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

www.cloeren.comocatherine@cloeren.com

+1 409-951-7632