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Extensional Characterization of Fluids

Seminar

Basics on Rheology

2

Why is there a need for Extensional Rheology ?

• Extensional flow fields are relevant in many technical applications

• Extensional behaviour can not be detected with rotational

rheometers

• Interest in extensional rheology is growing steadily in

R&D and QC

• Samples can behave similar in rotation but show pronounced differences in extension

3

Extrensional Rheometry

106 105

104 103

102

101

100

10-1

10-2

Range of zero-shear viscosity [Pas] and used method

Meissner Apparatus

Opposed Jet

4-Roll Mill

Porous Flow

4

Comparison of Flow Fields

Most real flow fields are complex. Aim of Rheology is to resolve that into

simple sections.

Uniaxial Extension

• Most simple extensional flow field

• Streamlines converge

• Velocity gradient in direction of flow

Shear Flow

• Streamlines parallel

• Velocity gradient vertical to flow field

y

X

vx

y

X

vx

5

HAAKE CaBER 1 – What is an extensional flow field ?

Deformation

Shear Rate

Shear Stress

1st Normal Stress Difference

Shear Viscosity

x

h

.

ln( ) L

(Hencky) Strain L0

(Hencky) Strain Rate

Extension

.

.

Shear

6

Impact of flow field on a droplet structure

Droplet in a laminar shearing

flow (a polymer coil would

behave exactly the same)

(im

ag

es T

reth

ew

ay (

20

01

)

• Deformation of a droplet at the infeed of a jet nozzle is determined by extension

7

ln ( )

Extensional Rheology: Parameters

(Hencky) Deformation

natural logarithm of rate of

extension

(Hencky) Deformation rate

temporal change of sample lenght in

regars to the instantenious value

Extensional Viscosity

ratio of tensile stress and rate of

deformation

Trouton-ratio

ratio of extesional viscosity and shear

viscosity

L

L0

. 1 dL

L dt

E . l0

L

Uniaxial deformation of a cylinder

[1/s]

[Pas]

Shear Flow

3eTr

/V h

8

HAAKE CaBER 1 Capillary Breakup Extensional Rheometer

Monitoring

D=f(t)

Sample

Laser Micrometer

Appare

nt E

xt.

Vis

cosity

Result Extensional Viscosity

“Mathematics”

Hencky Deformation

9

HAAKER CaBER 1 - CS or CR Rheometer?

No Controlled-Rate Rheometer

• Rate of Deformation

varies with time

( )2( )

( )

mid

mid

dR tt

R t dt

No Controlled-Stress Rheometer

• Capillary pressure

varies with time

( )driving

midR t

… but this kind of space- and time-dependent flow field driven by capillary

forces are commonly observed for so called free-surface

• Die-swell, Atomization, Misting, Roll-Coating, …

Extensional Viscosity ( )

( )( )

midE

R t

t

10

HAAKE CaBER 1 – Theoretical Backround

Surface Tension

• Fz Tensile Force on a fluid element

• s Zero-shear Viscosity

• zz- rr Normal-stress difference

Fz(t)

R(z,t)2 3 s

2

R

R

t zz rr R1 (R , R )

gR02Z0

R2

Tensile Force

In column

Viscous

stress

Non-Newtonian

stress

Capillary

Pressure

Gravitational

Body force

Force Balance Considers time-dependent Newtonian and non-

Newtonian phenomena

The Force Balance for the CaBER Experiment

gives

11

• Hencky strain : up to 0 = 10

( R0/R = 148, L/L0= 2,2 104 )

• Strain rate regime

Applied strain rate : 0.01 < < 300 s-1

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

• Range of shear viscosities : 10 -106 mPas

• Plate diameters : 4 < Dplate < 8 mm, Standard = 6 mm

• Temperature range : 0 – 80 C

• Laser resolution : 10 m

• Data aqusition rate : 0.1 ms

• Dimensions : 40 x 34 x 60 cm

CaBER 1 : Specifications

.

.

12

Applications

• Industry, R&D, QC

• Research, Extensional Rheology

• Paints, Coatings - Stringiness

- Spattering - Misting

• Food

- Stringiness - Mouth feeling

• Resins - Relaxation behavior

- Spinning behavior

• Personal care - Filling behavior

Applications:

Areas:

13

0.0 0.1 0.2 0.3 0.4 0.5 0.610

-2

10-1

100

diameter / mm

final Height: 11 mm

gap: 3 mm

striketime: 20 ms

time / s

Gravity

Surface Tension

Extension

Life-span

of Filament

HAAKE CaBER 1 - Diameter vs. Time

14

Extensional Viscosity

log Deformation rate / s-1

. log

Vis

co

sity

E

/ P

as

(Illu

str

ation

: C

rísp

ulo

Ga

lleg

os)

.

Extensional viscosities of different fluids in uniaxial extension

15

Strain hardening and shear thinning

Flow behavior of a dilute fibre solution in extensional and shear

deformation. Trouton ratio = 3 for or 0

log Deformation rate or [s-1] . .

log

Vis

cosity

or

E [P

a.s

]

Shear

Extension

(Illu

str

ation

: C

rísp

ulo

Ga

lleg

os)

Trouton ratio

. .

16

Extensional viscosity and Misting

0.0 0.5 1.0 1.5 2.00.0

0.5

1.0

1.5

diameter / mm

time / s

Film-split behavior for coating

applications

Misting 5% Acrylic A

10% CMC low

Short break-up time → less Misting Data : Norbert Willenbacher

• Aqeous thickener solution

17

Paper Coatings

0.0 0.2 0.4 0.60.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

10-2

10-1

100

101

102

103

10-1

100

101

102

103

diameter / mm

binder

XSB / A

XSB / B

S/A / C

S/A / D

time / s

viscosity / Pa.s

shear rate / Pa s

Data : Norbert Willenbacher

Extension Shear

• Influence of different binders

■ A1

A2

B1

B2

18

Cardboard Glue

Clear differentiation: ,,best’’ Sample with shortest break-up time

Sample D +

Sample C and A +/-

Sample B -

19

Wall Paint (1)

Squirting Behavior

Sample B (++) > Sample A (+) > Standard

Correlation with the filament break-up possible

20

Wall Paint (2)

Squirting Behavior

Sample B (++) > Sample A (+) > Standard

Correlation with the apparent extensional viscosity

21

Shampoo (1)

No correlation with shear viscosity possible

Filling behavior of Shampoos

1,2 + / 3,4,5 -

Nozzle

Fluid Thread

22

Shampoo (2)

Filling behavior of Shampoo

1,2 + / 3,4,5 -

Correlation with the break-up time

23

Shampoo (3)

Correlation with the apparent extensional viscosity

Filling behavior of Shampoo

1,2 + / 3,4,5 -

24

Polymer/Clay Nano-Composites (1)

Utilization of a small-wt.% nano-particles as filling agent to modify the material properties of “Engineering Plastics” (Giannelis et al., Adv. Polym. Sci. 1999)

• Fire guard, heat deformation, gas-Iimpermeability, wettability…

• No or minor changes to G-modulus, impact resitance, enhanced durability...

Shear flow : Major yield stress for 3 wt %

MMT

1 02

1 03

1 04

1 00

1 01

1 02

1 03

1 0 %

6 %

3 %

1 %

0 %

yx [Pa]

[P

a.s]

(H

oju

n L

ee

(2

00

3)

un

pu

blis

he

d)

25

Polymer/Clay Nano-Composites (2)

Beneath certain % threshold: nano-particles reduce extensibility (of the polymer chain)

Above a certain threshold %: ‘paste-like’ behavior

• High extensional viscosity at low deformation

• Reduced extensibility: material fracture at low deformation

4

6

8100

2

4

6

81000

Exte

nsio

na

l V

iscosity [P

a*s

]

8642

Strain

0%

3%

10%

Fit 0% Fit 3% Fit 10%

3 wt% Clay particles

10 wt% Clay particles (H

oju

n L

ee

(2

00

3)

un

pu

blis

he

d)

0 % Clay particles

26

Thank you for your attention

Any questions ?