temperature dependence of viscosity of non …...• definition of viscosity for newtonian...

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Technische Universität BerlinFakultät für Verkehrs- und Maschinensysteme , Institut für Mechanik

Lehrstuhl für Kontinuumsmechanik und Materialtheorie, Prof. W.H. Müller

Copyright © Prof. Dr. rer. nat. W.H. Müller, e-mail: [email protected], 2012

Fanny Rozière

Colloquium, 2012

Technische Universität BerlinInstitut für Mechanik

Lehrstuhl für Kontinuumsmechanikund Materialtheorie

Praktikum 2012 : Temperature dependence of viscosity

of non-Newtonian materials

Copyright © Prof. Dr. rer. nat. W.H. Müller, email: [email protected], 2012

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Rotational viscometer

• Viscosity measurement on non-Newtonian materials : toothpaste, skin cream, adhesives…

• Upper plate is turning

• Bottom plate can be heated from -20°C to 180°C and cooled by water⇒temperature dependence

• Shear stress vs. shear rate

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Rotational viscometer







• Shear stress vs. shear rate

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Modeling• Definition of viscosity for Newtonian materials:

• Apparent viscosity for non linear viscoelatic materials:

• Herschel-Bulkley model:

• Ziegler Arctan model:

• Inverse analysis: Finding µ, n and tau with the stress/strain rate

curve by minimizing the mean squared error (code in SciPy)

ijij dμσ =

τμσ += nd )( 1212

)'

arctan('2' 121212 n

ddπτμσ +=

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Measurements on signal toothpaste

Composition: Calcium Carbonate, Aqua, Sorbitol, Hydrated Silica, Sodium Laury Sulfate, Sodium Silicate, Sodium Monofluorophosphate, Aroma, Cellulose Gum, Potassium Citrate, Benzyl Alcohol,

Sodium Saccharin, Calcium Glycerophosphate, PEG-32, Limonene, CI 73360

0

50

100

150

200

250

0,00E+00 1,00E-01 2,00E-01 3,00E-01 4,00E-01 5,00E-01 6,00E-01 7,00E-01 8,00E-01

Shea

r str

ess

(Pa)

Shear rate (rad/s)

Signal toothpaste flow tests

20°C 25°C

30°C 35°C

40°C 45°C

50°C 55°C

T↗

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Signal toothpaste: Arctan FitSignal 25degC arctan fit

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y = 9E+07e-0,041x

R² = 0,9831

0200400600800

10001200

280 290 300 310 320 330

µ(Pa

/s)

T (K)

Viscosity vs Temperature

0102030405060708090

100

290 300 310 320 330

τ(Pa

)

T (K)

τ vs Temperature

0

0,01

0,02

0,03

0,04

0,05

0,06

0,07

290 300 310 320 330

n

T (K)

n vs Temperature

T(°C) µ(Pa/s) n τ(Pa)20 530 0,029 8925 422 0,036 8630 317 0,059 9235 235 0,065 9140 208 0,030 8145 182 0,019 7650 142 0,024 6855 124 0,0093 56

• Exponential trend for viscosity• Fall in τ between 35 and 40 °C

• No temperature dependence for n

Temperature dependence of parameters for Arctan model

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Strain gages’ adhesive

•Adhesive Kyowa CC33A

•BAM (Federal Institute for Material Research and Testing)Special thanks to Tabea Wilk

•Drop tests on containers

•Response at high temperatures? (150°C – 200°C)

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UHU glue : Hardening process

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700

strain

time (s)

Creep test on unfixed UHU glue at 55°C ‐ σ =10 Pa

σ (Pa)

t(min)

10

10

10




0

500

1000

1500

2000

2500

3000

3500

4000

0 2 4 6 8 10 12

Shea

r st

ress

(Pa)

Shear rate (s-1)

Flow tests on unhardened UHU at different temperatures

20°C exp 18625°C exp 18830°C exp 19040°C exp 19245°C exp 19345°C exp 194

2045

40

45

25

30


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0

5000

10000

15000

20000

25000

0 0,2 0,4 0,6 0,8 1 1,2

Shea

r st

ress

(Pa)

Shear rate (s-1)

Hardening of UHU glue

exp 220.1 40°C

exp 220.2 50°C

exp 220.3 40°C

exp 220.4 50°C

exp 220.5 40°C

exp 220.6 50°C

exp 220.7 40°C

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Test on hardened glue

0

5000

10000

15000

20000

25000

0 2 4 6 8 10 12 14

Shea

r st

ress

(Pa)

Shear rate (s-1)

Evolution with temperature of hardened UHU glue

exp 221.13 40°Cexp 221.1 45°Cexp 221.2 50°Cexp 221.3 55°Cexp 221.4 60°Cexp 221.5 65°Cexp 221.6 70°Cexp 221.8 75°Cexp 221.9 80°Cexp 221.10 85°Cexp 221.11 90°Cexp 221.12 95°C

T↗

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Strain gages’ adhesive• Parallel-plate geometry

diameter = 2.5 cm• Thickness of the sample =

20 μm⇒Small diameter and

thickness as .h

Rωγ =&

• No problem of hardening as for UHU glue

• Much stiffer than UHU glue

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Strain Gages´ adhesive

0

5000

10000

15000

20000

25000

30000

35000

0 5 10 15 20 25 30 35 40

Shea

r st

ress

(Pa)

Shear rate (s-1)

Flow tests on Kyowa CC33A adhesive

exp 240.3 150°Cexp 240.5 155°Cexp 240.7 160°Cexp 240.9 165°Cexp 240.11 170°Cexp 240.13 175°Cexp 240.15 180°C

T↗

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Resistance to Temperature

0

500

1000

1500

2000

0 500 1000 1500 2000

Stra

in

time (s)

Creep test I at 180°C - σ = 20 kPa

01

2

3

45

6

78

0 200 400 600 800 1000 1200

Stra

in

time (s)

Zoom

σ (kPa)

t(min)

20

30

creep testI

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Resistance to Temperatureσ (kPa)

t(min)

20

30 35

creep testI

relaxation

1700170217041706170817101712171417161718

0 50 100 150 200 250 300 350

Stra

in

time(s)

Relaxation step

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Resistance to Temperature

0

20000

40000

60000

80000

100000

120000

140000

160000

0 200 400 600 800 1000

Stra

in

Time (s)

Creep test II (T = 180°C/σ=20kPa)

σ (kPa)

t(min)

20

30 35 40

creep testI

relaxation

creep testII

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Oscillatory tests

• Input: (1)γ0 constant, ramp of frequency ω

• Output: G’ and G’’ defined as:

• and (1) =>

• Purely elastic material: and .

• Newtonian material: and .

)sin(0 tωγγ =

))cos('')sin('(0 tGtG ωωγσ +=

)cos(0 tωωγγ =& γω

γσ &''' GG +=

γ

t

0 ='G' G =G'

0 =G' μω ='G'

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Oscillatory tests

β

ββ

α

αα

α

αα ε

τε

τεσ

τσdt

dG

dtd

Gdt

d ijijije

ijij 0000 )( ++=+• Fractional Zener model:

αα

αβ

αππαββπ

20 )2cos(21))2)((cos()2(cos('

yyyyGGG e ++

−++=

αα

αβ

αππαββπ

20 )2cos(21))2)((sin()2(sin(''

yyyyGG

++−+

=

Chr. Friedrich., Mechanical stress relaxation in polymers: fractional integral model versus fractional dierential model., Journal of Non-Newtonian Fluid Mechanics, 46(23):307 - 314, 1993.

ty ω=

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Oscillatory tests

G’

G’’

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Conclusion

• Arctan and Herschel-Bulkley models does not suit the response of the adhesives=> New models to be found?

• Strain gages’ adhesive difficult to study with this device

• Resistance of the Kyowa adhesive to be seen with creep tests

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Thanks a lot for your attention!

Questions?

temperature dependence of viscosity of non …...• definition of viscosity for newtonian...

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