Capillary Rheometry: Application to the Extrusion Process and Equipment Design Olivier Catherine Technical Director - Cloeren Incorporated Orange, Texas SPE Webinar April 27, 2021
Capillary Rheometry: Application to the Extrusion Process and
Equipment Design
Olivier Catherine
Technical Director - Cloeren IncorporatedOrange, TexasSPE Webinar April 27, 2021
Introduction
Example of Cloeren Reflex™ Die for Cast Stretch film application – Running at K2019.
Cloeren Incorporated designs and manufactures Flat Film Extrusion Dies and Feedblocks
Why Is Viscosity Important for Extrusion?
Die Design Goals: • Uniform flow distribution• Pressure drop adapted to
process• Residence time distribution
adapted to the polymer
Simplified Flow analysis (Newtonian):Manifold channel ⇒ Pipe flow:
∆𝑃𝑃 =8𝜼𝜼𝑄𝑄𝑄𝑄𝜋𝜋𝜋𝜋4
Preland ⇒ Parallel plate flow:
∆𝑃𝑃 =12𝜼𝜼𝑄𝑄𝐿𝐿ℎ3𝑄𝑄
Shear Viscosity is a critical parameter for flow equations, which are at the basis of die design
Shea
r Vis
cosi
ty η
(Pa.
s)Newtonian
PlateauTransition Shear thinning
Power Law Region
Too slow deformation to
disentangle polymer melts
Competition between de-entanglement and
recoiling
MWD
Newtonian Plateau
Disentanglement rate > recoiling rate
Fully disentangled
Shear Rate �̇�𝛾 (1/s)
Shear Rheology
Measurement Techniques for Polymer Melts
MELT FLOW INDEX (MFI) is defined by the weight of material (in grams) collected for a time frame (e.g. 10 min) for a given plunger weight (2.16 kg) and temperature (190 °C)
The test gives no information about temperature or shear rate dependency, which is critical for extrusion
Melt Flow Index
Visc
osity
η(P
a.s)
Shear Rate ̇𝛾𝛾 (1/s)
Shear rate at which the MFI measurement is performed
Polymers with same MFI could have a different shear flow behavior
Melt Flow Index
Rotational Rheometry / Dynamic Measurements
Rotational Rheometry / Dynamic MeasurementsSmall Amplitude Oscillatory Shear (SAOS) Measurements
Delayed Shear stress response :
𝛾𝛾∗ = 𝛾𝛾0 exp 𝑖𝑖𝑖𝑖𝑖𝑖
𝜏𝜏∗ = 𝜏𝜏0 exp 𝑖𝑖 (𝑖𝑖𝑖𝑖 + 𝛿𝛿)
t
Dynamic strain is imposed:
𝛾𝛾∗
𝛾𝛾0 𝜏𝜏∗
𝜏𝜏0
Complex modulus
Real = elastic
Imaginary = Viscous
G*
G’
G”
δ
Ideally elastic
Polymer melts
Ideally viscous
Rotational Rheometry / Dynamic Measurements
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E-01 1.E+01 1.E+03 1.E+05
G' o
r G
” [Pa
]
aTxω [rad/s]
Viscous
Elastic
LDPE1– 7MI .917
T = 280°C1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E-01 1.E+01 1.E+03 1.E+05
G’ o
r G
” [P
a]
aTxω [rad/s]
ViscousElastic
T = 280°C
LDPE2– 7MI .917
G’
G”
G’
G”
Viscoelastic Behavior of Extrusion Coating Resins
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E-01 1.E+01 1.E+03 1.E+05
G’ o
r G
" [P
a]aTxω [rad/s]
Viscous
mPE – 19MI .918Elastic
T = 280°C1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E-01 1.E+01 1.E+03 1.E+05
G' o
r G
” [Pa
]
aTxω [rad/s]
Viscous
Elastic
LDPE1– 7MI .917
T = 280°C
G’
G”
G’
G”
Viscoelastic Behavior of Extrusion Coating Resins
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E-01 1.E+01 1.E+03 1.E+05
G’ o
r G
” [Pa
]
aTxω [rad/s]
Viscous
ElasticLDPE3– 16 MI .917
T = 280°C1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E-01 1.E+01 1.E+03 1.E+05
G' o
r G
” [Pa
]
aTxω [rad/s]
Viscous
Elastic
LDPE1– 7MI .917 LDPE
T = 280°C
G’
G”
G’
G”
Viscoelastic Behavior of Extrusion Coating Resins
1.E+00
1.E+01
1.E+02
1.E+03
1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05
Redu
ced
com
plex
vis
cosi
ty |
η*|/
a T[P
a.s]
Reduced angular frequency ω×aT [Rad.s-1]
LDPE1LDPE2
LDPE3mPE
T = 280°C
Viscoelastic Behavior of Extrusion Coating Resins
Convection ovenThermocouple
Extensional Rheometer
Fixture
Strain Rate 1.0 1/s (actual speed)
Transient Extensional Rheometry
1.E+02
1.E+03
1.E+04
1.E+05
1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03
Tran
sient
Elo
ngat
iona
l visc
osity
ηE+
[Pa.
s]
Time [s]
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03
Tran
sient
Elo
ngat
iona
l visc
osity
ηE+
[Pa.
s]
Time [s]
LVELVE
0.1 s-1
0.1 s-1
1 s-1
1 s-1
3 s-1
10 s-1
25 s-1
10 s-13 s-1
T = 140°C T = 120°C
0.3 s-1
mPE – 19MI .918 m-PELDPE1– 7MI .917
Capillary Rheometry
Rosand RH2000
Driven Plunger (PC controlled velocity)
Heated Barrel
Polymer melt
Pressure Transducer
Capillary Die
• Shear Rate calculated from Die Diameter, Plunger diameter and velocity
• Shear Stress calculated from Pressure measurement, Die Length, Die Diameter
• Viscosity = Shear Stress / Shear Rate• Corrections
Principle
�̇�𝛾 = 4𝑄𝑄
𝜋𝜋𝜋𝜋𝐶𝐶3
0
0.5
1
1.5
2
2.5
-1 -0.5 0 0.5 1
Velo
city
/ A
vera
ge v
eloc
ity
r/R0 0.1 0.2 0.3 0.4 0.5
0.6 0.7 0.8 0.9 1
“Apparent” shear rate calculation assumes a Newtonian velocity profile
Velocity profiles as a function of the pseudoplastic index
�̇�𝛾𝑐𝑐 =3𝑛𝑛 + 1
4𝑛𝑛 4𝑄𝑄
𝜋𝜋𝜋𝜋𝐶𝐶3Rabinowitsch corrected shear rate calculation uses the “local” pseudoplastic index n
𝑛𝑛 =𝑑𝑑 𝑙𝑙𝑙𝑙𝑙𝑙 𝜏𝜏𝑤𝑤𝑑𝑑 ̇𝑙𝑙𝑙𝑙𝑙𝑙 𝛾𝛾
Practically, 𝑛𝑛 is determined by plotting 𝑙𝑙𝑙𝑙𝑙𝑙 𝜏𝜏𝑤𝑤=f(𝑙𝑙𝑙𝑙𝑙𝑙�̇�𝛾) and fitting the plot with a polynomial function
Rabinowitsch Correction
1.E+01
1.E+02
1.E+03
1.E+04
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04
Shea
r vis
cosi
ty (P
a.s)
Corrected shear rate (/s)
PVB SAMPLE 3 - RABINOWITSCH CORRECTIONS
NO RABINOWITSCHCORRECTION -T=180°CLINEAR n -T=180°C
QUADRATIC n -T=180°C
CUBIC n - T=180°C
The Rabinowitsch correction will result in higher shear rates, especially in the area of higher shear-thinning.
Practically, the quadratic fit (2nd order polynomial function) and the cubic fit (3rd-order) are most accurate.
Rabinowitsch Correction
The pressure measurement is a combination of the entrance effect, the shear and
elongational flows in the capillary, and the exit effect.
LM
Entrance
PExit
Capillary Die: RC
LC
Pressure
ΔPE
ΔPC
ΔPEXIT
P MEA
SUR
ED
Bagley Correction
Extrapolating the pressure back to a zero length die should give a zero pressure drop.
Measure the pressure dropon a series of dies of decreasing length
Linear extrapolation to a Length:Die (L/D) ratio of 0
But, there is and entrance effect
𝛼𝛼1
𝛼𝛼𝑛𝑛 𝜏𝜏𝑤𝑤 = 𝜋𝜋𝑐𝑐𝛥𝛥𝑃𝑃𝑐𝑐2𝐿𝐿𝑐𝑐
𝛼𝛼𝑖𝑖 = 2𝜋𝜋𝑐𝑐𝛥𝛥𝑃𝑃𝑐𝑐,𝑖𝑖𝐿𝐿𝑐𝑐
𝜏𝜏𝑤𝑤,𝑖𝑖 =𝛼𝛼𝑖𝑖4
Bagley Corrected Shear Stress
Historical Bagley
• With a long capillary and “orifice die” (L/D≈0) on a twin-bore instrument it is possible to get direct measure of entrance pressure drop.
• No extrapolation is needed and the Bagley correction allows for accurate shear stress calculations
Twin-Bore Rheometer
1.E+01
1.E+02
1.E+03
1.E+04
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04
Shea
r vi
scos
ity
(Pa.
s)
Corrected shear rate (/s)
PVB SAMPLES - BAGLEY CORRECTION COMPARISON
SAMPLE 3 BAGLEYCORRECTON -T=180°C
SAMPLE 3 NOCORRECTON -T=180°C
Bagley Correction results in lower viscosity compared to uncorrected data.Depending on how elastic the melt is, the difference can be significant.
Example of Corrected vs. Uncorrected Data
Some fluoropolymers have a very distinct flow behavior with a very sharp transition from stable to unstable flow
Unstable flow is seen as melt fracture and is undesirable in extrusion
Understanding rheology can help design equipment to avoid unstable flow
FEP
PFA
Example Melt Fracture in unstable flow region observed in capillary
rheometry.
Melt Fracture / Flow instability
0
200
400
600
800
1000
1200
0
2
4
6
8
10
12
14
16
18
1 10 100 1000 10000
Shea
r rat
e (1
/s)
Pres
sure
(MPa
)
Time (s)
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05
Visc
osity
(Pa
.s)
Shear Rate (1/s)
350 °C (Input)370 °C (Input)390 °C (Input)350 °C (Carreau-WLF)370 °C (Carreau-WLF)390 °C (Carreau-WLF)
stable unstable
Unstable flow Stable flow
Critical Shear Rate
Flow Curves from capillary rheometerImposed Shear RateMeasured Pressure Determination of “critical shear rate / shear stress”
Melt Fracture / Flow instability
Temperature [⁰C]
Apparent Shear rate [s-1]
Corrected Shear rate [s-1]
Shear Stress [kPa]
370 3.4 3.7 53.9
385 10.2 12.7 126.4
400 20.3 25.1 163.7
• A customer is experiencing unstable flow at the edges of a PFA sheet.
• The die was manufactured by a competitor.
• Customer states that the lip gap is large and should not result in high shear stress.
Critical Shear Rate / Shear Stress is determined by capillary rheometry
Melt Fracture / Flow instability - Application
Flow simulation of the extrusion process reveals a high velocity at the edges, especially in the preland region
Melt Fracture / Flow instability - Application
Flow model show shear rates, shear stress above the critical shear rate values in the preland.
Flow is unstable at the edges!
Shear Stress > 90 kPaCritical Shear Stress = 54 kPa
Melt Fracture / Flow instability - Application
0
0.5
1
1.5
2
2.5
3
3.5
4
0 1000 2000 3000 4000
Mea
sure
d M
elt P
ress
ure
(MPa
)
Time (s)
Example of Time Sweep with Capillary for ECTFE
Polymer w/ additive at 290 ⁰C
Polymer w/ additive at 270 ⁰C
Neat Polymer at 270 ⁰C
Neat Polymer at 290 ⁰C
Thermal Stability
0
10
20
30
40
50
60
0 200 400 600 800 1000 1200
Resi
denc
e ti
me
(s)
Transverse Direction – Distance from CenterLine (mm)
• Residence time is not a simple number• It is important to consider the whole process (extruder, melt pipes, screen changers etc.)• A direct comparison between degradation time and residence time is not always
straightforward
Thermal Stability vs. Residence Time
PVB Film Extrusion Troubleshooting Example
A real example of PVB film extrusion:• A film die was designed specifically for the process• Die was installed in Asia on existing extrusion line• Initial flow distribution was not matching theoretical expectations• After manual and automatic lip adjustments, flow distribution and
film thickness became acceptable – however, the process did not behave as expected.
Background
10
100
1000
10000
1 10 100 1000 10000
Corr
ecte
d Sh
ear
Visc
osit
y [P
a.s]
Corrected shear rate [1/s]
180°C200°C220°C
( ) m
T
T
a
aT −
×+
×= 1
*
0
0
1
,
γτ
η
ηγη
PVB Sample supplied by processorData: capillary rheometer, Bagley (twin-bore), and Rabinowitsch corrections.
Model: Cross (shear rate dependent) and WLF (temperature dependent) model
( )( )
−+
−−=
ref
refT TTC
TTCa
2
1exp
Parameter Valueη0 (Pa.s) 6.67 ×103
τ∗(Pa) 2.14.104
m 0.38335Tref (K) 473.15 (200°C)
C1 104.26C2 (K) 2591.3
PVB Rheology
Process parameter
Value
Die wall temperature
210°C
Initial melt temperature
210°C
Extrusion output 800 kg/h
• Die designed by Cloeren Incorporated.• Constant cross-section manifold
channel• Optimization of non-linear preland
dimensions for uniform flow distribution
• Targeted pressure drop ≈10 MPa
Flow Simulation Conditions
Total Pressure drop = 12.5 MPaUniform development of isobars
Uniform velocity at die exitLinear decrease of flow rate in manifold channel
3D Flow Simulation Results
0
50
100
150
200
250
300
0 200 400 600 800 1000 1200 1400 1600
Velo
city
(mm
/s)
Distance from centerline (mm)
Exit Velocity profile predicted by 3D Flow Analysis:A 2σ variation to the average of 1.3%
Flow Distribution Prediction
Profile measured online in stable extrusion condition without any lip adjustment:
Average thickness = 780 μm
2σ = 16.8%Heavy end flow
Average thickness = 780 μm2σ <2%
Profile measured online in stable extrusion condition after lip adjustment:
Star
t-up
wit
h un
ifor
m li
p ga
pA
fter
Aut
omat
ic
lip a
djus
tmen
tStart-up Thickness Profiles
Die lipsPush Rod
Thermal translator (with heater)
Automatic Lip Adjustment
The initial online gauge measurement is not acceptable and far from design predictions – that is not usual.Investigations online and offline to determine the origin of this discrepancy:
1) Melt temperature measurement2) Confirmation with IR thermal imaging of melt curtain in air gap3) Rheology assessment of actual material extruded at start-up4) Possible CFD analysis if enough difference with design parameters is observed
Troubleshooting Methodology
vacuum
TSE, 11 barrel sectionsFilter 1
Filter 2
adapter 1
adapter 2
Barrel flange
Gear Pum
p
Static mixer (6x), oil temp control
Elbow
Die
P1P2P3
T Existing melt temperature TC
T Existing melt temperature TC
Melt Temperature Measurement
160
170
180
190
200
210
220
230
240
0 0.2 0.4 0.6 0.8 1
Mea
sure
d m
elt
tem
pera
ture
(°C)
Thermocouple Dimensionless Position (x/R)Implementation of a Variable Depth thermocouple to evaluate temperature gradients in melt flow channel at the elbow adapter, just upstream from the die
Near the centerline of the flow channel, melttemperature is ≈ 227°C for a 210°C targetNear the wall, measurements indicate 180°Cdue to the low temperature set point
Variable-Depth T/C
LHSLD: average = 211.3°C LHSLD: average = 217.9°C LHSLD: average = 212.1°C
202204206208210212214216218220
0 200 400 600 800 1000
Aver
age
curt
ain
tem
pera
ture
nea
r ce
nter
(°
C)
Extrusion output (kg.h-1)
• IR camera emissivity set at ε =0.95• No calibration –measurements are “relative”, not absolute.• Curtain melt temperature is higher than the melt
temperature target (210°C) or die temperature (200°C) on average.
• Strong influence of extrusion output indicate excessive shear heating in the extrusion system
Thermal Imaging
10
100
1000
10000
1 10 100 1000 10000
Shea
r vi
scos
ity (P
a.s)
Corrected shear rate (/s)
180°C
200°C
220°C
240°C
A PVB sample was taken during start-up and test was performed with same capillary rheometer as for the original sampleBagley and Rabinowitsch corrections are appliedCross and WLF model was fit to the data
Parameter Valueη0 (Pa.s) 2.25 ×103
τ∗(Pa) 9.303.104
m 0.17687Tref (K) 473.15 (200°C)
C1 3218.7C2 (K) 89559
( ) m
T
T
a
aT −
×+
×= 1
*
0
0
1
,
γτ
η
ηγη
( )( )
−+
−−=
ref
refT TTC
TTCa
2
1exp
Shear Rheology
Parameter Value𝜼𝜼𝟎𝟎 (Pa.s) 2.25 ×103
𝝉𝝉∗(Pa) 9.303.104
m 0.17687Tref (K) 473.15 (200°C)
C1 3218.7C2 (K) 89559
Parameter Value𝜼𝜼𝟎𝟎 (Pa.s) 6.67 ×103
𝝉𝝉∗(Pa) 2.14.104
m 0.38335Tref (K) 473.15 (200°C)
C1 104.26C2 (K) 2591.3
10
100
1000
10000
1 10 100 1000 10000
Shea
r Vi
scos
ity [P
a.s]
Corrected Shear rate [1/s]
Original
Start-up material Original
Start-up material
Viscosity models at reference temperatureComparison - Shear Flow
3D flow simulation considering the parameters observed during the start-up:• Melt temperature of 225°C (higher than originally specified)• New Rheological behavior (lower zero-shear viscosity, more shear-thinning at
high shear rate)
Total pressure drop through the die decreased to 10.4 MPa (compared to 12.5 MPa) due to overall lower melt viscosity.
New Flow Simulations
Velocity contour plot shows non-uniformity at die lips
New Flow Simulations - Velocity
0
50
100
150
200
250
0 200 400 600 800 1000 1200 1400 1600
Velo
city
(mm
/s)
Distance from centerline (mm)
Exit velocity profile shows heavy end flow.Standard deviation to average : 2𝜎𝜎
𝑎𝑎𝑎𝑎𝑎𝑎= 14.8%
Agreement with observed extrusion process and online gauge measurement during start-up (16.8%)
New Flow Simulations – Exit Velocity Profile
• Study shows excellent correlation between 3D CFD analysis and observations during extrusion trial
• When designing an extrusion die, the exact knowledge of the “melt quality”, i.e. temperature gradient in the melt stream and rheology, is critical to achieve the highest flow channel performance
• With slightly inaccurate “melt quality” parameters, the die still delivers good flow distribution but relies excessively on lip adjustment to achieve this result
• Rheology and flow characterization of polymer melts is the foundation of extrusion equipment design.
• While capillary and rotational / oscillatory rheometers have both their own advantages, capillary rheometry can provide a wealth of relevant information.
• Extrusion dies are custom-designed: there is no generic design. The best flow performance can only be achieved with careful characterization of the flow behaviors.
• A combination of rheology and flow simulation is a powerful tool for design and process troubleshooting.
• Interpretation of data is as important as data accuracy.• Understanding phenomena that can affect the viscosity data is critical:
• Flow instability• Non-classic flow behaviors (rubbers, highly loaded materials)• Thermal degradation
Conclusions
Thank You!
Olivier CatherineTechnical Director - Cloeren Incorporated
+1 409-951-7632