Evaluating the exit pressure method for measurements of normal stress difference at high shear rates

Abstract

A challenge for polymer rheology is the reliable determination of shear dependent first normal stress difference (N 1 values) at high shear rates (>10 s −1 ). Here, we evaluate the correctness of the commonly applied exit pressure method focusing on polypropylene and high and low density polyethylene melts at 200°C. It is demonstrated that the linear extrapolation of pressure values toward the die exit, which is a key step in the application of the exit pressure method, is affordable to determine N 1 values despite that these extrapolated exit pressure values are characterized by a relative deviation of 25%-40%. The validity of the exit pressure method is further supported by an excellent match with rheological data from the Laun rule (exponent close to 0.7) and a representative simulation of extrudate swelling data in the width and height direction, considering tuned parameters for the Phan-Thien-Tanner constitutive model. Also, the absence of a significant viscous heating effect near the die exit is highlighted based on numerical analysis.

Analysis of Bubble Growth in Supercritical CO2 Extrusion Foaming Polyethylene Terephthalate Process Based on Dynamic Flow Simulation

“…The calculated fully developed stresses by the PTT model (shear stress components and , normal stress components , and ) at the die exit are shown in Figure 8 . In the 2D simulation, the value of other shear stress components, and , were thought to be zero owing to the zero-velocity gradient [ 27 , 28 , 30 ]. It should be pointed out that the numerical value of was almost one order of magnitude larger than , and .…”

“…It was shown in Figure 2 that the simulation results based on Mesh 2 and Mesh 3 were basically the same. This phenomenon illustrated that Mesh 2 and Mesh 3 had enough nodes to obtain more accurate pressure profiles compared with Mesh 1 [ 30 ]. Therefore, Mesh 2 with 4875 elements was determined to compromise in calculation accuracy and calculation costs in the subsequent study.…”

State of the‐Art for Extrudate Swell of Molten Polymers: From Fundamental Understanding at Molecular Scale toward Optimal Die Design at Final Product Scale

“…Very recently dedicated parameter tuning of the PTT model was therefore performed considering die swell for PP, HDPE, and LPDE melt at 200 °C and considering full 3D simulations. [71,142] A sensitivity analysis highlighted that indeed the appropriate tuning of the PTT model allows us to capture many experimentally die swell variations. Moreover, this sensitivity can be translated in several swelling directions as illustrated in Figure 8 focusing on a comparison of the final swelling data of a full 3D model (black full lines) compared to a simplified 2D model (blue dashed dotted lines) for slit dies with different aspect ratios (red lines; rectangle).…”

“…[55,56] Hence, experimental as well as modeling research has been conducted to capture extrudate swell, as also highlighted in Table 1, listing important references for both types of research making a distinction between polymer types and ranges of processing temperatures. It follows that most focus has been on standard polymers such as polyolefins, [20,23,27,47,142,147,179] polystyrene (PS), [62,72,88,181] and poly(vinyl chloride) (PVC). [63,88] To a limited extent, one has covered extrudate swell involving less conventional polymers or also blending partners such as multiwall carbon nanotube (MWCNT) or calcium carbonate (CaCO 3 ) or glass beads (GBs).…”

In‐process rheological monitoring of extrusion‐based polymer processes

“…The first normal stress difference, N 1 , can be estimated from the exit pressure or the hole‐pressure method. In the exit pressure method, 39 the errors associated with extrapolation of the pressure jeopardize its practical reliability 40 . The hole‐pressure method is potentially attractive, as it may yield N 1 , the second normal stress difference N 2 and N 1 − N 2 .…”