Die gap geometry and wall boundary condition effects on the formation of extrusion surface instabilities for polyethylene melts

R.P.G. Rutgers¹, MR. Mackley², L.E. Rodd¹, A. Bernnat³

¹ Department of Chemical Engineering, University of Queensland, Brisbane 4072, Qld, Australia

² Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK

³Institut fur Kunststofftechnologie, Boeblingerstrasse 70, D-70199 Stuttgart, Germany

ABSTRACT

We study the onset and development of surface instabilities in a planar contraction die. The experimentally observed amplitude of the surface instability is dependent on die gap, exit geometry and wall boundary condition. Confirming LLDPE birefringence data, it is shown through numerical simulations that the extensional stresses in planar contraction flow is highest at the surface at the exit of the die. Comparison of the simulations with Rheotens data demonstrates that the stress in the material close to the surface reaches levels characteristic for extensional melt rupture. Numerical simulations show that the magnitude of the exit stress peak follows the same die geometry dependence as the instability.

KEYWORDS: sharkskin, melt fracture, rheotens, lldpe, ldpe, k-bkz, pom-pom, simulation

INTRODUCTION

During the extrusion of linear polyethylenes, surface instability may occur due to critical extensional stress levels at the exit of the die [1] [2] [3]. The extensional stress results from the modification of the flow field at the boundary condition transition. Alternative mechanisms have been proposed involving amongst others instability of the boundary condition at the wall near the exit (see e.g. [3] [4]) or constutive instabilities (see e.g. [5]). This paper aims to further investigate the role of a local rupturing mechanism, but does not intend to eliminate the possibility of aggravating effects of unstable boundary-conditions [3] which were not experimentally observed in this work, nor the presence of a critical extensional deformation rate [1].

In order to investigate the flow close to the wall near the exit of the die, experimental birefringence data may be complemented with numerical simulations. The K-BKZ constitutive equation with a Wagner damping function has been shown to predict global planar contraction flow fields quite accurately for LLDPE [6]. This model does not accurately predict the stress fields for low density polyethylene (LDPE), which typically shows no surface instabilities except at very low temperatures [6]. Early results with the molecular “pom-pom” model indicate that the break points in extensional LDPE data might be an inherent constitutive property [7]. For LDPE therefore, we attempt to predict the absence and onset of surface instabilities the pom-pom model developed by [9].

experimental

The materials studied are BP Amoco LLDPE grades (LL05 and LL09) and an LDPE (LD10). The simple shear behaviour was characterised using an RDSII parallel plate rheometer. The materials were processed using a 25 mm Betol single screw extruder, fitted with a melt pump and an abrupt contraction slit die with quartz windows for flow visualisation. Flow birefringence was used as described elsewhere [6] to validate the global numerical prediction of the LLDPE flow and to study the global flow fields under conditions where surface instabilities occur. The extrudate surface distortion was characterised qualitatively using a Leica SEM 430 scanning electron microscope and its development was studied quantitatively with a Taylor Hobson Pneumo Form-Talysurf 120-L surface profile measurement technique with a standard diamond cone stylus 112/1836. Rheotens measurements were carried out according to a modified version of the methodology described in [8].

In order to allow a more in-depth analysis of local flow fields underlying the onset of instabilities than would have been possible within the constraints of experimental resolution, the flow field was numerically simulated using Polyflow software. The LLDPE was modelled for this purpose with an multi-mode Wagner model as previously described [6]. Preliminary one-dimensional simulations of the LDPE using a differential Pom-Pom model developed by [9] were carried out for streamlines close to the wall. The model parameters were obtained from simple shear and rheotens measurements using methods described by [10] and [8].

results and discussion

Extensional stress levels at exit of planar slit die

The onset and development of the instability was investigated for two grades of LLDPE of different average molecular mass and compared to the behaviour of low density polyethylene (see Table 1).

Table 1: Physical properties of materials studied

M_w M_w/M_n MFR

LL09 119k 4.23 0.9

LL05 139k 3.93 0.5

LD10 99k 5.35 1.0

The development of surface instability for the two linear materials shows a comparable shear stress dependence (Fig. 1).

Fig 1: Amplitude of surface instability of LL09 and LL05 as a function of wall shear stress at 180^oC.

Die geometry effects and the effects of alterations to the die wall and the die exit were also studied. Whereas die length did not affect the instability, increasing the die gap shifts the instability to lower wall shear stresses (see Fig. 2). A rounded die exit decreases the instability amplitude at comparable wall shear stress, and a PTFE insert that induces a slip boundary condition along the die land, wholly eliminates the instability.

Fig 2: The effect of die gap on amplitude of the instability for LL09 as a function of scaled wall shear stress.

Confirming global experimental birefringence data for flow through a planar contraction, it is shown through numerical simulations that the extensional stress level is highest at the surface at the exit of the die (see also [6]). The below discussion regards stress peaks observed along the streamline 50 mm from the wall. Numerical simulation of the different dies shows that the magnitude of the exit stress peak follows the same trends as the experimentally observed instability amplitude (see Fig. 3): The instability amplitude correlates to the magnitude of the extensional stress peak.

Fig 3: Stress peak at the exit as a function of predicted wall shear stress: effect of molecular architecture and die gap.

Comparison with Rheotens critical extensional stresses

Comparison of the simulations with Rheotens experimental data demonstrates that the stress in the material close to the surface may reach levels characteristic for melt rupture in extension:Fig. 4 shows experimental Rheotens rupture stresses (open symbols) and predicted extensional stress levels at the exit near the surface for LL09 (closed symbols). The curves linking the simulated stress levels are solid in regions where no instabilities were observed, and dotted when surface instability was present. The shaded zone indicates the onset of surface instability and appears to correlate with the critical Rheotens melt rupture stress.

Fig. 4: Rheotens rupture stress and predicted extensional stress peak at the die exit near the extrudate surface for LL09 at 180^oC. Dotted lines and shaded area indicate conditions where surface instabilities were observed.

b

LDPE stresses in planar slit die compared to Rheotens

LDPE exhibits no surface instability at ordinary procesing temperatures (e.g. 180^oC). At 140^oC however, instabilities of lower amplitude than the LLDPE were observed (Fig 5). If the occurrence of critical stress levels for local melt rupture is to explain the onset of instabilities, the absence of surface instabilities must signify that such stress levels are not achieved for LDPE at 180^oC. Rheotens melt rupture stress levels for LD10 (Fig 6) are indeed significantly higher than for LL09 (Fig. 4).

Fig 5: Amplitude of instability of LD10 as a function of scaled wall shear stress t_wT_o/T at T_o=180^oC.

Fig. 6: LD10 Rheotens melt rupture stresses as a function of upstream shear rate.

In order to predict the extensional stress levels near the die exit we attempt to use a multi-mode differential constitutive equation based on the “pom-pom” model. Using the reported [6] simple shear relaxation spectrum for the parameters t_bi and g_i, the extensional parameters of the “pom-pom” model (t_si and q_i) are obtained by fitting the model to apparent viscosity versus strain-rate curves obtained from LD10 Rheotens curves according to [8] (see Fig. 7). Fig. 8 shows how the predicted extensional viscosity of a single mode pom-pom depends on the “priority” q (number of arms).

Fig 7: Apparent elongational viscosity of LD10 for different die exit velocities at T=190^oC.

Fig. 8: Normalised viscosity as a function of strain rate of a single mode pom-pom polymer for q=2, 5 and 8.

A centreline comparison of the multimode pom-pom model with planar contraction flow birefringence data is presented. A rough estimate of the extensional stresss levels near the die exit is obtained from a preliminary one-dimensional prediction of the pom-pom model response to a simulated deformation rate profile along the streamline at 50 mm from the wall It is suggested that full pom-pom model simulation of the flow field will be useful to to confirm that extensional stress levels at the exit are insufficiently high in LDPE to cause extrusion surface instabilities, exept at very low temperatures where critical levels may be reached.

conclusions

For the LLDPE grades studied here, it is found that extensional stress levels at the surface of the extrudate near the die exit reach critical levels that are comparable to independently determined melt failure stresses in Rheotens experiments. A surface instability map is presented which relates predicted extensional stress levels downstream of the die exit to Rheotens melt rupture stresses and to the onset of extrusion surface instability. The observed qualitative and some quantitative aspects of the instability may be explained in terms of a local crack formation, which depends on geometry and conditions. Cracks of greater magnitude would be formed under conditions where the critical stress level reaches greater distances from the surface, and vise versa. This model could be used to predict the onset and development of the instability on the basis of the rheological parameters and the characteristic melt rupture stress of the material. Preliminary simulation results are presented of a pom-pom model in comparison to experimental LDPE contraction flow. These early results indicate that the pom-pom model may be useful to explain the absence of extrusion surface instabilities for LDPE.

acknowledgements

Rutgers and Bernnat thank BP-Amoco and the EPSRC for funding significant parts of this work. S.N. Bhattacharya (RMIT) is thanked for providing some of the Rheotens data. Taylor Hobson Pneumo is thanked for the use of their surface profile measurement equipment.

references

1. Cogswell F.N., J. Non-Newton. Fl. Mech. 2 (1977) 37-47.

2. El Kissi N., Piau J.-M., Toussaint F., J. Non-Newton. Fl. Mech. 68 (2/3) (1997) 271-290.

3. Kurtz S.J., SPE Antec ’95 (1995).

4. Wang S.-Q., Drda P.A., Rheol. Acta 36 (2) (1997) 128-134.

5. Koopmans R.J, Molenaar J., SPE Antec, Indianapolis, May 6-9 (1996).

6. Mackley M.R., Rutgers R.P.G., Gilbert D.G., J. Non-Newton. Fl. Mech., 76 (1998) 281-297.

7. McLeish T.C.B., Conference Proceedings, PPS 15, s’Hertogenbosch, The Netherlands, May 31-June 4 1999.

8. Wagner M.H., Bernnat A., Schultze V., J. Rheol. 42 (4) 917-928

9. McLeish T.C.B., Larson R.G., J. Rheol. 42 (1) (1998) 81-110.

10. Inkson N.J., McLeish T.C.B., Harlen O.G., J. Rheol, 43 (4) (1999) 873-896.

11.

12.

13.

14.

15.

16.

17.

18.