A revised theory is presented of slit- and capillary-die rheometry, which, contrary to the earlier ones, predicts that the ratio of the second normal stress difference to the first, (Srr−Sθθ)/(Szz−Srr), is negative in sign and its magnitudes is always less than unity. In order to test the theory, use is made of exit-pressure measurements for five polymer melts and six polymer solutions. Exit pressures of polymer melts were obtained from both slit and capillary dies, and exit pressures of polymer solutions were obtained from slit dies with flush-mounted pressure transducers. The values of first normal stress differences determined from exit-pressure measurements show good agreement with the ones measured with a Weissenberg rheogoniometer. It has been found that (Srr−Sθθ)/(Szz—Srr) lies between −0.4 and −0.6 under the conditions investigated for five polymer melts. This is in line with recent measurements of the normal stress ratio of various polymer solutions.
In recent years some theoretical studies which dealt with the flow of viscoelastic fluids through a converging channel bounded by two nonparallel planes (Kaloni, 1965a; Schummer, 1968;Wissler, 1971) and through a conical duct (Kaloni, 1965b; Schummer, 1967;Ramacharyulu, 1967) have been reported in the literature.Interestingly enough, these studies predict velocity profiles with superposed secondary circulatory motion. Unfortunately, however, little experimental study which supports such a theoretical prediction has been published. Adams et al. (1965) measured the stress-birefringent patterns for a viscoelastic polymer solution (12% polyisobutylene in decalin) flowing through a converging-diverging channel. These investigators showed quantitative stress distributions in a converging channel with no evidence of the existence of secondary circulatory motion.From a practical point of view, on the other hand, a better understanding of the flow behavior of viscoelastic fluids, in particular, polymer melts, in converging ducts is very important to the polymer processing industry which is concerned with, for instance, the fiber spinning and film extrusion. It has long been known, also, to polymer processing engineers that the entrance geometry of an extrusion die plays an important role in maintaining stable operation and sometimes in increasing productivity.Very recently, the author has measured wall normal stresses (sometimes referred to as wall-tap pressures) to better understand polymer melt flow in a converging channel bounded by two nonparallel planes and in a conical die. In view of the previous studies which were concerned with the wall normal stress measurements in straight circular tubes (Han et al., 1969; Han et al., 1971) and in straight rectangular ducts (Han, 1971a;1971b), the results obtained in this study were quite unusual in both the distributions of wall normal stress and extrudate swell behavior. In this paper some of the results will be presented that seem worth reporting. EXPERIMENTThe apparatus consists of an extruder, a reservoir section, and a die section. Polymer melt flows from an extruder into a reservoir section. From there, melt flows into the die section. The arrangement of these pieces of equipment is essentially the same as that described in a recent paper by Han (1971a).In the present study, however, new dies were constructed. Figure 1 gives the detailed layout of the converging channel die having three pressure tap holes (0.099 cm in diameter and 0.508 cm in length) along the center line of the upper plane. Note that pressure transducers (Dynisco, Model PT422) were mounted perpendicular to the wall of the upper plane. Also, a conical die was used having a half-angle of 15". According to Han (1972), the presence of pressure tap holes should not affect the wall pressure measurements insofar as polymer melt is concerned. It should be noted, however, that there can be substantial pressure-hole errors in the flow of polymer solutions over a certain range of concentration (Han and Kim, 1972)...
A study is carried out on the flow of polymer melts in a rectangular duct. As the theoretical study a three‐constant Oldroyd model is used to derive expressions which correlate the rheological properties of materials with the distributions of wall shear rates and wall normal stresses in the rectangular duct. As the experimental study, a die of rectangular cross section having an aspect ratio of 6 is designed, and then melt extrusion experiments are performed with high density polyethylene. In the experiments wall normal stresses are measured along two adjacent walls of the rectangular duct as a function of the axial position. The measurements permit one to obtain the normal stress differences at the duct exit, and then to calculate the distributions of shear rates at two adjacent walls of the rectangular duct, by use of the theoretically derived expressions. Also measured is the extrudate swell, showing trat more pronounced extrudate swell occurs at the long side of the rectangular duct than at the short side. This behavior of extrudate swell correlates with the exit pressure measurements at two adjacent walls of the rectangular duct.
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