Problem 13.1 Figure 13.3 gives wall normal stress profiles of an HDPE, with and without a chemical blowing agent (generating nitrogen), flowing through a cylindrical tube. It is seen that the wall normal stress profile of the HDPE melt with solubilized gascous component (filled symbols) begins to show curvature (concave down) at about the middle of the cylindrical tube, whereas the wall normal stress profile of the neat HDPE (open symbols) shows a constant slope. (a) Explain what might have occurred in the cylindrical tube while the HDPE melt with solubilized gaseous component approached the die exit. (b) Why does the shape of the pressure gradient of the HDPE melt with dispersed gas bubbles concave downward? 628 RHEOLOGICAL BEHAVIOR OF POLYMERIC MATERIALS Figure 13.3 Wall normal stress profiles along the axis of a capillary die (diameter of 0.3175cm ) for an HDPE at 200C without blowing agent (open symbols) and with blowing agent (Celogen CB, generating N2 ) (filled symbols), flowing through a cylindrical die with a length-to-diameter ratio of 4 at two different shear rates (s1) : (O,0)377.8 and (,) 149.2. (Reprinted from Han et al., Journal of Applied Polymer Science 20:1583. Copyright (1) 1976, with permission from John Wiley \& Sons.)