© 2016 The Korean Society of Rheology and Springer 167

Korea-Australia Rheology Journal, 28(3), 167-174 (August 2016)DOI: 10.1007/s13367-016-0016-5

www.springer.com/13367

pISSN 1226-119X eISSN 2093-7660

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: Walter.Friesenbichler@unileoben.ac.at

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

T x( ) = Tw +

Δp

ρcp

--------x

L---

T

111 2 2 (1 3 )

( )2 (1 4 )(2 5 )

41 exp

L1 2 2 (1 3 )

(1 4 )(2 5 ) 1 2

n nn

w

n n

kv H n n nT x T

n n n

xCa

n n n n

n n n n

λ

−+ ⎡ ⎤+ +⎛ ⎞ ⎛ ⎞

= + ×⎢ ⎥⎜ ⎟ ⎜ ⎟+ +⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟− −⎢ ⎥⎜ ⎟

⎡ ⎤+ +⎛ ⎞ ⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟ ⎜ ⎟⎢ ⎥⎜ ⎟+ + +⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦⎝ ⎠⎣ ⎦

Fig. 2. (Color online) Viscosity curve of PP ExxonMobil

1095E1 at 190°C and temperature correction according to Schus-

chnigg (2004).

Fig. 3. (Color online) Temperature corrected viscosity curve

formed out of 5 different experiments.

Walter Friesenbichler, Andreas Neunhäuserer and Ivica Duretek

170 Korea-Australia Rheology J., 28(3), 2016

performed on the capillary rheometer. With continuously

variable slit-heights, 4 pressure sensors, 2 temperature

sensors, a throttle unit, and a parting knife, it is possible to

characterize unfilled as well as high-filled extrusion-type

polymers. This system works for single- and twin-screw

extruders (PVC, wood plastic composites (WPC) etc.).

When working with plasticized PVC or rigid PVC it is

possible to control the pressure at the screw top with the

help of the throttle unit. Therefore, in terms of melt prepa-

ration processing conditions like in PVC extrusion pro-

cesses can be reproduced for rheological measurements of

different PVC-types.

3.2. Injection molding rheometersKnappe and Krumböck (1986) firstly adapted an injec-

tion molding machine with slit-dies for rheological char-

acterization of rigid PVC (Fig. 5). This system consists of

a continuous adjustable slit-height, direct pressure mea-

surement, and a flow-rate measurement system with a

backwards running opposed piston. With this rheometer it

was possible to investigate the wall-slipping behavior of

rigid PVC and the relevant material laws. In order to avoid

wall-slipping the slit surfaces were saw-tooth profiled.

Friesenbichler (1992) and Krumböck (1984) performed

systematic experiments for rigid PVC as a function of

shear stress and showed onset of wall-slip (Fig. 6) for dif-

ferent PVC types at particular yield stresses. The yield

stresses were found to be a function of melt temperature

and K-value which is an indication for the molecular

weight. Out of these measurements material laws for pure

shear-flow, pure wall-slipping, superimposed shear, and

slip-flow were compiled dependent on the viscosity (K-

value) and the wall shear stress. These were worked out

with the method of Mooney (1931).

Based on the work done by Friesenbichler (1992) and

Krumböck (1984), a vertical rubber injection molding rhe-

ometer was developed by Holzer (1996) and Holzer and

Langecker (1997). As displayed in Fig. 7 the rheometer is

Fig. 4. (Color online) By-pass extrusion rheometer (left) and comparison of viscosity measurements of cone-plate, capillary and by-

pass extrusion rheometer (right); HPCR High pressure capillary rheometer, BP-EXR By-pass extrusion rheometer; CPR cone/plate rhe-

ometer.

Fig. 5. Injection molding machine rheometer opened (left) and sectional illustration (right); A mold platen, B machine platen, C slit

entrance (change from round to rectangular geometry) and slit-die, D wedge for slit height adjustment from 0.3 mm to 3.5 mm, E injec-

tion unit, F cylinder, outlet valve, and piston for flow rate measurement, G tempering channels, T1, T2 temperature measurement, P

pressure measurement (entrance E and positions 1 to 4).

Rheometry of polymer melts using processing machines

Korea-Australia Rheology J., 28(3), 2016 171

equipped with 4 pressure sensors, 4 temperature sensors (2

infrareds, 2 thermocouples), a flow-rate measurement pis-

ton and a patented shear and heating-unit to reach higher

mass temperatures in the slit compared to the plasticizing

unit. The rheometer itself is designed as split mold and

opens the measuring gap as wide so that the crosslinked

rubber specimen can be taken out of the mold.

In 2005 a “Micro Rheology Technique” (Fig. 8) was

developed by Friesenbichler et al. (2005) and Schus-

chnigg (2004). It consists of a slit-die system which can be

used on a conventional capillary rheometer as well as on

the injection molding machine instead of the injection

nozzle. The system has “micro-slits” ranged from 0.1 mm

to 0.15 mm height and 5 mm width. Due to these low slit

heights it is possible to measure in the very high shear rate

range e.g., for low-viscous packaging materials. The mea-

surable shear rates range from 103 to 106 s−1.

With help of the thermocouples T1 and T3 placed 1 mm

below the surface the wall temperature increase along the

slit could be estimated. The thermocouples T2 and T3

placed 3 mm and 1 mm below the surface allow for esti-

mating the wall temperature of the slit applying a linear

approximation. Measured viscosities using this system are

shown in Fig. 3 up to shear rates of 1,200,000 s−1.

At the same time Gornik (2005) developed an injection

molding machine rheometer dedicated to characterizing

thermoplastic melts and powder injection molding (PIM)

feedstocks. Again the injection molding machine was used

to prepare the material under shear conditions related to

the injection molding process which particularly is of cru-

cial importance for PIM feedstocks. The slit-die insert was

exchangeable and shows a height of 3 mm and a width of

Fig. 6. (Color online) Onset of wall-slip for unplasticized PVC

with a K-value of 58.2.

Fig. 7. (Color online) Rubber injection molding machine rheometer with shear and heating unit (left) and measured viscosity curve

for EPDM at a reference temperature of 93°C (right); E0 activation energy.

Fig. 8. (Color online) Micro rheology measurement system for

capillary rheometer (above left) and injection molding machine

(above right); temperature profile in the steel body and extrap-

olated wall temperature (below, left), cross-sectional illustration

of the slit-die system (below, right), 1 die housing, 2,3 conically

shaped slit-die inserts, 4 thermal insulation, pv pressure sensor at

the inlet, T1, T2, T3 temperature sensors.

Walter Friesenbichler, Andreas Neunhäuserer and Ivica Duretek

172 Korea-Australia Rheology J., 28(3), 2016

15 mm. The pressure measurement was realized with 4

flush-mounted pressure sensors. With those settings shear

rates ranging from 102 - 105 s−1 were possible.

In 2009 a rheological injection molding machine rhe-

ometer based on an injection mold and slit-dies was devel-

oped by Friesenbichler et al. (2011). The new concept of

an injection mold with implemented conically shaped slit-

dies (Fig. 9) allowed for easily changing the slit inserts

while the mold is open and for performing rheological

measurements without time consuming change of the

machine nozzle. As well the melt preparation is close to

practical conditions. The rheometer mold mounted in the

clamping unit of the injection molding machine is shown

in Fig. 9.

The wall temperature of the slit-die is controlled by self-

developed heat-flow-sensors. For the measurement of low

or high viscous melts various inserts (different width/height

ratios) are available. The shear rates that can be achieved

reach from 102 to 106 s−1. The piston for the determination

of the volume flow rate can be servo-hydraulically regu-

lated to a certain back pressure. With this technique, it is

possible to measure the pressure dependence of viscosity

very precisely. Fig. 10 shows results of the measurements

for polystyrene PS 454C (left) and for polypropylene PP

HG313MO measured under back pressures up to 600 bars

(Fig. 10, on the right). After measurement the reciprocat-

ing piston injects the melt into the open air while the mold

is open. A stripper blade cleans the parting area.

Based on the Barus equation (Eq. (6)) the pressure coef-

ficient βp was determined for polystyrene PS 454C with

0.023 MPa−1, and for polypropylene PP HG313MO with

0.024 MPa−1. In further measurements the pressure coef-

ficient βp was measured for polystyrene PS 495F with

0.0312 MPa−1, and for PP ExxonMobil 1095E1 with 0.0058

MPa−1.

. (6)

Additionally, this setup allows measuring non-cross link-

ing rubber compounds e.g., NBR, EPDM, SBR, etc. Addi-

tional experiments verified that results of the measurements

with the injection molding machine rheometer and the

ones of a capillary rheometer match perfectly if the mea-

sured viscosity values are temperature corrected for vis-

cous dissipation. In order to understand the dissipation

even better and to be able to perform measurements under

non-isothermal conditions a further development of the

concept was made at Montanuniversitaet (Fig. 11). The

new rubber injection molding machine rheometer allows

for measuring non-crosslinking rubbers as well as cross-

linking rubbers over a wide range of shear rates. The mov-

able mold half is as well equipped with a reciprocating

ηp = η

p0

eβpp p

0–( )

⋅

Fig. 9. (Color online) Measurement system with rheological mold (left) and the mold in cross-sectional illustration (right).

Fig. 10. (Color online) Pressure dependent viscosity of PS 454C (left) and of Polypropylene PP HG313MO with a calculated pressure

coefficient βp of 0.024 MPa−1.

Rheometry of polymer melts using processing machines

Korea-Australia Rheology J., 28(3), 2016 173

piston to measure the volume flow rate and to apply back

pressure. A split-mold system allows demolding the cross-

linked specimen. A double flat-centering and sealing unit

in the split mold allows to apply back pressures to up to

600 bars with nearly no leakage flow. As can be seen in

Fig. 11, the mold is equipped with 2 heat flux (position a)

and 4 pressure sensors along the measuring slit (position

b).

In an ongoing research, the pressure dependent viscosity

of rubbers compounds will be measured. Because of the

high injection pressure in rubber injection molding (2,500

to 3,000 bar) for the prediction of the pressure demand

necessary for filling multi-cavity molds pressure depen-

dent viscosity is of crucial importance.

4. Summary

The first developments of slit-dies go back to 1963. In

a sequence of scientific works, the advantages of using

such measuring systems compared to conventional capil-

lary rheometers became very clear. Most of all, the direct

pressure measurement along the slit-die and the possibility

to measure the melt temperature in the slit allows fast

detection of viscous dissipation and non-isothermal con-

ditions. Flow anomalies like wall-slipping and stick-slip

effects are visible very fast. First works regarding the tem-

perature correction of the viscosity curves relate to the

years 1972 and 1973. As a result of the complexity of this

phenomenon it doesn’t come as a surprise that the first

usable mathematical models in rheological evaluation

software were achieved in 1999/2000. The works per-

formed by Agassant et al. (1991), Hay et al. (1999),

Schuschnigg (2004), and Friesenbichler et al. (2005) were

crucial in order to reach this goal.

Another field where slit-dies have a huge impact is rhe-

ology on processing machines like single- or twin-screw

extruders and injection molding machines. With process-

ing machines it is possible to perform measurements near

to processing conditions in the industry (especially regard-

ing pre-shearing and preparation of the melt). In this field

developments at Montanuniversitaet for machine rheom-

eters are highlighted, measuring materials like unfilled

thermoplastics, rigid PVC (PVC injection molding machine

rheometer, by-pass extrusion rheometer), crosslinking and

non-crosslinking rubbers (rubber injection molding machine

rheometers), high-filled compounds (e.g., PIM-feedstocks)

and wood plastic composites. The reachable shear rates

range from 100 s−1 up to 1,000,000 s−1, if micro-slits with

heights of 0.1 mm are used in the rheological systems,

which are placed as a nozzle at the injection unit. For most

of the materials characterized at shear rates higher than

5,000 s−1 viscous dissipation has to be taken into account

by means of temperature correction of the viscosity values

evaluated.

Within the last years slit-die systems were implemented

into injection molds and equipped with servo-hydrauli-

cally controlled back pressure units for measuring the

pressure dependence of viscosity. The developed injection

molding machine rheometers allow for characterizing

thermoplastics and rubber compounds regarding their tem-

perature-, shear- and pressure-dependent viscosity near to

processing conditions. The pressure coefficients of the vis-

cosity values measured for polystyrene and polypropylene

are in good agreement with literature. A new setup for

cross-linking rubber compounds will be used in future

research to characterize different rubber types.

Acknowledgments

The authors want to thank the EU, the Austrian Research

promotion Agency FFG and the Polymer Competence

Center Leoben (PCCL) for the financial support of the

research projects. Additionally, the authors want to thank

the industry partners Engel Austria GmbH, Semperit

Technische Produkte GmbH, Rosendahl Nextrom GmbH,

and Greiner Extrusionstechnik GmbH for their financial

support and providing processing machines. Furthermore,

we have to thank the companies Solvay Vienna GmbH

and Borealis A/S in Linz/Austria for providing thermo-

plastic materials. Further thanks go to Eduard Leitner for

Fig. 11. (Color online) Sectional view of a rheological split-mold with slit-die, operated on a horizontal rubber injection molding

machine; a: heat flux sensors, b: pressure sensors, c: piston for applying the counter pressure.

Walter Friesenbichler, Andreas Neunhäuserer and Ivica Duretek

174 Korea-Australia Rheology J., 28(3), 2016

the outstanding construction work done for the rubber

injection molding rheometer and Leonhard Perko, Michael

Fasching, and Bernhard Lechner for carrying out the rhe-

ological experiments for rubber compounds.

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