Extension thickening

Figure 15 Three microscopic hematoxylin and eosin (H E) stained cross-sections of a rabbit artery two weeks post PDT treatment with lutetium(III) texaphyrin PCI-0123 (lOpmol/kg per day for three days and illumination with 200J/cm, 250mW/cm and 732 nm laser light 5 h post injection). Here, (A) and (C) are above and below the treatment site and (B) is at the treatment site. The aorta, above the treatment zone, is shown. The intima (i) is extensively thickened and heavily ladened with foam cells. The atheroma completely lines the wall, thereby significantly narrowing the lumen (1). The outer wall, adventitia (a), and media (m) are normal and show no evidence of infiltrating disease. The photoirradiated site (B) is now normal (i.e., devoid of lesions), while the media muscular wall is intact with no necrotic regions being visible. The field below the treatment site (C) is heavily burdened with plaque (x40). Reproduced from [243] by permission of Mary Aim Liebert, Inc. Publishers...

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. 

Long chain branching (LCB) has several benefits relating to the polymer processability because it affects melt viscosity, temperature dependence of viscosity, melt elasticity, shear thinning, and extension thickening. The effect of LCB on the melt-state properties of polyethylene depends on the number, length, and distribution of the branches, on molecular weight, and on MWD. 

Therefore we can conclude that as long as -lAa.o/V i.o < 0.5, the first departures of from the Newtonian value will be positive. Hence fluid X will be extension thickening at low extension rates. A similar calculation for equal biaxial extension (Larson, 1988) shows that rn, = 6r] - 6(rjt + 2 2) ... 

This viscosity is extremely extension thickening, since it rises to infinity as k approaches 1/2X. Recall that the second-order fluid equation predictsonlyalinearriseof t)u withe, while the Newtonian fluid predicts no dependence of on e. 

Figure 7.8.S shows the flow field for a Boger fluid obtained by Binding and Walters (1988). The pictures show that as the flow rate increases, vortices generated in the comers of the contraction increases in size as a result of the extension-thickening nature of the fluid.

Fig. 2.14a-c. Linitis Plastica of the stomach. Double Contrast barium study (a) shows a marked circumferential narrowing of the fundus and proximal body of the stomach. Ultrasound (b) and CT (c) confirm extensive thickening of the gastric wall. Multiple biopsies confirmed the presence of linitis plastica... 

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. 

Another end-separation method was recently described by Bach et al. [201]. Their filamentstretching rheometer (FSR) is an adaptation of a device originally developed for dilute polymer solutions [202,203 ] and later used for concentrated solutions [203,204]. As shown in Fig. 1024, the filament is formed from a small sample by stretching it between two cylindrical, steel fixtures to which it is attached by the direct adhesion of the sample to the metal. The strain in this device is not uniform, and the measurement is based on the portion of the filament midway between the end fixtures, where its diameter is a minimum. As a result, several preliminary experiments are required to establish an empirical relationship between the radius at this point, where the Hencky strain is -2[ln(R/Ro)] and the distance between the fixtures, L (t). The data for e < 1.0 are not reliable, but steady state was reached in experiments by Bach et al. for an LDPE and an LLDPE, making it possible to determine the extensional viscosity [201]. The results agreed with data from an RME. This technique has also been used to demonstrate extension thickening in linear polystyrene [204]. 

The simplest nonlinear tube model is the classical Doi-Edwards (DE) constitutive equation for linear polymers, which accounts for reptation and affine rotation of tube segments. The Doi-Edwards equation predicts thinning in both shear and extension, because it accounts for orientation of tube segments, but it is unable to predict extension thickening because it neglects the stretching of tube segments. Inclusion of tube stretch leads to the Doi-Edwards-Marrucci-... 

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