Prediction of surface
instabilities for polyethylene extrusion and film blowing
R.P.G. Rutgers1, M.R. Mackley2,
J. Husny3, N Clemeur1
|
1Dep. of
Chemical Engineering University of Queensland St Lucia, Queensland 4072, Australia
|
2Dep. of
Chemical Engineering University of Cambridge Cambridge, CB2 3RA U.K. |
3Dep. of
Chemical Engineering University of Melbourne Melbourne, VIC Australia. |
We study the onset and development
of surface instabilities (also referred to as sharkskin) during slit die
extrusion and film blowing of linear low density polyethylene (LLDPE). The
experimentally observed amplitude of the surface instability is dependent on
die gap, exit geometry and wall boundary condition. Through flow birefringence
measurements and numerical simulations with a K-BKZ constitutive equation, high
stress levels are demonstrated at the surface at the exit of the die. Rheotens
data demonstrates that the numerically predicted stress peak at the die exit
reaches levels characteristic for extensional melt rupture. It is demonstrated
that this stress peak follows the same die geometry dependence as the amplitude
of the instability. Preliminary results using a “pom-pom” constitutive equation
indicate that low exit stress levels may account for the absence of surface
instabilities for branched low density polyethylene extrusion. LLDPE film
blowing experiments show that the surface instability only occurs on the inside
of the film. Numerical simulation of annular extrusion is used to demonstrate
that this is due to higher extensional stresses at the inside die lip than at
the outside die lip.
It is believed that surface instability during linear
polyethylene extrusion may occur due to critical extensional stress levels at
the exit of the die1, 2, 3. The extensional stress results from an
abrupt change in flow field at the exit boundary. Other mechanisms have been proposed
such as instability of the boundary condition at the wall near the exit3,
4 or constitutive instabilities5. In this paper we discuss the
role of a local rupturing mechanism, however we do not eliminate the
possibility of aggravating effects of unstable boundary-conditions3
although these were not experimentally observed in this work, nor the presence
of a critical extensional deformation rate1.
In order to investigate the flow close to the wall
near the exit of the die the flow is simulated using Polyflow and a K-BKZ
constitutive equation with a Wagner damping function, which has previously been
shown to predict global planar contraction flow fields quite accurately for
LLDPE6. For low density polyethylene (LDPE), which typically shows
no surface instabilities except at very low temperatures6, we
attempt to predict the absence and onset of surface instabilities using the
pom-pom model developed by McLeish and Larson7.
The materials studied are BP Amoco LLDPE grades (LL05 and LL09) and an LDPE (LD10). The
rheological characterisation, extrusion conditions, flow birefringence set-up
and numerical simulation method where described elsewhere6, 8 The
extrudate surface distortion was characterised through scanning electron
microscopy and surface profile measurements6, 8. Rheotens
measurements were carried out according to a modified version of the
methodology described by Wagner et al.9. Preliminary
one-dimensional simulations of the LDPE using a differential Pom-Pom model
developed by McLeish and Larson7 were carried out for streamlines
close to the wall. The model parameters were obtained from simple shear and
Rheotens measurements using methods described by Inkson et al.10
and Wagner et al.9.
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. It was reported previously that the surface instability
for the two linear materials shows a comparable shear stress dependence8,
and that die length did not affect the instability, increasing the die gap
shifts the instability to lower wall shear stresses11. 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 instability11.
Confirming
global experimental birefringence data for flow through a planar contraction,
numerical simulations show that the extensional stress level is highest at the
surface at the exit of the die6, 8. Numerical simulation of stress
peaks at the exit along the streamline 50 mm from the wall in
the different dies shows that the magnitude of the exit stress peak follows the
same trends as the experimentally observed instability amplitude. The
instability amplitude correlates to the magnitude of the extensional stress
peak.
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: Surface instability is observed as the predicted
extensional stress peak reaches values of order 0.7 MPa, which is the extensional
stress at which melt rupture occurs for these materials in Rheotens
experiments.
LDPE
exhibits no surface instability at ordinary processing temperatures (e.g. 180oC).
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 180oC.
Rheotens melt rupture stress levels for LD10 are indeed significantly higher
than for LL09. 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. 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. Full pom-pom model simulation of the flow field will
be useful to confirm that extensional stress levels at the exit are
insufficiently high in LDPE to cause extrusion surface instabilities.
Films
were produced on a Kiefel extruder at BP Chemicals, Meyrin, Switzerland. Either
the set temperature or the throughput was varied in the different trials. It
was found that the instability only occurred on the inside of the film.
Numerical simulation of the converging annular extrusion die is used to
investigate the difference in extensional stress level at the internal and
external die lip.
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. This correlation can be used to predict the onset and development
of the instability for film blowing and other extrusion processes on the basis
of the rheological parameters and the characteristic melt rupture stress of the
material. Early results indicate that this correlation between exit stresses
and melt strength may also explain the absence of extrusion surface
instabilities for LDPE.
The
authors are grateful to BP-Amoco and the EPSRC for funding significant parts of
this work.
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