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Optimisation of multi layer extrusion Die Flow by varying Slip, using Visco-elastic Simulations

M. Klaassen CORUS RESEARCH, DEVELOPMENT & TECHNOLOGY [email protected] C.J. Waringa CORUS PACKAGING PLUS CORUS PO Box 10.000, 1970 CA Ijmuiden, The Netherlands ABSTRACT During extrusion coating of a PET (Polyethylene Teraphthalate) coating, the thickness of each layer can vary across the width of the film. To investigate the parameters governing layer thickness differences during coextrusion of an a-symmetric coating, a production die, which is used to produce this coating, has been modelled using Polyflow. Previously, non-Newtonian simulations have been performed without visco-elastic effects. In this article the extrusion die is simulated visco-elastically to identify instabilities. The coathanger and preland are simulated separately, to investigate the stability and effects on the flow. From practice it was established that some wall slip must be applied to obtain realistic results from the simulations. Based on literature and rheometer data, a slip model was selected and fitted to the experimental data.

INTRODUCTION

Several flow instabilities can occur during the co-extrusion of a multi-layer PET (Polyethylene Teraphthalate) film. During the last decade a lot of research was performed and a number of articles addressed the causes of these instabilities. Many articles describe (lab) experiments (capillary or otherwise), however a few discuss numerical simulations. At present simulations are becoming more and more popular, since the advantages are many, if the extrusion process can be simulated and optimised without expensive experimental trials. One of the instabilities that could occur in a three-layer film is the encapsulation of the top layer by one of the other layers or vice-versa, resulting in layer-to-layer thickness differences in the final film, web or coating. For the production of polymer coated packaging steel, a PET coating (polymer coated steel is aimed at restortable applications) is co-extruded. As described earlier (reference 1) the three layer coating applied onto the steel, is asymmetric consisting of three different compositions. The layer build-up consists of an adhesion layer (for adhesion to the steel), a bulk layer (containing for example pigment) and a top layer (modified for ink adhesion or for example product release). Since the three layers are modified for different purposes, they all have different rheological properties, resulting in different flow behaviour of the layers. In order to get more insight into the layer distribution, an extrusion die was simulated with the commercial simulation package Polyflow (Fluent). In the previous article (reference 1), the flow in the die was simulated with non-Newtonian fluids. These simulations did not include visco-elastic effects. To get more reliable results, it was necessary to simulate the extrusion die with visco-elastic fluids. This article describes the challenges that were faced to create a visco-elastic simulation of the full die with a symmetric layer build up. The adhesion and top layer will have the same properties while the bulk layer has significantly different rheological properties.

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In the first part of the paper the flow results of the coathanger part and the preland part (figure 1) are discussed and a comparison is made with the flow in the complete die. In this part it becomes clear that the boundary condition at the wall has a significant influence on the flow of the multi-layer system and on the stability of the flow in the extrusion die. There are many models that describe what happens in theory and on a microscopic level when slip occurs (the velocity at the wall is no longer zero, for example references 2 and 3), yet there is little information available as to how to incorporate such a model into a numerical simulation. The commercial package used for this paper has a limited number of slip models available and a practical (and macroscopic) solution has been sought to determine the amount of slip that can be expected in the extrusion die. From literature (references 2 and 4) it is known that the transition of 'no slip' to a 'slip' condition can be determined with a plate-plate measurement in a rheometer experiment. The second part of the paper therefore describes slip experiments performed in a plate-plate set up of a rheometer. The advantage of the plate-plate set up is, that the apparatus that is used to determine the rheological properties (complex viscosity, storage and loss modulus) can also be used to determine the slip properties. These experiments are then used to tune a slip model in a simulation of the rheometer test. After this the tuned slip model can be used in the simulation of the complete die. The material used in the simulations and in the experiments is based on several blends of PET. The difference between the complex viscosity of the top and bulk layers is significant (factor 2.5). Only the slip properties of the top layer (contacting the die walls) were measured in an experiment.

VISCO- ELASTIC SIMULATIONS OF A FULL DIE

One of the most important parameters in the simulation of a polymer flow is the choice of the material model. Different models are available with varying accuracy and complexity. Often a more accurate or complex model results in extensively more computer power. For the simulations in this paper a Giesekus model with one mode was chosen for the material properties. From comparison with other models, it turned out that a 3-D approach in modelling with only one mode showed a good balance in accuracy, computer power and reliability. The material data was fitted to the experimental data that was measured in-house with a plate-plate rheometer (see the paragraph: Experiments with the Rheometer). To investigate the instabilities that can occur in the die, the die is split into a coathanger part and a preland part (figure 1). This also allows for a finer mesh in both parts. The second reason is the different flow patterns in both parts of the extrusion die. Within the preland the flow is almost restricted to one direction. This is not the case for the coathanger part since the flow needs to change its direction. It is therefore likely that instabilities will occur in the coathanger part. Figure 1 shows a set up of the simulation with boundary conditions. Using symmetry, only a quarter of the coathanger die is modelled and half of the preland.

view A

2 inlets outlet / die lips

coat hanger channel

preland

view B

symmetry li separation line

Figure 1 Set up of the simulation model of the coathanger part and the preland part As mentioned in the literature (reference 5) it is assumed that the flow in the coathanger behaves as a semi-plug flow and all forces on the exit are set to be zero. This is a major difference with the simulations of the Newtonian flow (reference 1). If a different boundary condition is set on the exit, unrealistic peaks appear in the velocity profile of the exit. This boundary condition can also be explained from a physical point of view as the pressure build up by the flow occurs only in the coathanger. In the first simulations, no slip is allowed in the material at the die wall, meaning that the tangential velocity at the wall is zero.

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Figure 2 Normalised velocity and thickness distribution on the exit of the coathanger part Figure 2 shows the normalised velocity field at the exit of the coathanger die. The velocity field at the exit is non-uniform. It can also be seen from the thickness distribution at the exit that the `encapsulation' already starts here (initial thickness of the bulk layer on the inlet is 0.66), even though shear rates are not extremely high. This `encapsulation' is the result of the complex flow in the coathanger. This indicates that it is not wise (as mentioned before in reference 6) to match the viscosities of the layers, only based on the high shear rates that occur in the preland. The flow in the coathanger die plays an important role in the layer distribution.

thickness/ total thickness

v/ v-inlet

View A

The surprise comes when a simplified velocity field and a corrected layer distribution from the coathanger simulation are set as the entrance conditions in the preland simulation (figure 3). It is known from literature (reference 1) that encapsulation takes place in regions with a high shear rate. Since high shear rates occur in the preland it was assumed that the preland would worsen the layer distribution. In the preland the bulk layer (high viscosity) is pushed outwards leading to encapsulation of the top layer (the opposite of what was assumed before performing these simulations). This is probably the result of the no-slip wall condition and the large width of the preland. It emphasises the necessity to use a correct slip model.

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Figure 3 Concentration distribution on the preland exit (no slip) When this result is combined with the previous results from the coathanger part, it can be concluded that the preland somewhat corrects the layer distribution, since it pushes the adhesive layer slightly outwards and slightly corrects the encapsulation that occurred in the coathanger channel. Encapsulation can therefore be influenced by modifying the inlet velocity (which is connected to the shear rate that is created in the preland) or by an adapted layer distribution at the inlet of the extrusion die. Since it was not known whether slip would occur, some simulations were performed with slip. The velocity profile on the exit can be seen in figure 4 and can be compared with figure 2.

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visco-elastic simulation, velocity profile in the top layer

coathanger part, with slip coathanger part, no slip total die, with slip

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Figure 4 Velocity profile of the exit of the coathanger part and complete die, different wall condition

thickness/total thickness

velocity (mm/s)

View B

This velocity profile was seen in practice and it indicated that slip could have a significant effect on the velocity distribution in practice and in the simulation. Moreover the layer distribution became more realistic (verified with practice) when wall slip was applied. Since it was not known how much slip would occur, the next part of this paper is dedicated to the determination of the slip properties of the slip model used in the simulation.

EXPERIMENTS WITH THE RHEOMETER

Rheometer experiments were performed at 260°C (extrusion temperature), with a 20 mm plate-plate set up. The samples were first dried thoroughly under vacuum at 150°C for 12 hours and care was taken to avoid degradation during the test. The rheometer is an Anton Paar MCR301 with an ETD400 heating cell and a 20 mm plate/plate configuration. The gap was set at 0.6 mm and a new sample was taken for each measurement. The cell was flushed with nitrogen. For two samples, three consecutive measurements were performed to determine whether time (thixotropy) had an influence on the measurements. A small difference was seen between the first and second measurement. No difference has been seen between the second and third measurement. The difference could be caused by permanent damage of the material at the first measurement of the slip moment. Since the difference was small, the first measurement has been used to tune the slip model of the simulation. Samples were measured in an oscillation measurement at a fixed strain of 50% with a varying angular frequency of 10 to 300 s-1. Examples of a measurement are shown in figure 5. The effects of strain and the gap width were investigated.

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shear stress (Pa)

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top layer blend, gap 0.6 mm top layer blend, gap 0.4 mm

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Shear rate (1/s)

Figure 5 Example of the measured slip properties with a different gap The amount of 50% strain was large enough to cause slip, but also small enough to allow reproducibility of the data. The rheological data such as the complex viscosity, the storage and loss modulus were obtained with a much smaller strain of 5%. Why do we follow this way to obtain the slip properties? The answer lies in the fact that fitting the experimental data with the numerical simulation data, we hope to avoid a boundary layer problem. As mentioned before, the required amount of memory for the numerical simulation is quite extensive. This precludes the use of a very accurate boundary layer at the wall to partly solve the slip condition. By fitting the data with a simulation with the same size of elements as used in the extrusion die, some of the trouble of the slip layer is avoided. Another advantage is that the influence of roughness is taken into account with the experiment and by fitting these data also within the simulation.

FITTING OF THE SLIP PROPERTIES The set up of the simulated rheometer can be seen in figure 6. The side is a free surface and only the top plate moves. The slip condition is applied to the top plate.

velocity profile

Figure 6 Set up of the rheometer simulation Since it is difficult to simulate the oscillatory movement of the rheometer, only the first turn has been simulated. Several simulations are needed to create a similar graph as shown in figure 5. Figure 5 also shows the different behaviour at the end of the stable no-slip region. It is clear that this is not easy to model. For a first approximation the experimental curve is fitted with a Navier function (reference 7):

f s = Fslip (v wall - v s ) abs (v s - v wall )

(eslip -1)

Since there are only two parameters, Fslip (force density at which slip occurs) and eslip (which determines the shape of the slip profile), the function can be tuned to the experimental data. A result of the fit of the slip properties of the top layer is shown in figure 7.

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Figure 7 Fitting the slip properties with a generalised Navier slip model The slip model was tuned by equalising the amount of torque needed for the experimental rheometer test with the torque needed in the numerical simulation. Figure 7 shows that the unstable region is not modelled properly at present. This is to be improved by applying the threshold slip model (future work). At this moment the fit is made manually. This procedure is to be automated in the future. It should be mentioned that this `calibration' method must be performed again when the material or the roughness of the die wall or other process conditions such as temperature, change.

Now the fit of the slip model has been made, it will be applied in the extrusion die simulation. This will also be done in the future.

CONCLUSIONS AND FUTURE WORK

In a co-extrusion process, instabilities and coating quality issues can be created in the coathanger die. These can be partly corrected in the preland. By simulating the coathanger and preland part, solutions can be found for preventing instabilities in the layers and the layer-to-layer distribution. Up to now the slip properties of the material were not known. Slip has a significant effect on the results of the simulated extrusion die; hence it is important that the slip parameters to be determined correctly. The work done for this paper showed that it is possible to determine the slip properties of a material in a shear flow by using a plate/plate rheometer. Once the properties have been determined they can be used to fit a slip model for use in numerical simulations, thereby eliminating an unknown parameter. By using this method to determine the slip behaviour; the surface roughness, element size at the wall and material properties are taken into account and deviations are avoided. It is the intention to do some more investigations into different blends of PET and to investigate the different parameters that affect the slip properties (macroscopic process). Next the influences of temperature and pressure need to be investigated (reference 8). In addition a validation is needed of a simulation of the complete die with the fitted slip model.

ACKNOWLEDGEMENTS

The authors would like to thank Cathy Gomez from Polyflow and Marcel de Pender from Anton Paar for their support.

REFERENCES

1.

2.

Roel Mallens, Cor Waringa, "Polyester Co-extrusion on Steel, Investigation of Layer Thickness Distribution", PLACE Conference 2004, August 2004 F. Brochard, P.G. Gennes , "Shear-Dependent Slippage at a Polymer/solid Interface ", Journal of Surfaces and Colloids 21, 1992, pp. 3033-3037 A. Yarin, M. Graham , "A Model for Slip at Polymer/ Solid Interfaces", Journal of rheology 42(6, Nov 1998, ), pp. 1491-1504 D.M Kalyon, H Gevgilili , "Wall slip and extrudate distortion of three polymer melts", Journal of Rheology 47(3), May/June 2003, pp. 683-699 L. Robert, Y. Demay, B. Vergnes , "Stick-slip flow of high density PE in a transparent slip die investigated by laser Doppler velocimetry", Rheologica Acta 43, 2004, pp. 89-98 H. Mavridis, R. Shroff , "Multilayer Extrusion: Experiments and Computer Simulations", Polymer Engineering science, April 1994, vol. 34, no. 7, pp. 559-568 Fluent inc., Software manual "Userguide Polyflow version 3.10", 2003 T.J. Person, M.M. Denn , "The Effect of Die Materials and Pressure dependent Slip on the Extrusion of linear PE", Journal of Rheology 41 (2), April 1997, pp. 249-265 K.P. Adewale, A. L. Leonov , "Modelling spurt and stress oscillations in flows of molten polymers", Rheologica Acta 36, 1997, pp. 110-127

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4.

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6.

7. 8.

9.

10. G. Georgiou, M. Crochet, "Compressible viscous flow in slits with slip at the wall", Journal of Rheology 38 (3), 1994, pp. 639-654 11. C. M. Macosko, "Rheology. Principles, measurements and applications", 1994, Wiley-VCH inc., ISBN 1-56081-579-5 12. M. Denn, "Surface induced Effects in Polymer Melt Flow", Theoretical and applied Rheology, Congres on Rheology, Brussels, Belgium, 1992, pp. 45-49 13. N. Kissi, J Piau, "The different capillary flow regimes of entangled PDMS polymers: Macroscopic slip at the wall, hysteresis and cork flow", Journal of Non-newtonian Fluid Mechanics, 37 (1990), pp. 55-94 14. S.Q. Wang, P.A. Drda , "Stick-Slip Transistion in Capillary flow in linear PE, part 3 Surface conditions", Rheologica Acta 36, 1997, pp. 128-134 15. J. Vleck, W. Kopytko, "The Effect of Material Selection in Feed-block Coextrusion of a three Layer Film", 2005 PLACE conference, 27-29 September, Las Vegas 16. J. Perez-Gonzalez , "Study of the Stick-slip Phenomenon of Linear LDPE", Journal of Rheology 49(3), 2005, pp. 571-583

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