Elongational/extensional flow

The rheology of polymer melts in shear flow is considered. It is included with limited data for rheological properties of some PO melts in uniaxial elongational (extensional) flow. Table 1 systematizes the following. 

Demonstrations are given of the importance of extensional or elongational viscosity in the foam process. New polypropylenes are compared in extensional flow and it is shown how rheological differences allow the prodnction of low density foam on tandem extrnsion equipment. 6 refs. 

The mechanism of formation of jets such as that in Fig. 6 is not clear but apparently is associated with swelling of the La or L3 phase (the latter can also exist at very low surfactant concentrations, as shown in Fig. 1). The phenomenon resembles the tip streaming observed in drops of liquids subjected to shear or extensional flows with surfactants present [12,13]. In these cases shear stresses from the flow in the external phase cause the drop to elongate and form a jet with a conical shape similar to that seen in Fig. 6. No such external flow is present here, but perhaps flow inside the drop accompanying the swelling process produces a similar effect. 

Figure E7.2 compares a stepwise increase in interfacial area in simple shear flow with optimal initial orientation, and simple shear flow where, at the beginning of each step, the interfacial area element is placed 45° to the direction of shear. The figure shows that, whereas in the former case the area ratio after four shear units is 4.1, in the latter case the ratio is 6.1, with a theoretical value of 7.3 when the 45° between the plane and direction of shear is maintained at all times. We note, however, that it is quite difficult to generate steady extensional flows for times sufficiently long to attain the required total elongational strain. This is why a mixing protocol of stepwise stretching and folding (bakers transformation) is so efficient. Not only does it impose elongational stretching, but it also distributes the surface area elements over the volume.

Extensional flow (also called elongational flow) is defined as a flow where the velocity changes in the direction of the flow dvi/ dxy in contradistinction with shear flow where the velocity changes normal to the direction of flow (dv1/dx2). In uniaxial flow in the x1 direction the extensional rate of strain is defined as ... 

The drop in the extensional flow is slightly more elongated than in the simple shear flow. Although the deformation is small in all cases for the limit Ca 1, the slight difference in shape indicated by (8-86) and (8 87) is illustrative of the general principle that extensional flows are more efficient at stretching deformable bodies than flows that contain vorticity, such as the simple shear flow. 

Han and Funatsu [1978] studied droplet deformation and breakup for viscoelastic liquid systems in extensional and non-uniform shear flow. The authors found that viscoelastic droplets are more stable than the Newtonian ones in both Newtonian and viscoelastic media they require higher shear stress for breaking. The critical shear rate for droplet breakup was found to depend on the viscosity ratio it was lower for < 1 than for A, > 1. In a steady extensional flow field, the viscoelastic droplets were also found less deformable than the Newtonian ones. In the viscoelastic matrix, elongation led to large deformation of droplets [Chin and Han, 1979]. 

We have illustrated the many ways in which elongational flow behavior can provide novel information about the behavior of macromolecules. Special emphasis has been given to rheological changes associated with extensional flow fields. 

As concentration is increased, the elongational flow behavior reveals the important role of molecular interactions, which in strong flow fields can occur at much lower concentrations than generally realized. These interactions are interpreted as the development of transient networks such networks often are responsible for extreme dilatant behavior in extensional flow. Many anomalous non-Newtonian effects reported previously in flows that contain appreciable elongational components parallel these phenomena, particularly pore flow, and are themselves due to the existence of transient networks. 

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