001_CaBER 2006

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HAAKE CaBER 1

Jint Nijman

Thermo Electron, Karlsruhe, Germany

2

Contents

• Introduction- Why an extensional rheometer?

• Basics of extensional rheometry- Types of extensional flow- Rheological quantities- Shear and extensional flow curves

• Experimental techniques- for melts- for fluids

• The HAAKE CaBER® 1- how it works- the instrument

• Theory

• Applications

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Why an extensional rheometer ?

• Extensional flows occur in many industrial processes

and applications and influence these processes often to

a great extent.

• As a consequence the knowledge of extensional

properties is important.

• Extensional properties can not be measured with

rotational rheometers.

• In industry and research the interest in extensional

rheometry is growing.

• A commercial available extensional rheometer for fluids did not exist until now.

4

The CaBER 1

The only commercially available extensional rheometer for fluidsThe only commercially available extensional rheometer for fluids !!!!

Developed by :Developed by :

Designed and built by :Designed and built by :

CaBER closed CaBER half opened CaBER fully opened

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Basics of extensional rheometry

A short introduction

y

X

v x

6

Kinematics

• Most flows are complex. The goal of rheometry is todecompose flow into primary elements

• Uniaxial Extensional Flow

– Simplest extensional deformation

– Streamlines converge

– Velocity profile in direction of

the flow

• Steady Simple Shear Flow

– Streamlines are parallel

– Velocity profile perpendicular to

the direction of the flow

y

X

v x

y

X

v x

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A Complex Flow

• Die entrance – Shear flow plus extensional flow.

The extension rate is highest inthe center of the flow

• Die channel – Shear flow

– Partial relaxation of extensional deformation

• Die exit – Unrelaxed extensional

deformations result in “die swell“.

( I l l u s t r a t i o n : P a h l , G l e i ß l e ,

L a u n )

Flow (extrusion) of a polymer solution or melt through a die.

8

Extensional flow

• Motion of a droplet inshear flow

( i m a g e s T r e t h e w a y ( 2 0 0 1 )

• Deformation of a dropletin the entrance region(arrow) is dominatedby extensional flow

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Shear flow

x

Extensional flow

Extensional Flow

γτη

τ

γ

&/viscosity

stressshear

/strain

21

21

=

= h x 0

22 11

22 11

Hencky strain ln( / )

stressviscosity ( ) /

e

L Lε

τ τ τη τ τ ε

=

∆ = −= − &

Property : “Slimy” Property : “Sticky”

10

• The main extensional deformation is e0 = e11

• The secondary extensional deformation is smaller by a factor m

• In the case of incompressible media the sum of allthe extensional deformation rates is zero

• That defines the third extensional deformation

Types of extensional deformation

1

2

3

Before after

extension

011 εε =

022εε m=

033 )1( εε m+−= Top view side view

• Uniaxial m = -1/2

• Biaxial m = 1

• Planar m = 0

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Types of extensional deformation

• Uniaxial

– fiber spinning

• Biaxial

– Film blowing

– thermoforming

• Planar

– Calendering

– Compression

molding

Squeeze flow

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Extensional flow – rheological quantities

(Hencky) strain

natural logarithm of the relativeextension

(Hencky) strain-ratechange of strain per unit of time

Tensile stress

Force per surface areaExtensional viscosity

Quotient of tensile stress andstrain-rate

Trouton-RatioQuotient of elongational andshear viscosity.

)ln(0 L

L=ε

L

FN FN

A

Uniaxial extension of a cylinder

[1/s]

[Pa]

[Pa.s]

Shear flow

L0

dt

dL

L

1=ε&

n F

A

τ∆ =

e

τη

ε

∆=

&

/V hγ =&

γ

21τ

η

3eTr η

η= = Newtonian

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Extensional flow

Typical flow curves

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Extensional viscosity

Extensional flow curves of various kinds of liquids

log Deformation rate ε [s-1]

. l o g V i s c o s i t y

η E

[ P a s ]

( I l l u s t r a t i o n : C r í s p u l o G a l l e g o s )

.

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Strain hardening and Shear thinning


L a u n )

Extensional flow curves of polymer melt

16


Extensional flow curve of solution of polybutadiene in decalineshowing three different regions

log Deformation rate ε /s-1

. l o g V i s c o s i t y η E

[ P a . s

]

Coilstretchregion

Extensional thickening region

( I l l u s t r a t i o n : C r í s p u l o G a l l e g o s )

Extensionalthinning

region

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Shear and extensional viscosity

Shear thinning of a dilute fibre solution in extensional and shear deformation. Trouton ratio = 3 for γ or ε à 0

log Deformation rate γ or ε [s-1]. .

l o g V i s c o s i t y η

o r η

E [ P a · s

]

Shear

Extension

( I l l u s t r a t i o n : C r í s p u l o G a l l e g o s

)

Trouton ratio

. .

Extensional flow

Experimental techniques

F z (t)

R(z,t)

g

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Experimental techniques for melts

• Cogswell / Münstedt

– Uniaxial flow

– Isothermal homogenousextension

– Controlled stress or controlled strain

– Sample in or on oil bath

• Meißner (Rheometrics/TA)

– Uniaxial or biaxial flow

– Rotary clamps hold sample

– Force measurement

– Sample floating on oil bath

( I l l u s t r a t i o n : P a h l , G l e i ß l e

, L a u n )

Heated oil intransducer

sample

Moving grip

Insulated chamber

wire

motor

encoder

Motor control and

Transducer readout

pulley

20

Experimental techniques for melts

• Extensional die (Thermo Electron)

– isothermal conditions

– Flow rate is applied, pressure drop is

measured

– suited for online measurement

• Rheotens (Götffert)

– Extruded melt is extended using two rolls

– Flow rate is applied, force is measured

– Difficult to achieve isothermal conditions

( I l l u s t r a t i o

n : P a h l , G l e i ß l e ,

L a u n )

.

– Strain rate is not spatially constant

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Experimental techniques for fluids

• Siphon flow

– Fluid is “sucked“ upwards intonozzle

– Extensional deformation rate iscalculated from flow rate

– Tensile stress is calculated fromforce acting on nozzle.


L a u n )

Extended fluid jet

Tractor jet

• Triple jet flow

– Centre jet is pulled by two side jets

– Extensional deformation is“measured“ from images

– Tensile stress is calculated from

force acting on centre nozzle.

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L

2 R

pressure

p laminar

p c

Entrance flow

–Extensional deformation rate iscalculated from flow rate

–Tensile stress is calculated from pressure drop

+ Stationary flow

+ Relatively easy to handle

- inhomogeneous flow-field

- Big sample volume

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Q

A d ε =

⋅&

E

F d

Qη

⋅=

Vacuum

Forcemeasurement

Sample fluid

Opposed jet Dehnrheometer (u.a. Rheometics RFX)

Q

A d ε = ⋅&

+ Stationary flow

- inhomogeneous flow-field- Big sample volume

- Difficult to handle

Two opposed jets of fluid create anextensional flow at the position where

they hit

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Problems with techniques for extensional flow of fluids

– They are difficult to handle

– The measured forces are very small

– Inertia forces and shear forces at boundaries need to betaken into account.

– The flow is not uniform

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Extensional Rheometry

106

105

104

103

102

101

100

10-1

10-2

Available techniques for measuring the extensional viscosity:

Zero-Shear Rate Viscosity [Pa.s]Meissner

Apparatus

• Ideal Elastic Liquids (Boger fluids)

• Concentrated Solutions

• Adhesives

• Suspensions

• Physical gels & colloidal systems

• Paints, Foodstuffs, Dyes...

Filament Stretching Rheometers

C a p i l l a r y B r e a k u p R h e o m e t e r s

M e l t s

D i l u t e S o l u t i o n s

Opposed Jet Devices

Contraction Flows

“Apparent Extensional

Viscosity Indexers”

HAAKE CaBER 1

The Capillary Break-up Extensional Rheometer

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The CaBER 1

The only commercially available extensional rheometer for fluidsThe only commercially available extensional rheometer for fluids !!!!

Developed by :Developed by :

Designed and built by :Designed and built by :

CaBER closed CaBER half opened CaBER fully opened

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CaBER: How it Works

D0

A small quantity of asample is placedbetween two parallelcircular plates.

Phase I :The fluid is exposed to a rapid extensionalstep strain by moving the upper plateupwards, thereby forming a fluid filament.

A laser micrometer measures themidpoint diameter of the graduallythinning fluid filament, after the upper plate has reached its final position.

[Click to continue][Click to continue]

Sample volume < 0.2 mlSample volume < 0.2 mlPlate diameter = 6 mmPlate diameter = 6 mmInitial gap = 3 mmInitial gap = 3 mm

The duration of a measurementvaries between ca. 100 ms and100 s. This time is solely influencedby the sample properties.

Phase II :Phase II :TheThefilament evolution is controlled byfilament evolution is controlled bythe balance of surface tension andthe balance of surface tension andviscous/elastic forces.viscous/elastic forces.Surface tension is trying to "pinch off" theSurface tension is trying to "pinch off" thefilament and the extensional rheologicalfilament and the extensional rheological

properties of the fluid are trying toproperties of the fluid are trying toprevent thatprevent that..

[Click image to repeat animation]

CaBER means : Capillary Breakup Extensional Rheometer

[Click to continue][Click to continue]

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CaBER: How it Works in Short Words

What we do What we measure

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CaBER: how it works

Examples of two different CaBER measurementsExamples of two different CaBER measurements

[Click image to repeat animation] [Click image to repeat animation]

M o v i e s : D r .

A T r i p a t h i

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Different Flow Behaviour

Newtonian Oil

500 ppm

Polymer Solution

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CaBER: how it works

Measurement

D=D(t)

Sample

Laser micrometer

Result : Apparent extensional

viscosity

A p p a r e n t v i s c o s i t yData conversion

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0.0 0.1 0.2 0.3 0.4 0.5 0.610

-2

10-1

100

diameter / mm

final Height: 11 mmgap: 3 mm

striketime: 20 ms

time / s

↑ Gravity

↓ Surface tension

Extensional

rate = dR/dt

Amountof

extension

Filament

life time

CaBER 1: Diameter vs Time

dt

dR

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CaBER 1, a CS or a CR rheometer ?

• Not a controlled-rate instrument

– The extensional rate changesas a function of time

( )2( )

( )

mid

mid

dR t t

R t dt ε = −&

• Not a controlled-stress instrument

– The capillary pressure ( tensilestress ) changes as a functionof time

... but close to technical processes like

jet break-up, atomization and spraying, misting, coating flow

... and easy-to-use !


)()(

t Rt

mid

E

στ ≈

dt

t dRt t

mid

E E )()(

)(σ

ε

τη ≈=

&

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CaBER 1: how it works

Linear motor

Laser micrometer

Micrometer screw

Plates

Main components

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CaBER 1: how it works

Temperature control

Connection to circulator

Connected with micrometer screw

Connected with linear motor

Upper plate

Lower plate

Temperature controlled block

Inert gas connection

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CaBER 1: specifications

• Hencky strain : up to ε0 = 10

(i.e. R 0/R = 148)

• Strain rate rangeImposed strain rate : 0.01 < ε < 300 s-1

Strain rate in sample : 10-5 < ε < 10 s-1

• Shear viscosity range : 10 - 106 mPa·s

• Plate diameter : 4 < D plate < 8 mm, standard = 6 mm

• Temperature range : 0 – 80 °C

• Laser micrometer resolution : 10 µm

• Data acquisition rate : 30,000 Hz

• Dimensions : 40 x 34 x 60 cm

.

.

HAAKE CaBER 1

Application Examples

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Application areas

• Industry; product development, quality control

• Research; extensional rheology

• Adhesives / coatings- measurement of “tackiness”- misting, stringiness in roll coating- influence of solvent loss or gain

• Food products- strand formation / stringiness- time to breakup- relaxation of dough

• Industrial resins- relaxation time spectrum- spinnability- constitutive modelling

• Consumer goods- filling of bottles- time to breakup- processability

• „Personal care“ products- Filling of shampoo

Applications :

Application fields :

40

Example: Filling of containers (shampoo)

No correlation with shear viscosity

„Filling properties“ of shampoos

1,2 good – 3,4,5 bad

Nozzle

Fluid filament

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Short break-up time is the wanted behaviour

good bad

42


good

bad

Short break-up times correlate with lower extensional viscosities

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Example: Printing or Coating

The printing speed is oftenlimited by the formation of

small droplets, the so

called „misting“.

The release of the ink

follows an elongational

pattern.

Coating roll

Material to which coating is applied

Coating material

44

Example: Offset Printing

Offset inks, which performed good could not be differentiated by

rotation or oscillation measurements from samples showing misting

during the printing process.

Rotation Oscillation

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less misting

The break-up times showed a significant difference.

Shorter times lead to less misting.

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Also the extensional viscosities of the two inks were significantly

different with the better ink having the lower ext. viscosity.

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0.01 0.1 1

1

10

100

2

3

5

6

Hencky strain / -

app. extensional viscosity / Pa s

0.01 0.1 1 10 100 1000

0.1

1

10

100

2

3

5

6

·γ / s-1

RVM

conc. CylindersT = 23 °C

η / Pa·s

Com 90350

Example: Paper coating colors

Samples that behave (very) similar in shear flow, clearly differentiatein extensional flow

Data: N. Willenbacher, BASF

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Example: Wall paint (1)

Spattering of wall paint (during application with a roller)

Sample B (good) > Sample A (better) > Standard

Correlation with filament lifetime → shorter lifetime = less spattering

40

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Example: Wall paint (2)

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Spattering of wall paint (during application with a roller)

Sample B (good) > Sample A (better) > Standard

Correlation with extensional viscosity → lower ?E = less spattering

50

Example: Cardboard glue

• Corrugated cardboard manufacturing

• Glue is applied with a roll

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Example: Pressure Sensitive Adhesives (PSA)

• Concentrated polymer solution consisting of a copolymer mixedwith a resin (tackifier) and a plasticizer

• Widely used in industry

– Packaging, release coatings, labels, pharmaceutical applications

• Processing Instabilities: Roll Coating

– Flow becomes spatially or temporally inhomogeneous

– Fibrillation, ribbing, “stringiness”

• Seven PSA samples

– Rated according to easeof processability (“ strand formation”)

A1 ‘OK’ C7

A2 ‘Good’ C7

A3 ‘Good’ C7

A4 ‘OK’ C6/C7

A5 ‘Bad’ C6

A6 ‘Good’ C7A7 ‘Bad’ C6

Name Rating Solvent

( T r i p a t h i , W h i t t i n g s t a l l , a n d M c K i n l e y ( 2 0 0 0 ) R h e

o l . A c t a ,

3 9 ,

3 2 1 - 3 3 7 . )

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“Good”

Processability

“Bad”

Processability

Fluid A2

Fluid A5

Strand formation

6mm

Example: Pressure Sensitive Adhesives

( T r i p a t h i , W h i t t i n g s t a l l , a n d M c K i n l e y ( 2 0 0 0 ) R h e o l . A c t a ,

3 9 ,

3 2 1 - 3 3 7 . )

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Example: Pressure Sensitive Adhesives

•Measure Dmid (t) for all

seven adhesiveformulations

•Shorter break-up timecorrelates with better performance

Increasing Ad

( T r i p a t h i , W h i t t i n g s t a l l , a n d M c K i n l e y ( 2 0 0 0 ) R h e

o l . A c t a ,

3 9 ,

3 2 1 - 3 3 7 . )

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Example: Polymer/Clay Nanocomposites

• Use of a small wt.% of nanosized clay filler particles to enhance the materialproperties of engineering plastics (Giannelis et al., Adv. Polym. Sci . 1999)

– Enhanced flame-retardance, heat distortion, gas impermeability, wettability...

but – Little or no degradation in modulus or impact resistance, enhanced toughness...

• In steady shear flow: Strong yield stress observed for φ ≥ 3 wt.%

MMT

102

103

10

4

100

101

102

103

10 %

6 %

3 %

1 %

0 %

τyx

[Pa]

η

[ P a .

s ]

( H o j u n L e e ( 2

0 0 3 ) u n p u b l i s h e d )

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Example: Polymer/clay nano-composites

4

6

8100

2

4

6

81000

E x t e n s i o n a l V i s c o s i t y [ P a * s ]

8642

Strain

0%3%10%

Fit 0%Fit 3%Fit 10%

3 wt% Nano clay

10 wt% Nano clay ( H o j u n L e e ( 2 0 0 3 ) u n p u b l i s h e d )

0 % Nano clay

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• Below certain wt% value: nano clay particles reduce chain extensibility

• Above certain wt% value: ‘paste-like’ response

– High extensional viscosity for small strains

– Little extensibility or ‘cohesive strength’: Failure of material at small strains

56

Example: Enhanced Oil Recovery

Injection Well Production Well

Use of aqueous polymer solution for enhanced oil recovery.Flow through porous media with changing pore sizes

Pore with large diameter

Pore with small diameter

Porous stone

or

sand particles

Relaxed polymer

Extended polymer

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5000 ppm Polymer in Saltwater (Polymer 1 and 2)

Difference in break-up time

Shape indicates extended coils

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Steady Drop in Viscosity

Increasing Viscosity


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20 °C

80 °C

5000 ppm Polymer in Saltwater (Polymer A)

Shape Indicates Flexible Coil

shorter brake-up time

i.e. longer relaxation time

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Application range of the CaBER 1

… any questions?

Thank You for Your Attention…

001_CaBER 2006

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