Yield Stress Fluids, Meeting #1 · Yield Stress Fluids, Meeting #1 1. Introduction to yield stress fluids understand definition/caveats of apparent yield stress fluids develop a feel

Yield Stress Fluids, Meeting #1

1. Introduction to yield stress fluidsunderstand definition/caveats of apparent yield stress fluids develop a feel for yield stress and viscosity values

2. Rheometry with yield stress fluidsidentify and avoid slip artifactscorrect for parallel plate artifactsrecognize LAOS response of yield stress fluids

Randy H. EwoldtJune 26, 2009

Part of the summer 2009 Reading Group: Yielding, Yield Stresses, ViscoelastoplasticityNon-Newtonian Fluids (NNF) Laboratory, led by Prof. Gareth McKinley

2

References

• Barnes, H. A., "The yield stress - a review or `pi alpha nu tau alpha rho epsilon iota' -everything flows?," Journal of Non-Newtonian Fluid Mechanics 81(1-2), 133-178 (1999)

• Bonn, D. and M. M. Denn, "Yield Stress Fluids Slowly Yield to Analysis," Science 324(5933), 1401-1402 (2009)

• Brunn, P. O. and H. Asoud, "Analysis of shear rheometry of yield stress materials and apparent yield stress materials," Rheologica Acta 41(6), 524-531 (2002)

• Yoshimura, A. S. and R. K. Prudhomme, "Response of an elastic Bingham fluid to oscillatory shear," Rheologica Acta 26(5), 428-436 (1987)

3

Yield Stress Fluids:

Apparently solid at low stress, σ < σYApparently fluid at high stress, σ > σY

e.g. paint, toothpaste, hand lotion, concrete, snail slime, nuclear waste sludge

Yield Stress Fluids:

Apparently solid at low stress, σ < σYApparently fluid at high stress, σ > σY

e.g. paint, toothpaste, hand lotion, concrete, snail slime, nuclear waste sludge

Idealized example:linear scale

Idealized example:log-log scale

4

Toothpaste

Carbopol 980, polymer microgel (0.2wt%)

Tomato puree

Mayonnaise

Viscosity, σηγ

=

Apparent yield stress fluids:

1. Initially “high”viscosity

2. Dramatic viscosity drop over narrow range of stress

3. Flows

Apparent yield stress fluids:

1. Initially “high”viscosity

2. Dramatic viscosity drop over narrow range of stress

3. Flows

Detailed experiments

5

Viscosity, η ≈ 108 Pa.sIg Nobel Award, Physics (2005) - Presented jointly to John Mainstone and Thomas Parnell of the University of Queensland,

Australia, for patiently conducting the so-called pitch drop experiment that began in the year 1927 — in which a glob of congealed black tar pitch has been slowly dripping through a funnel, at a rate of approximately one drop every nine years.

Started: 1927Drop #1: 1938Drop #8: 2000 (12 years between drops #7 and #8)Drop #9: ????

6

7

An estimated 5 to 8 percent of all human-generated atmospheric CO2 worldwide comes from the concrete industry.

Concrete creep is caused by the rearrangement of particles at the nano-scale.

The basic building block of cement paste at the nano-scale -- calcium-silicate-hydrates, or C-S-H -- is granular in nature.

A more dense phase of C-S-H can be induced by additional smaller particles that fit into the spaces between the nano-granules of C-S-H, which greatly hinders the movement of the C-S-H granules over time.

The rate of creep is logarithmic, which means slowing creep increases durability exponentially.

A nano-indentation device allows them to measure in minutes creep properties that are usually measured in year-long creep experiments at the macroscopic scale.

Professor Franz-Josef Ulm M.I.T. Dept. of Civil and Env. Eng.

Vandamme and Ulm, PNAS, 2009

η ≈ 1014 Pa.s

η ≈ 1019 Pa.s

8

Blood

Hematocritcontent

Olivine (a rock),various grain sizes

Plasticine(modelling material, like putty)

Apparent yield stress fluids?

Barnes, JNNFM, 1999

9

Slime & simulant rheology: Flow

Carbopol (polymer microgel)Carbopol 940 in DIW, pH→7 with NaOH

Laponite (particulate gel)Laponite RD in DIW

Ewoldt et al., Soft Matter, 2007

10

Magnetorheological Fluid

AR-G2 rotational rheometer, parallel plates with 600 grit sandpaper, h=500µm

D=40mm for ambient testD=20mm for magnetic field tests Using MRF Rheometer Cell from Murat Ocalan, Ph.D. Thesis (in progress), MIT

LORD Corp. MRF-132DGcarbonyl iron particles (1-20µm) in silicone oil

B

no field field-activated

Magnetic Field 0.462 T 0.221 T 0.100 T 0.046 T 0.030 T 0.012 T ambient

5 -21.4 10 Pa.Tα = ⋅

10-5 10-4 10-3 10-2 10-1 100 101 102 103100

101

102

103

104

105

Cor

rect

ed S

hear

Stre

ss, σ

R [P

a]

Rim Shear Rate [s-1]

(a)

Ewoldt, Ph.D. thesis, 2009

11

Magnetorheological fluid

100 101 102 103 104 10510-1

100

101

102

103

104

105

106

107

108

(b)Magnetic Field

B=0.462 T B=0.221 T B=0.100 T B=0.046 T B=0.030 T B=0.012 T ambient

C

orre

cted

Vis

cosi

ty, η

[P

a.s]

Corrected Shear Stress, σR [Pa]

12

Apparent Yield Stress FluidsSome quotes from Barnes, JNNFM, 1999

Yield stresses were usually only a ‘figment of peoples’ extrapolation

The existence of an essentially horizontal region in a double-logarithmic plot of stress versus strain rate is the most satisfactory criterion for the existence of a ‘yield stress’(quote from Evans [36])

[Barnes] is in substantial agreement with Evans in this view, especially if then term ‘yield stress’ is prefixed with the adjective ‘apparent’!

Nguyen and Boger [38] reviewed experimental methods of measuring the flow properties of yield stress fluids in 1992: … the especial value of which is the emphasis on possible sourcesof error in measurement.

[36] I. Evans, J. Rheol. 36 (7) (1992) 1313.[38] Q.D. Nguyen, D.V. Boger, Ann. Rev. Fluid Mech. 24 (1992) 47.

13

Despite the practical importance, there is no reliable way at present to predict the onset of flow.

Perhaps the main difficulty with much of the literature on yield stress fluids is the prevailing presumption that the solid-liquid transition occurs at a single invariant stress. This assumption ignores the fact that the microstructure may adjust dynamically when flow begins.

Foams, emulsions, and Carbopol gels (such as hair gel) are probably closest to “ideal” yield stress materials, because they do not usually show measurable rejuvenation or aging; in these cases, a yield stress may be a material property

In the few direct comparisons between computed and experimental velocity fields for the falling sphere, the agreement is poor (14), probably because the yielding process in the experimental fluids is not adequately described by the models. Much fundamental work thus remains to be done.

14

Examples of “ideal” yield stress fluids(negligible thixotropy)

• Nivea Lotion ~ 4 Pa• Gilette foamy shaving cream ~10 Pa• Aloe gel ~60 Pa• Nivea Cream, Toothpaste and Mayo ~200-300 Pa• Magnetorheological fluid 10 ~ 10,000 Pa

15

Experimental Issue: Slip

161.000E-6 0.01000 100.0

shear rate (1/s)

1.000

10.00

100.0sh

ear s

tress

(Pa)

NiveaLotion-0001f

NiveaLotion-S02-h1050-0001f, Steady state flow stepNiveaLotion-S02-h450-0001f, Steady state flow stepNiveaLotion-S02-h700-0001f, Steady state flow stepNiveaLotion-S03-h1050-0001f, Steady state flow stepNiveaLotion-S03-h450-0001f, Steady state flow stepNiveaLotion-S03-h700-0001f, Steady state flow stepNiveaLotion-S04-h1050-0001f, Steady state flow step

Sandpaper required to avoid slip

FILLED)P/P w/ sandpaper, 3 different gaps

OPEN)P/P, NO sandpaper, 3 different gaps

Sandpaper from McMaster-CarrPart #) 47185A51Adhesive-backsandpaper, 8” dia. disc, 600 grit

Nivea Lotion

M

17

Flow curves: different perspectives

1.000E-6 0.01000 100.0shear rate (1/s)

0.1000

1.000

10.00

100.0

1000

10000

1.000E5

1.000E6

1.000E7

visc

osity

(Pa.

s)

NiveaLotion-0001f


1.000 10.00 100.0shear stress (Pa)

0.1000

1.000

10.00

100.0

1000

10000

1.000E5

1.000E6

1.000E7

visc

osity

(Pa.

s)

NiveaLotion-0001f


18

Parallel plate correction, steady flow

10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 1031

10

100

OPEN: Apparent stress FILLED True stress

h=1050 µm h= 700 µm h= 450 µm

Sh

ear S

tress

, σ

[Pa]

Shear Rate [s-1]

Nivea LotionParallel plates with sandpaperD=40mm

M

19

Parallel plate stress correction2

02 ( )

RM r r drπ σ= ∫

3

2( )AMRR

σπ

=

43

A

Y

σσ

→

3

ln32 lnR

R

M d MR d

σπ γ

= +

ln34 lnA A

RR

dd

σ σσγ

= +

for ( ) Yrσ σ=

M

( )r Hrσ =

4/3 ratio mentioned by Brunn and Asoud, Rheol. Acta, 2002

Torque balance

Linear assumption

Apparent rim stress

Error for perfect plastic

Correction formula

20

Parallel plate stress correction, Nivea lotion steady flow

10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 1031

10

100

OPEN: Apparent stress FILLED True stress

h=1050 µm h= 700 µm h= 450 µm

Sh

ear S

tress

, σ

[Pa]

Shear Rate [s-1]

Nivea LotionParallel plates with sandpaperD=40mm

21

Roughened Cone – Works!

10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 1031

10

100

S02, P/P, h= 1050µm (uncorrected, for reference) S02, P/P, h= 700µm S02, P/P, h= 450µm S04, P/P, h=1050µm S05, Cone

Shea

r Stre

ss, σ

[P

a]

Shear Rate [s-1]

Nivea Lotion on AR-G23 different samples to show repeatability (S02, S04, S05)

all geometries with sandpaperP/P) D=40mm, with plate-plate correctionCone) D=60mm, α=2o, no correction necessary

22

Nivea lotion flow curve

10-3 10-2 10-1 100 101 102 103 10410-1

100

101

102

103

104

105

106

S02, P/P, h= 1050µm S02, P/P, h= 700µm S02, P/P, h= 450µm S04, P/P, h=1050µm S05, Cone

Vis

cosi

ty, η

[P

a.s]

Shear Stress [Pa]

Nivea Lotion3 different samples to show repeatability (S02, S04, S05)

all geometries with sandpaperP/P) D=40mm, with plate-plate correctionCone) D=60mm, α=2o, no correction necessary

23

Creep tests, low stress

Cannot determine a steady flow viscosity below the yield stress

NEGATIVE strain-rates? Is this remnant elastic recovery from the previous flow test? I saw this also with the stress-ramp flow tests, from high-to-low stresses, that at sufficiently low stresses the strain-rate was negative (see Sample #1). Or maybe it’s instrument artifact?

0 100.0 200.0 300.0 400.0 500.0 600.0time (s)

-0.50000

0

0.50000

1.0000

1.5000

2.0000

2.5000

% s

train

NiveaLotion-S04-h1050-0002c

NiveaLotion-S04-h1050-0002c, CreepNiveaLotion-S04-h1050-0003c, Creep

OPEN) σ0 = 0.1 Pa

CLOSED) σ0 = 1 Pa

24

1.000E-5 1.000E-3 0.1000 1.000 10.00 100.0shear rate (1/s)

1.000

10.00

100.0

shea

r stre

ss (P

a)

NiveaLotion-S05-ConeSP-0001f

NiveaLotion-S05-ConeSP-0001f, Steady state flow stepNiveaLotion-S06-ConeSP-0001f, Steady state flow stepNiveaLotion-S06-ConeSP-0005f, Steady state flow step

Repeatability with Rough Cone

S05-Run1, initial flow test

S06-Run1, initial flow testS06-Run5, flow after LAOS

Nivea Lotion

25

Yield Stress ModelsSt

ress

, σ

/ Pa

( )( )

B

H-B

Casson

12 2

Carreau 0 1

Y Pm

Y

Y p

n

Kσ σ µ γ

σ σ γ

σ σ µ γ

σ γη λγ−

= +

= +

= +

= +

(Sisko is subset of Carreau)

Barnes, JNNFM, 1999 (hypothetical data)

26

0.1000 1.000 10.00 100.0 1000ang. frequency (rad/s)

1.000

10.00

100.0

1000

G' (

Pa)

1.000

10.00

100.0

1000G

'' (Pa)

NiveaLotion-S06-ConeSP-0004o

NiveaLotion-S06-ConeSP-0004o, Frequency sweep step

Linear viscoelasticity

0.5% strain amplitude

27

Large amplitude oscillatory shear

0.010000 0.10000 1.0000 10.000 100.00 1000.0 10000% strain

0.1000

1.000

10.00

100.0

1000

G' (

Pa)

0.1000

1.000

10.00

100.0

1000

G'' (P

a)


NiveaLotion-S06-ConeSP-0002o, Strain sweep stepNiveaLotion-S06-ConeSP-0003o, Strain sweep step

“strain-controlled”LAOS on AR-G2

Run 2) 10 rad/sRun 3) 1 rad/s

28

Nivea lotion LAOS

0.000 0.001 0.002

0.0

0.1

0.2

Stre

ss [P

a]

Strain [-]

Nivea Lotion, AR-G2ω=10 rad/s, 6cm 2deg cone with sandpaper, T=23 C

0.00 0.01 0.02-1.0

-0.5

0.0

0.5

1.0

1.5

Stre

ss [P

a]Strain [-]


-0.1 0.0 0.1-10

-5

0

5

10

Stre

ss [P

a]

Strain [-]


0.0 0.5 1.0 1.5 2.0-20

-10

0

10

20

Stre

ss [P

a]

Strain [-]


-10 -5 0 5 10-60

-40

-20

0

20

40

60

Stre

ss [P

a]

Strain [-]


0.010000 0.10000 1.0000 10.000 100.00 1000.0 10000% strain

0.1000

1.000

10.00

100.0

1000

G' (

Pa)

0.1000

1.000

10.00

100.0

1000

G'' (P

a)


NiveaLotion-S06-ConeSP-0002o, Strain sweep step

γ0=0.13% γ0=1% γ0=10.6%

γ0=108%

γ0=1052%Needs inertia correction to

determine sample stressω = 10 rad/s

29

Model responses to LAOS

30

Pseudoplastic and yield stress fluid response to LAOS

( )( )1

2 20( ) 1

n

σ γ γη λγ−

= +

0( ) cost tγ γ ω ω=LAOS deformation

Purely viscous Carreau model

Response:

0 : yield stress1 : Newtonian

nn==

Ewoldt et al., submitted

0

( ) costy tγ ωγ

= =

1 0n = →

310

( ) sintx tγ ωγ

= =0

( ) costy tγ ωγ

= =

Pseudoplastic and yield stress fluid response to LAOS

( )( )1

2 20( ) 1

n

σ γ γη λγ−

= +

0( ) cost tγ γ ω ω=LAOS deformation

Purely viscous Carreau model

Response:

0 : yield stress1 : Newtonian

nn==

Ewoldt et al., submitted

max 0( ) at 10tσ σ λγ ω =

32

33

Elastic Bingham model

Y pE

Y

E EYGσ

σ σ µ γ

γ

γ

γ γ

γ

<

= + =

=

Yoshimura & Prud’homme., Rheol. Acta, 1987

Elastic before yield

Bingham model after yield

Important things to keep in mind:

1) Not a full continuum model as represented here2) Elastic strain can be recovered when flow reverses3) Strain-induced yielding, therefore a well defined yield surface in plate-plate tests

34

Elastic Bingham model - LAOS

Y pE

Y

E EYGσ

σ σ µ γ

γ

γ

γ γ

γ

<

= + =

=




00

maximum imposed strain~yield strainY

γγ

Γ =

0 maximum viscous stress~yield stress

p

Y

Nµ γ ωσ

=

35


Y pE

Y

E EYGσ

σ σ µ γ

γ

γ

γ γ

γ

<

= + =

=




00

Y

γγ

Γ = 0p

Y

Nµ γ ωσ

=

36


Y pE

Y

E EYGσ

σ σ µ γ

γ

γ

γ γ

γ

<

= + =

=




00

Y

γγ

Γ = 0p

Y

Nµ γ ωσ

=

37

Elastic Bingham model – Pipkin space

Y pE

Y

E EYGσ

σ σ µ γ

γ

γ

γ γ

γ

<

= + =

=




00

Y

γγ

Γ =

0p

Y

Nµ γ ωσ

=

0max 6.0Γ =

max 0.3N =

38

LAOS plate-plate artifacts

Lissajous curves of (apparent) stress σ(t) vs. strain γ(t).

Maximum (apparent) stress shown above curve, σA/σY

1. Smoothes out sharp transitions, since a portion of the material is always in the linear strain regime

2. Over-estimates stress for shear-thinning fluids, by factor of 4/3 for a perfect plastic response

Homogeneous (e.g. cone/plate) Plate-plate response

39


Y pE

Y

E EYGσ

σ σ µ γ

γ

γ

γ γ

γ

<

= + =

=

00

Y

γγ

Γ =

model from: Yoshimura & Prud’homme., Rheol. Acta, 1987

0p

Y

Nµ γ ωσ

=



00

Y

γγ

Γ =

0p

Y

Nµ γ ωσ

=

40


Y pE

Y

E EYGσ

σ σ µ γ

γ

γ

γ γ

γ

<

= + =

=

00

Y

γγ

Γ =

model from: Yoshimura & Prud’homme., Rheol. Acta, 1987

0p

Y

Nµ γ ωσ

=



00

Y

γγ

Γ =

0p

Y

Nµ γ ωσ

=

41

( ) ( )( )0 ma

2

x

0 1

1 Perfect Plastic4 0.785 Newtonian

0 Purely Elast2 2

icd pp

dE GE γ σ

πγφ π→

′′ = = → = →

Perfect plasticdissipation ratio

42

Experiments

43

Shear-thinning xanthan gum (0.2wt%)

( )0 1

max


40 Purely Elastic

d

d pp

E GE

πγφ πσ

→′′ ≡ = → =

→

44

Drilling fluid

( )0 1

max


40 Purely Elastic

d

d pp

E GE

πγφ πσ

→′′ ≡ = → =

→

45

Nivea lotion LAOS

0.000 0.001 0.002

0.0

0.1

0.2

Stre

ss [P

a]

Strain [-]


0.00 0.01 0.02-1.0

-0.5

0.0

0.5

1.0

1.5

Stre

ss [P

a]Strain [-]


-0.1 0.0 0.1-10

-5

0

5

10

Stre

ss [P

a]

Strain [-]


0.0 0.5 1.0 1.5 2.0-20

-10

0

10

20

Stre

ss [P

a]

Strain [-]


-10 -5 0 5 10-60

-40

-20

0

20

40

60

Stre

ss [P

a]

Strain [-]


0.010000 0.10000 1.0000 10.000 100.00 1000.0 10000% strain

0.1000

1.000

10.00

100.0

1000

G' (

Pa)

0.1000

1.000

10.00

100.0

1000

G'' (P

a)


NiveaLotion-S06-ConeSP-0002o, Strain sweep step

γ0=0.13% γ0=1% γ0=10.6%

γ0=108%

γ0=1052%

Needs inertia correction

Outline revisited

1. Introduction to yield stress fluidsunderstand definition/caveats of apparent yield stress fluids develop a feel for yield stress and viscosity values

2. Rheometry with yield stress fluidsidentify and avoid slip artifactscorrect for parallel plate artifactsrecognize LAOS response of yield stress fluids

Randy H. EwoldtJune 26, 2009

Part of the summer 2009 Reading Group: Yielding, Yield Stresses, ViscoelastoplasticityNon-Newtonian Fluids (NNF) Laboratory, led by Prof. Gareth McKinley

Documents

Yield Stress Fluids, Meeting #1 · Yield Stress Fluids, Meeting #1 1. Introduction to yield stress fluids understand definition/caveats of apparent yield stress fluids develop a feel