Solution to Design Problem II

Design Problem II at the beginning of this chapter requires you to design an annular die for LDPE at 170 °C considering the fact that the extrudate increases in both thickness and diameter on leaving the die. The die dimensions must therefore be less than those of the extrudate. The constraints are the output from the extruder or the onset of melt fracture. 

TABLE 3.4 Predicted Values of Ni, NiHxyx, and Extrudate Swell (Hp/Ho) for LDPE (NPE 953) at 170 °C Using the Phan-Thien-Tanner Model 

Values of N l2xyx and HplHp are calculated and listed in Table 3.4, but they are unreasonably low at high shear rates. This is due to the predictions of the PTT model at high shear rates when only a single relaxation time is used. Hence, the PTT model does not allow us to properly estimate thickness swell. 

Finally, one other approach is to use the White-Metzner model (see Table 3.1), as at least the viscosity function can be fit to the viscosity data (parameters for the Carreau viscosity model are found using nonlinear regression and are rio = 23,000 Pa-s, n = 0.587, and A = 19.7 s). Values of N cannot 

TABLE 3.5 Experimental Values of Ni and N Hxyx for LDPE and Calculated Values of Hp/Ho (Eq. 3.51) 

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