line color corresponds to the simulated ones. The conq)arison between the measured and the calculated mass flow rate dependent vortex size is depicted in Figure 6b. It is nicely visible that the vortex size versus the mass flow rate is non-monotonic (runs through a maximum), which can be attributed to the non-monotonic behavior of the planar extensional viscosity.

The effect of the melt temperature on the vortex size development has been studied experimentally as well as theoretically. The most important results are depicted in Figme 7. It is obvious, that the vortex area primarily increases, reaches a maximum and then it decreases again with increasing temperature. This behavior can be explained by the temperature dependency of the nonmonotonic shape of the planar extensional viscosity predicted by e improved mWM model, which is depicted in Figure 8. In more detail, the planar extensional viscosity maximum moves fi om low extensional strain rates to higher ones for increasing melt temperatures. This seems to be the driving mechanism for the maximum appearance in the vortex size vs. temperature flmction. 

Viscoelastic FEM analyses of the vortices of LDPE have been performed for different temperatures, flow rates and flow geometries. The theoretical results were compared with corresponding experimental data. It has been suggested that for the LDPE melt the planar extensional viscosity can be different (slightly lower) compared to uniaxial extensional viscosity at the maximum of the steady extensional viscosity curve. It seems that the non-monotonic function of the vortex size on the temperature for a constant mass flow rate can be explained by the temperature dependency of the planar extensional viscosity curve. Finally, it has been found that the proposed modification of the mWM model significantly improves the model behavior in the planar extensional flows. 

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