The Influence of Die Design and Extensional Rheology on the Onset of Wave Interfacial Instabilities in Coextrusion Flows

by Martin Zatloukal & Petr Saha, Tomas Bata University in Zlin; John Perdikoulias, Comuplast Canada, Inc.; and Costas Tzoganakis, University of Waterloo. Email the author(s) at perdis@compuplast.com

Following is an expanded summary of a complete paper available on the TAPPI web site at tappi.org. On the page, click "the PLACE" in the section designated "Journals."

Application: Flow history dependent viscoelastic stress calculation can investigate the role of die design and rheology of coextruded materials. Die geometry and extensional rheology have a crucial effect on interfacial wave instability.

Coextrusion is a process to extrude two or more layers of polymers through a single die. The coextrusion process can produce multi-layer sheet, blown film, cast film, tubing, wire coating, profile, and other products. It has had use since the early 1950s to improve product quality and process efficiency. Under certain conditions, the coextrusion process exhibits some flow instability phenomena that are not fully understood. The flow of viscoelastic polymeric materials causes unstable interfaces and undesirable layer distribution. These can significantly affect product quality. These interfacial instabilities have been referred to as “zig-zag” and “wave” types.

Earlier work suggested the importance of velocity rearrangement upon combination of materials considering a stability viewpoint. The work showed that determination of stream bending or particle acceleration through FEM simulation might explain the origin of flow instabilities. The work speculated that minimizing the streamline bending and elongation stress jump at the point of merging reduce the possibility for interfacial instabilities.

In general, instability is a time-dependent phenomenon. To develop and use a numerical code for such a flow situation is extremely difficult. Even if such a code was available, it would have all the problems arising from the simulation of visco-elastic flows, and the practical use will be very limited since a steady state operation of the process is always necessary. Therefore, we have developed a step procedure for simulating the flow history dependent behavior of the system.

According to earlier work, a purely viscous shear flow simulation determines the flow field. This paper shows that material elasticity does not significantly influence the flow fields and interface position. The limiting condition for using this approach is streamlining of the flow domain and no vortexes in the flow area.

After flow field determination, calculation of stresses considers flow history dependent behavior of the materials. In the first step, a purely viscous shear thinning FEM method simulates coextrusion flow. The FEM, non-viscoelastic simulation gives the velocity, deformation rates, and streamline fields. Our simulations used the exponential temperature dependent Carreau-Yasuda model. The FEM simulation then gives the interface position and the fields needed for further computations — streamlines, velocities, residence time, vorticity, and deformation rate tensor components.

Total Normal Stress Difference
Using total normal stress difference (TNSD) means that the amount of the first normal stress difference determines how particles at the flow area stretch. In our definition, TNSD is positive when the particles in the major layer stretch more than the particles in the minor layer. The appearance of a negative sign means that the minor layer stretches more.

If TNSD changes sign from positive to negative, the coextrusion interface moves toward the die wall due to the minor layer stretching. Subsequently, it moves from the die wall due to major layer stretching. This elastic after-effect or recoil evidently destabilizes the coextrusion flow. In an extreme case when TNSD becomes intensively negative, the minor layer stretches so much that it becomes very thin and the layer breaks up.

A question is why would a small local region of negative TNSD along the interface that is relatively close to the merging point lead to instability. Why does it not fade away? The explanation can be that the wave is due to an elastic after-effect or recoil as Figure 1 shows.

To understand the role of extensional strain hardening in coextrusion flow considering interfacial instability, the authors did simulations for the same and different materials flowing through the original die geometry. For the same materials in both layers, an original LDPE underwent modification by introducing significant extensional strain softening for one material and strain hardening for a second material. Using the modified extensional properties, we can state that extensional strain softening materials in both layers stabilize coextrusion flow. TNSD is positive. Strain hardening materials in both layers destabilize the flow. TNSD changes the sign.

For different materials in both layers, different extensional behavior occurred with the two modified compared with the orginal LDPE. TNSD criterion suggest that extensional strain softening and strain hardening in the minor layer stabilizes (TNSD is positive) and destabilizes (TNSD changes the sign) for coextrusion flow, respectively.

Role Of Die Design
Eight different geometries underwent testing by simulations using variations of the original die geometry. The work revealed that destabilizing and stabilizing effects of the changed geometries increased with certain geometries and decreased with others. Geometries that allow higher pre-acceleration of the minor flow relative to the original geometry have higher stabilizing influence.

The stabilization effect of particular geometries is due to lower stretching or compression in an extreme case of pre-accelerated minor flow at the merging area without an elastic after-effect. TNSD becomes more positive. De-accelerated minor flow becomes intensively stretched at least for a certain moment. An elastic after-effect occurs. TNSD changes the sign. In the extreme case, the stretching of the minor flow becomes too high. The layer breaks. TNSD becomes more negative.

Conclusion
This work has developed a novel TNSD criterion evaluating layer stretching in coextrusion flow that can serve for potential detection of wave interfacial instabilities. Die geometry influencing merging of the layers has a crucial effect on interfacial instability. Each geometry change that depresses the velocity rearrangement at the merging point causes stabilization of flow. From a qualitative viewpoint, geometry permitting high pre-acceleration of minor flow before the merging point has the highest stabilization influence. For identical materials in both layers, increase of elongational strain hardening gives a pronounced interfacial instability.

For different materials in layers, strain softening of a minor layer stabilizes the flow. Strain hardening destabilizes it. For optimum resin performance, coextruded materials with extensional thinning and no strain hardening are preferable.


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