High Extensional flow behavior

Figure 3.21 shows the influence of extensional viscosity on the flow behavior of an aqueous PEO solution. The high extensional viscosity in comparison with the relatively low shear viscosity can cause the upper container to empty when pouring, even when the liquid surface is below the glass rim. This is visible in Fig. 3.21 by the liquid level markings. In the case of the viscous silicone oil however, the liquid thread breaks as the pouring container is tipped back (not shown here). 

Strands that terminate with a branch point at both of its ends can neither reptate nor completely retract. Relaxation of such strands presumably occurs by more complex, hierarchical processes discussed by McLeish (1988b). Here we simply note that the presence of branch points at both ends of a strand leads to much more strain hardening in extensional flows (Bishko et al. 1997 McLeish and Larson 1998). Low-density polyethylenes (LDPEs), which are highly branched, are well known for their extreme strain hardening behavior in extensional flows (Meissner 1972 Laun 1984) (see Fig. 3-39). The steady-state shear viscosity, as a function of shear rate, seems to be little affected by long-chain branching, however. 

From the point of view of tube models, the two key elements of nonlinear behavior are tube orientation and tube or chain stretch. The former nonlinearity can be probed using shear flow, but shear flows are not effective in generating significant chain stretch. As we have seen, chain stretch in shear is strongly suppressed by the mechanism of convective constraint release (CCR) up to extremely high shear rates. The CCR mechanism of relaxation is qualitatively much less important in extensional flows than in shear flows, because in the former molecules on neighboring streamlines move at the same velocity. Thus, extensional flows are of particular importance in the study of nonlinear viscoelasticity. 

Another strain measure that is closely related to the one defined by Eq. 10.14 was proposed by Wagner etal. [ 14]. This tensor involves a new scalar, which they call the molecular stress function. When used in an integral constitutive equation it was found to be able to describe the behavior of a high-density polyethylene in shear flow and several types of extensional deformation. 

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