"Melt fracture" in polymer extrusion: a visco-elastic instability

In the plastics industry, there are essentially two ways of making a plastic. Injection molding refers to the process in which a polymer melt is injected into a mold of the object one wants to make. The other process is extrusion. Extrusion is essentially the process in which a plastic wire or sheet is made by pumping a polymer melt through a pipe or slit, and having it solidify.

One of the basic problems that has plagued polymer industry since long is that when the polymer exits too fast from an extruder, the the surface starts to exhibits undulations or irregularities. The behavior is illustrated in the figure below, which shows five photographs of a polymer flowing out of a syringe, with the flow rate increasing to the right. For slow flow rates (the two pictures on the left), the flow is smooth. The middle picture is near the onset of the undulations, while the two rightmost pictures show that the undulations become progressively stronger as the flowrate increases. At even higher flow rates, the distortions can become so severe that they cause the extrudate to break --- hence the name melt fracture. A detailed understanding of this phenomenon has remained elusive for over 40 years.

five pictures of an extrudate for increasing flow rate

Figure 1:
Five pictures of a of molten polyethylene flowing out of a pipe, visible at the top. The flow rate increases from left to right. Note that in the two leftmost photographs the extrudates are nice and smooth, while in the middle one undulations start to develop. As the flow rate increases even further towards the right, the amplitude of the undulations gets stronger. When the flow rate is enhanced even more, the extrudate can break. Hence the name "melt fracture".

The type of undulations we show in figure 1 are not the only ones that one encounters in practice. Depending on the geometry and type of polymer, various other types of distortion can occur. The short wavelength deformations of the interface often refered to as "sharkskin" instability appear to originate at the outlet: the extrudate quasi-periodically sticks to the outlet, widens, snaps loose and narrows. In the "spurt-flow" regime, the extrudate shows intermittent bands of smooth and irregular surfaces; there is good evidence that this has to do with a stick-slip phenomenon at the wall of the die. In spite of the multitude of possibilities, there is every reason to believe that when these instabilities are absent, as in the experiments of figure 1, polymer flow exhibits some generic bulk flow instability: According to the engineering literature, a qualitative change in the flow behavior appears to occur at a more or less constant ratio of the normal stress difference of the melt over the shear stress for almost any polymer.

In collaboration with Daniel Bonn and his group in Paris, we have recently been able to throw new light on this old problem. Already in 1976, Ho and Denn studied the linear stability of the flow of a polymer through a pipe (Poiseuille flow). They found that this flow is linearly stable. This has been the reason that most people since then discarded the possibility that the undulations could result from a flow instability in the "die", i.e., in the pipe or slit through which the polymer flows. However, we realized that even if the flow is linearly stable, it could well be nonlinearly unstable. This means that while the flow is stable to any infinitesimally small perturbation, it is unstable to perturbations of small but finite size. In fact, this is precisely what happens in the transition to turbulence in regular fluids like water!

Armed with this insight, Bernard Meulenbroek (then an undergraduate student, now a PhD student in Amsterdam), Kees Storm (then a graduate student, now a postdoc in the US) and I set out to investigate this possibility theoretically using a so-called "amplitude expansion" to cubic order. We did find that our results corroborated our expectations completely! In fact, the results are almost too good to be true: the flow rates ("Weissenberg numbers", in technical terms) where the nonlinear instability sets in according to our calculations is quite close to the values that the engineers report. Experiments by Volfango Bertola, Christian Wagner and Daniel Bonn are also consistent with the scenario we propose: the wavelength of the undulations in their experiments is nicely consistent with our predictions. Moreover, they also observe the transition to be hysteretic, just as one would expect for a subcritical transition.

It is important to stress what we do and do not say. We do not claim that stick-slip behavior does not occur, or that the explanation of the shark-skin patterns is incorrect. We do say that if these effects are suppressed, then the nonlinear instability that we have found will always remain - it is a fundamental flow instability of visco-elastic polymer flow that one will not be able to circumvent, but other instabilities could certainly preempt it. Likewise, other effects (like shear thinning) can also play a role in practice and change the numbers, but they are not the crucial effects.

Alexander Morozov, a postdoc in Leiden, has been able to follow up on many of these results. He has been able to perform a similar expansion of the polymer flow equation for the case of Couette flow (flow between two plates which move in opposite direction). His results not only confirm the scenario, but also make it much more solid, as he has been able to extend the expansion to higher order. Stay tuned for his results!



References to the literature can be found in our papers on the subject which are listed below:
1. B. Meulenbroek, C. Storm, V. Bertola, C. Wagner, D. Bonn and W. van Saarloos, Intrinsic Route to Melt Fracture in Polymer Extrusion: A Weakly Nonlinear Subcritical Instability of Viscoelastic Poiseuille Flow, Phys. Rev. Lett. 90, 024052 (2003).
2. V. Bertola, B. Meulenbroek, C. Wagner, C. Storm, A. Morozov, W. van Saarloos and D. Bonn, Melt fracture in polymer extrusion, Phys. Rev. Lett. 90, 114502 (2003).

A nice web page with lots of information on the industrial importance of melt fracture is the one of Chris Rauwendaal.



Some articles about it in the Dutch press:

Popular introductions:
1. In Dutch, Mare 30 januari 2003

2. In Dutch, FOM Persbericht 20 februari 2003

3. In Dutch, Leids Dagblad 27 februari 2003

4. In Dutch, De Volkskrant 1 maart 2003

5. In Dutch, NRC Handelsbad 19 april 2003.

5. In Dutch, PetroChem juni 2003, pagina 21.

Wim van Saarloos
June 30 2003

[Pattern formation] [Wim van Saarloos] [Instituut-Lorentz]