An experimental and numerical analysis of the exit flow in a slit die for polymer melts

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Virginia Polytechnic Institute and State University


A slit die has been constructed to use both flow birefringence and direct pressure measurements to study the extrapolated exit pressure (Px) and the exit pressure theory used to evaluate the magnitude of the primary normal stress difference (N1) from the value of the exit pressure. Flow birefringence is used to directly assess the principal assumptions in the exit pressure theory and to evaluate the magnitude of Px from an expression derived from the macroscopic momentum balance equation. The effect of stress field rearrangement upstream of the die exit plane on the value of the exit pressure was then evaluated using flow birefringence data. The effect of stress field rearrangement was also shown to affect the pressure drop ΔP/ΔL in the exit region of the die and the pressure distribution from the centerline of the slit to the die wall. To complement the experimental investigation, a mixed penalty method finite element simulation of the die swell problem was performed using the White-Metzner and upper-convected Maxwell constitutive equations.

The flow birefringence experiments were performed for a polystyrene (Styron 678), LDPE (NPE 952), and HDPE (LY600-00) melts for the following shear rate (γ̇) and wall shear stress (σw) 0.05 ≤ γ̇w ≤ 3.2 s⁻¹ and 4.84 ≤ σw ≤ 16.4 KPa. It was found that the flow in the die exit region is not a unidirectional shear flow, which is direct violation of the assumptions in the exit pressure theory. Normal stresses generated by an elongational flow field were observed along the slit centerline and in the region adjacent to the die walls. Also, shear stress contributions due to stress field rearrangement evaluated using an expression obtained from a macroscopic momentum balance, comprise over 50% of the magnitude of the calculated exit pressure. The numerically calculated stress field was in good agreement with the results of the flow birefringence results. Convergence for the numerical technique was limited to Deborah numbers of 0.61 for the White-Metzner model and 0.75 for the upper-convected Maxwell constitutive equation.