fluid avalanches: from hairgel to quicksand and...

Fluid avalanches: from hairgel to quicksand and landslides

Julie DRAPPIER

Daniel Bonn(LPS de l’ENS-Paris and WZI-Amsterdam)

with:N . Huang, J. Meunier (ENS)

E. Khaldoun, S. Jabbari, E. Eiser, G. Wegdam (WZI-Amsterdam)

P. Coussot, G. Ovarlez, F. Bertrand (LCPC, Paris)

yV0

x

σ

.γ

Viscosity

shear rate :xvy

∂∂

=γ

Stress : σ xy =FT

A

Viscosity :

.

η =σÝγ

FT

γ

η =σÝγ

viscosity

“Yield stress fluids”

Julie DRAPPIER

-in your refrigerator: mayonnaise, ketchup, yoghurt, whipped cream…-in your bathroom: beauty creams, hairgel, shaving foam…-in civil engineering: (wet) sand, concrete, cement….-in geophysisics: sand, quicksand, quick clay…

Liquid and solid at the same time!

Simple yield stress fluids: Herschel-Bulkley modelYield stress fluids

σ

ητ

γ&

Noflow

« Flow curve »

σ

σ = σ y + kÝ γ n

σ y

σ y

Yield stress, thixotropy and aging

Two HUGEproblems:

1. Yield stress is difficult, if not impossible to measure experimentally (‘παντα ρει’)

2. Herschel-Bulkley model does NOT account for shear localization (shear banding)

10-4 10-3 10-2 10-1 100 101 102100

101

102

Emulsion (Mayonnaise)

Shea

r stre

ss (P

a)

Shear rate (1/s)

Stress increase Stress decrease

10-3 10-2 10-1 100 101 102 103 104100

101

102

Bentonite suspension

She

ar s

tress

(Pa)

Shear rate (1/s)

Stress increase Stress decrease

Stress loop: increase then decrease(time on the order of 2 min.) for

different pasty or granular materials

1. Measurement of the yield stressBentonite suspension: a typical colloidal clay gelMayonnaise: a stable emulsion

QuickTime™ et undécompresseur codec YUV420

sont requis pour visionner cette image.

2. Shear localization (banding)

0,01

0,1

1

10

100

1000

0 5000 10000 15000

com

plex

vis

cosi

ty (P

as)

aging time (s)

Aging: increase of the viscosity at rest, and at zero (or very low) shear

Bentonite 5%

A first important clue: aging

“house of cards”structure

clay gel

aging

rejuvenation

Can aging be reversed by shear?

Second important clue: « shear rejuvenation »(«French yoghurt effect )

Abou et al. J. Rheol. 2003

0,1

1

10

100

1000

104

0 100 200 300 400 500 600 700

stress 4Pa

stress 6Pa

stress 10Pa

visc

osity

(Pas

)

time (s)

Competition between aging and shear rejuvenation is general for soft materials,and leads to AVALANCHES

Bentonite avalanche on an inclined plane

Yield stress, aging and shear rejuvenation

σ y = ρgh sin(α)

Sand avalanches

McDonald and Anderson, 1988

Aging/shear rejuvenation of a clay gel


E ∝ number of connectionsvolume

∝σ c

0.01

0.1

1

10

100

1000

104

1 10 100 1000

26201612986.565

visc

osity

(Pas

)

time (s)

stress (Pa) Aging

Shear rejuvenation

RHEOLOGY: VISCOSITY BIFURCATION

Bentonite (colloidal gel), 5% Coussot et al., PRL 2002

0.01

0.1

1

10

100

1000

104

1 10 100 1000

26201612986.565

visc

osity

(Pas

)

time (s)

stress (Pa)

100

1000

104

105

106

107

1 10 100 1000

6264687072

visc

osity

(Pas

)

time (s)

stress (Pa)

0,01

0,1

1

10

100

1000

104

105

106

0 500 1000 1500 2000 2500 3000

visc

osity

(Pas

)

time (s)

The phenomenon is general!

Colloidal glass(Laponite)

Colloidal gel(Bentonite)

Polymer gel(hairgel)

100 101 102

10-2

10-1

100

101

Stress (Pa):

Foam

She

ar ra

te (1

/s)

Time (s)

190 185 180 175 150

Granular matter(polystyrene beads)

Foam(shaving foam)

100 101 10210-1

100

101

Polystyrene beads

Torque (mNm):

Rot

atio

n ve

loci

ty (r

ad/s

)

Time (s)

4.24 4.1 3.98 3.87 3.72 3.66 3.61 3.59 3.58 3.55 3.5 3.2 2.1

QUESTION: WHATHAPPENS IF A SHEAR RATE

IS IMPOSED THAT ISNOT ACCESSIBLE WHEN

FIXING THE STRESS?

Coussot et al., PRL 2002Da Cruz et al PRE 2003

The phenomenon is general!

2 cm gapr1

r2

ω

12 cm

Vertical MRI, 40cm borehole, 0.5-2.4TInserted rheometer

Controlled rotation velocity

Tangential velocity measuredin a central fluid portion

θv Material

MRI velocity profile measurement in a Couette cell

Deformation of fictive lines within the material in a Couette geometry

Série1

Speed Posi

tion

MRI measurements of the velocity profileUnder imposed shear rate (unstable region)

Competition between aging and shear rejuvenationnaturally leads to the viscosity bifurcation, which

in turn implies SHEAR BANDING!

QuickTime™ et undécompresseur TIFF (LZW)


Velocity profiles: shear localization

Increasing speed

Instantaneous state of structure(degree of jamming)

λ )1()( 0nληλη +=

dλdt

= 1τ

−αÝ γ λ

e.g.

10-2 10-1 100 101 102

100

101

102

103

Stress:

Visc

osity

Time

0.1 1 1.5 1.85 1.98 2.02 2.5 4 10

Simplest possible model

Coussot et al.,PRL 2002J. Rheol. 2002

E ∝ λ

τcτ

η

cτ

τ

γ&

Noflow

«Unstable flow curve »

Yield stress, shear rejuvenation & aging

σ

σ

σ

Herschel-Bulkley

‘real’ fluid

‘real’ fluid

Herschel-Bulkley

Coussot et al., PRL 2002, J. Rheol. 2002

σ

Applications in geophysics: Quicksand and Quickclay

Julie DRAPPIER

Three Quicksand Myths:1) once in, don't move2) once in, hard to get out3) once in, one drowns

A. Khaldoun, E. Eiser, G. Wegdam, Daniel Bonn (van der Waals-Zeeman Insitute, University of Amsterdam and

LPS, ENS-Paris)

What is quicksand?Natural quicksand

From Qom-Iran (salt lake)And Tarfaya-Maroc (close to the sea)

Sand+water + CLAY +SALT

Size of the sand particles 20-50µm

7 %3%15%25%50%

Swelling Clays

HematiteCristobalite

QuartzGypsum

Results of X-ray analysis

0 50 100 15010-2

10-1

100

101

102

103

104

105

104

105

0 200 400 600 800 100010-2

10-1

100

101

102

103

104

105

1.6Pa

1.35Pa1.4Pa 1.5Pa

1.3Pa

1Pa

(a)

Fig.1Rheology of quicksand

By mixing sand and clay (bentonite) in salt water, “laboratory quicksand” can be created.

salinity 10-1 mole/l salinity >2.10-2 mole/l

0,01

0,1

1

10

100

1000

0 5000 10000 15000

com

plex

vis

cosi

ty (P

as)

aging time (s)

Aging: increase of the viscosity at rest, and at zero (or very low) shear: characteristic of clays

Bentonite 5%

Viscosity increase: aging


clay gel

..combined with liquefaction under shear

“house of cards”Structure is destroyed

E ∝ number of connectionsvolume

∝σ c

0 50 100 15010-2

10-1

100

101

102

103

104

105

104

105

0 200 400 600 800 100010-2

10-1

100

101

102

103

104

105

1.6Pa

1.35Pa1.4Pa 1.5Pa

1.3Pa

1Pa

(a)

Fig.1….and phase separation

Salt is essential for the collapse: salinity needs to be >2.10-2

mole/l for the laboratory quicksand

From salt lake: salinity 10-1 mole/l

To get your foot out you have to introduce water in the sand packing:

at 1 cm/s : F=104 N!

Phase separation:sedimented sandwith a very high viscosity:You’re stuck!

ωφ ≈ 0.8

water

sand

0 50 100 15010-2

10-1

10

5 10 15 20 25 30 35 40 45

101

102

103

104

105

200 400 600 800 1000

1.6Pa

1.4Pa 1.5Pa

Elastic modulus from rheology

Quicksand can support the weight of an adult person at φ=0.4!FA

= 50kg*10m /s2

10−2 m2 = 5⋅104 Pa ≈ E (supposing normal and shear forces to be similar)

Electron microscopy of quicksand

quicksand

« house of cards structure »in which a dilute (φ=0.40) sand packing

is stable against sedimentation because of the yield

stress of the clay suspension.

Both the packing and the house ofcards structure are unstable against

mechnical perturbation.

The high salt concentration makes the colloids flocculate, making the

liquefaction even more spectacular.

Next questions: -buoyancy?-normal/viscous stresses

Sinking test….

QuickTime™ et undécompresseur DVCPRO - PAL


Sinking away in quicksandSinking ball (aluminum) on a shaker

Clay: ball sinks immediately; sand: ball doesn’t move

Ball of density 1 floats! You cannot drown in quicksand !

0 1 2 3 4 5 6 7 8 9 10

103

104

7.11

6.32

5.535.054.74

3.633.16

2.37m/s2 Bead stops

Distance (cm)

Vis

cosi

ty (P

a.s)

Density 1 g/cm3

QuickTime™ et undécompresseur DVCPRO - PAL


Density of quicksand: approximately 2g/cm3

Quicksand

Julie DRAPPIER

Three Quicksand Myths:1) once in, don't move: TRUE2) once in, hard to get out: TRUE3) once in, one drowns: FALSE

……but what is the difference with Quick clay????

What is quickclay?Natural quickclay

From Trondheim-Norway)

water + non-swelling CLAY+sandNO SALT!

Size of the sand particles 5-30µm

A few %50%50%

sandChloriteIllite

Results of X-ray analysis

Quick clay landslides

QuickTime™ et undécompresseur Cinepak-kodek fra Radiussont requis pour visionner cette image.

Quick clay landslides (the Rissa raset)

QuickTime™ et undécompresseur Cinepak-kodek fra Radiussont requis pour visionner cette image.

Laboratory landslides

QuickTime™ et undécompresseur


Laboratory landslides

0 10 20 30 40 50 60 70 800

2

4

6

8

10

liquid regime 55w% yield stress regime 59w% land slid regime 61w%

Quick clay: viscosity bifurcationNatural quick clay

Trondheim, norwaySand+water + clay (Illite/Clorite),

NO SALT

0,01

0,1

1

10

100

1000

104

105

106

0 500 1000 1500 2000 2500 3000

visc

osity

(Pas

)

time (s)

1% difference In watercontent

Quick clay

Particle (sand+clay) suspension

NO house of cardsToo much water:

Yield stress disappears

Sand particles (10-100 mm) and clay (Illite and Chlorite)Illite and Chlorite are non-swelling clays: no electroststaticinteractions and thus no house-of-cards structure.

Aging and shear rejuvenation (thixotropy) are GENERAL forstructured complex fluids and lead naturally to

-a viscosity bifurcation-shear localization

Providing a common framework (the rheological properties)To describe glasses, gels, granular matter, emulsions, clayey soils…..

Applications in geophysics: landslides, quicksand

General conclusion

Coussot et al., Phys.Rev.Lett 2002, Huang et al., Phys.Rev.Lett 2005,Quicksand: Khaldoun et al, Nature, september 2005

Questions/remarks: [email protected]

fluid avalanches: from hairgel to quicksand and...

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