Polyethylene extensional thickening

The extensional thickening of polymer solutions is one form of viscoelastic behavior. This ability to support a tensile stress can also be demonstrated in a tubeless syphon with dilute aqueous solutions of polsrmers such as polyacrylamide or polyethylene oxide. If you suck up solution with a medicine dropper attached to a water aspirator and then lift the dropper out of the solution, the solution will still be sucked up. In shear, viscoelastic fluids develop normal stresses, which causes rod climbing on a rotating shaft, as opposed to the vortex and depressed surfaces that form with Newtonian liquids. Polsrmer solutions and semiliquid poljnners exhibit other viscoelastic behaviors, where, on short time scales, they behave as elastic solids. Silly putty, a childrens toy, can be formed into a ball and will slowly turn into a puddle if left on a flat surface. But if dropped to the floor it boimces. 

Figure 1-14 compares the time-dependent extensional viscosity to the time-dependent shear viscosity, after onset of flow, at various shear and extension rates, for the same molten polyethylene described in Figs. 1-9 to 9-11 (Meissner 1972). This figure shows that the behavior of the extensional viscosity can be very different from that of the shear viscosity the former increases while the latter decreases with increasing strain rate at a fixed time after inception of steady flow. Thus, while the shear viscosity is shear thinning, the extensional viscosity is extension thickening. 

When describing dilatant behavior, the maximum stretch rate, e, in the converging flow at the contraction is a better parameter, but more difficult to be calculated. Instead of the term stretch rate, other authors also used deformation rate (e.g., Chauveteau, 1981) or elongational rate (e.g.. Sorbic, 1991). The shear-thickening viscosity is also called elongational viscosity (often referred to as the Trouton viscosity Sorbie, 1991) or extensional viscosity in the literature. James and McLaren (1975) reported that for a solution of polyethylene oxide (a flexible coil, water-soluble polymer physically similar to HPAM), the onset of elastic behavior at maximum stretch rates was of the order of 100 s and shear rates of the order of 1000 s. In this instance, the stretch rate is about 10 times lower than the shear rate. However, some authors use shear rate instead of stretch rate in defining the Deborah number—for example, Delshad et al. (2008). 

Figure 10.19 shows the extensional viscosity data of Laun and Munstedt [187] for several low-density polyethylenes made in tubular reactor. We note that these branched polymers are Newtonian at low strain rates, become extension thickening at higher strain rates, and finally exhibit extension thinning. This is similar to the behavior observed by Kurzbeck ef a. [ 184] for a crossKnked polypropylene. In Chapter 11, it will be shown that the pom-pom model predicts this type of extensional viscosity curve. 

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