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Rheometry of polymer melts using processing machines
Walter Friesenbichler1,*, Andreas Neunhäuserer
1 and Ivica Duretek
2
1Department Polymer Engineering and Science - Institute of Injection Molding of Polymers, Montanuniversitaet Leoben, Leoben A-8700, Austria
2Department Polymer Engineering and Science - Institute of Polymer Processing, Montanuniversitaet Leoben, Leoben A-8700, Austria
(Received July 10, 2016; final revision received July 28, 2016; accepted July 29, 2016)
The technology of slit-die rheometry came into practice in the early 1960s. This technique enables engineersto measure the pressure drop very precisely along the slit die. Furthermore, slit-die rheometry widens upthe measurable shear rate range and it is possible to characterize rheological properties of complicated mate-rials such as wall slipping PVCs and high-filled compounds like long fiber reinforced thermoplastics andPIM-Feedstocks. With the use of slit-die systems in polymer processing machines e.g., Rauwendaal extru-sion rheometer, by-pass extrusion rheometer, injection molding machine rheometers, new possibilitiesregarding rheological characterization of thermoplastics and elastomers at processing conditions near topractice opened up. Special slit-die systems allow the examination of the pressure-dependent viscosity andthe characterization of cross-linking elastomers because of melt preparation and reachable shear rates com-parable to typical processing conditions. As a result of the viscous dissipation in shear and elongationalflows, when performing rheological measurements for high-viscous elastomers, temperature-correction ofthe apparent values has to be made. This technique was refined over the last years at Montanuniversitaet.Nowadays it is possible to characterize all sorts of rheological complicated polymeric materials under pro-cess-relevant conditions with viscosity values fully temperature corrected.
Keywords: applied rheometry, slit-die, temperature correction, pressure dependency, rubber compound
1. Introduction
In conventional rheology for thermoplastics and elasto-
mers round dies are used. Measurements are usually per-
formed for 3 different capillary diameters and 3 different
die lengths. In order to perform a correct measurement,
the material has to be filled and compressed into a cylin-
drical chamber. In this chamber, the material gets melted
and heated to a defined measurement temperature, ideally
to future processing temperatures. Once the material is
heated it gets pressed through the capillary at 10 to 15 dif-
ferent piston speeds. Afterwards, the inlet pressure drop
has to be corrected according to Bagley (1957). This pro-
vides the true wall shear stress. The apparent flow-curve
provides the true shear rate after the Weissenberg/Rab-
inowitsch-correction (Eisenschitz et al., 1929). Problems
are encountered if polymer melts with flow-anomalies
(slip-stick or wall slipping) are measured. The main weak-
nesses of the capillary rheometry with round dies are the
non-flush mount pressure sensors. In this case, the pres-
sure is determined via a pressure hole, a small hole filled
with molten polymer. When working with high-filled
polymers, this method is highly inaccurate since the Bag-
ley correction for this type of polymers provides non-lin-
ear or even negative values. More problems that come
along with measuring high-filled polymers is the imprac-
tical melt-preparation in the cylindrical preparation cham-
ber (no material-shearing) and the impossibility of measuring
the melt temperature directly.
The use of slit-die systems allows measuring the pres-
sure drops and temperatures very precisely and directly
during the measurement process. Friesenbichler (1992)
and Knappe and Krumböck (1986) showed that it is pos-
sible to control the linearity of the pressure profile and to
detect wall-slipping with the help of multiple pressure
sensors along the slit.
2. Historical Background
2.1. Slit-die systemsIn the year 1963 Eswaran et al. (1963) developed the
first slit-die system with a width/height ratio of 10/1 and
direct pressure measurement and, for the first time ever it
was possible to determine the inlet pressure loss without
the Bagley correction. Wales et al. (1965) showed that the
experimental values for different PE-types where nearly
the same for round-die and slit die systems. In 1972 Offer-
mann (1972) performed rheological tests on wall-slipping
rigid-PVC with slit-dies. During his work he developed an
# This paper is based on an invited lecture presented by the correspondingauthor at the 16th International Symposium on Applied Rheology(ISAR), held on May 19, 2016, Seoul.*Corresponding author; E-mail: [email protected]
Walter Friesenbichler, Andreas Neunhäuserer and Ivica Duretek
168 Korea-Australia Rheology J., 28(3), 2016
iterative calculation model regarding dissipative shear
heating under non-isothermal flowing conditions. This
model showed the significance of wall-slip effects on the
viscosity function. Laun (1983) published a model and a
detailed mathematical analysis of the pressure dependency
of viscosity for the slit-die rheology. The non-linear pres-
sure curve along the length l of the slit die, measured with
3 pressure sensors is approximated with a quadratic poly-
nomial (Eq. (1)). With the coefficients of the quadratic
polynomial a, b, and c the pressure coefficient βp is cal-
culated according to Eq. (2), but using only 3 measure-
ment points. In Eq. (2), ηap is the apparent viscosity and
the apparent shear rate.
p(l) = a + bl + cl2, (1)
. (2)
The pressure coefficient allows calculating the viscosity
at various pressure levels. It is important to eliminate pos-
sible negative influences such as inaccurate pressure mea-
surements and non-isothermal flow conditions due to
viscous dissipation as these lead to severe errors and bad
results. When using this model, it is recommended to
operate with shear rates < 5,000 s−1 and to use 4 to 5 pres-
sure sensors along the slit die.
2.2. Temperature correction of viscosity due to vis-
cous dissipationFurther achievements were made by Daryanani et al.
(1973). In this work the authors experimentally verified
viscous dissipation in non-isothermal flow and suggested
a calorimetric method for correcting the viscosity due to
viscous dissipation. Fig. 1 shows the measurement system
that was used in these experiments. In the first step, the
melt was heated up to measurement temperature. After-
wards the hot melt was pressed through a thin steel tube.
During the experiment the temperature rise, as a result of
viscous dissipation, was measured with thermocouples in
2 sections along the flow path. Afterwards, the power of
the heating system for the tube was reduced in order to
regain isothermal conditions in the capillary. This exper-
imentally found frictional heat was used for the tempera-
ture correction and the shifting of the viscosity curve to
lower temperatures.
One year later, Cox and Macosko (1974) investigated
viscous dissipation in round- and slit-dies and developed
a model for the calculation of the temperature profile in
the flow channel. This model was experimentally verified
with the use of infrared radiation pyrometers. They inves-
tigated isothermal and adiabatic boundary conditions as
well as non-isothermal flows with viscous heating in flow
direction. The onset of non-isothermal flow was found for
shear rates higher than 3,000 s−1. Other notable works on
viscous dissipation and its calculation were issued by
Brinkmann (1951), Laun (2003), and Winter (1977).
Agassant et al. (1991) came up with a simplified math-
ematical method for the viscous heating of Newtonian flu-
ids in round- and slit-dies. This method was further
developed by Schuschnigg (2004) for the calculation of
viscous heating of pseudo-plastic fluids and experimen-
tally verified on highly non-isothermal rheological exper-
iments on an injection molding machine (Duretek et al.,
2006; Friesenbichler et al., 2005; Friesenbichler et al.,
2010).
For the evaluation of apparent viscosity data viscous dis-
sipation is taken into account in case of non-isothermal
capillary flow. For each measurement the degree of non-
isothermal condition is estimated by calculating the Cam-
eron number Ca (Eq. (3)) which is equal to the inverse
Graetz-Number Gz. Ca represents the ratio between heat
conduction in direction of flow and convective heat trans-
port in flow direction. If Ca is higher than 1 the flow is
isothermal and no viscosity correction is needed.
. (3)
In Eq. (3), λ is the thermal conductivity, L the length of
the slit, ρ the density at melt temperature, cp the specific
heat at melt temperature, the average velocity in the slit,
γ·ap
βp =
∂ ln ηapγ·ap
( )( )
∂p-------------------------------- =
2c
b2
-----
Ca = λL
ρcpvH
2----------------- =
1
Gz-------
v
Fig. 1. (Color online) Measurement system for the determination of friction heat (left) and temperature shifted viscosity curve (right)
(Daryanani et al., 1973).
Rheometry of polymer melts using processing machines
Korea-Australia Rheology J., 28(3), 2016 169
and H the slit height. In case of very high shear rates adi-
abatic flow conditions will prevail (Ca < 10−2). In this
case, Eq. (4) is used for calculating the temperature rise,
(4)
where (x) is the average melt temperature of the cross
section as a function of flow length, TW is the wall tem-
perature of the slit-die, Δp is the pressure drop, and x the
flow coordinate in flow direction. For calculating the tem-
perature development in the transition regime (0.01 < Ca
< 1), Eq. (5) is used (Friesenbichler et al., 2005; Schus-
chnigg, 2004) where k is the consistency and n the expo-
nent of the power law.
. (5)
For the polypropylene PP ExxonMobil 1095E1 (Figs. 2
and 3) below shear rates of 5,000 s−1 isothermal flow was
found. Within the shear rate range of 5,000 s−1 to 500,000
s−1 a rise in average melt temperature over the whole slit
volume up to 23°C was found und taken into account for
temperature correction of the viscosity. At shear rates
higher than 500,000 s−1 adiabatic boundary conditions were
found. At a shear rate of 1,200,000 s−1 a temperature
increase of 40°C was calculated.
Fig. 2 shows the temperature corrected viscosity curve
at 190°C for PP Exxon-Mobil 1095E1 while Fig. 3 dis-
plays the viscosity curve that is formed out of measure-
ments on the cone-plate-, high pressure capillary-, and
injection molding rheometer over more than 8 decades of
shear rates with temperature correction of viscosity for
shear rates higher than 5,000 s−1. The shifting direction of
the viscosity due to temperature increase (see Fig. 2) fits
perfectly to the results that were achieved by Daryanani et
al. (1973).
Hay et al. (1999) developed a method how to calculate
the temperature increase in non-isothermal melt flow due
to dissipation and compression. These methods were fur-
ther developed by Friesenbichler et al. (2005) and Friesen-
bichler et al. (2011) for correcting the measured viscosity
values due to viscous dissipation. Perko et al. (2014)
found a way to successfully combine these methods for
measuring and calculating shear and elongational viscos-
ities for elastomers and was able to determine the heating
caused by shear and elongational flows for rubber com-
pounds.
3. Slit-die Rheometry Using Processing Machines
When working with viscoelastic materials, the material
prehistory is from utter importance. In order to be as close
to processing conditions regarding the melt treatment, the
first rheological measurements under processing condi-
tions were performed during the 1980s.
3.1. Extrusion rheometerRauwendaal and Fernandez (1984) developed a slit-die
rheometer for an extrusion line. The shear rate was reg-
ulated by the screw speed. The problem with using the
screw speed for setting the shear rate is that viscous dis-
sipation increases with rise of the screw speed and influ-
ences the pressure drop measured. As a result, the measured
viscosity values on the extrusion rheometer developed by
Rauwendaal and Fernandez were significantly lower com-
pared to those on the capillary rheometer.
These above mentioned problems were avoided by
Duretek and Friesenbichler (1994) with a by-pass extru-
sion rheometer (BP-EXR), displayed in Fig. 4. The mea-
surements of the BP-EXR match very well with the ones