Fluid avalanches: from hairgel to quicksand and landslides

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- JulieAmsterdam) DRAPPIER P. Coussot, G. Ovarlez, F. Bertrand (LCPC, Paris) Viscosity x F σ = T f Stress : xy A . ∂ vy F f shear rate : γ = T σ ∂x f Viscosity : η = V0 y γÝ

σ viscosity σ η = γÝ . γγ “Yield stress fluids”

-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 andJulie solid DRAPPIER at the same time! Yield stress fluids Simple yield stress fluids: Herschel-Bulkley model η σ = σ + γ n y kÝ τσ

No flow σ y «Flow curve»

σ σ γ y & Yield stress, thixotropy and aging

Two HUGE problems:

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) 1. Measurement of the yield stress

Bentonite suspension: a typical colloidal clay gel Mayonnaise: a stable emulsion Stress loop: increase then decrease (time on the order of 2 min.) for

different pasty or granular materials 102 Stress increase Bentonite suspension Emulsion (Mayonnaise) Stress decrease 102

101

101 Shear stress (Pa) stress Shear Shear stress Shear(Pa) stress

Stress increase Stress decrease 100 100 -4 -3 -2 -1 0 1 2 10-3 10-2 10-1 100 101 102 103 104 10 10 10 10 10 10 10 Shear rate (1/s) Shear rate (1/s) 2. Shear localization (banding)

QuickTime™ et un décompresseur codec YUV420 sont requis pour visionner cette image. A first important clue: aging

Aging: increase of the viscosity at rest, and at zero (or very low) shear 1000 clay gel Bentonite 5% 100 “house of cards” structure

10

1 complex viscosity (Pas) viscosity complex 0,1

0,01 0 5000 10000 15000 aging time (s) Can aging be reversed by shear?

aging

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

104

1000

stress 4Pa 100 stress 6Pa

stress 10Pa 10 viscosity (Pas)

1

0,1 0 100 200 300 400 500 600 700

time (s) Abou et al. J. Rheol. 2003 Yield stress, aging and shear rejuvenation

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

σ = ρ α Bentonite avalanche on an inclined plane y ghsin( ) Sand avalanches

McDonald and Anderson, 1988 Aging/shear rejuvenation of a clay gel

“house of cards” structure

number of connections E ∝ ∝σ volume c RHEOLOGY: VISCOSITY BIFURCATION

104 stress (Pa) Aging 26 1000 20 16 12 9 8 6.5 100 6 5

10

1 viscosity (Pas) Shear 0.1 rejuvenation 0.01 1 10 100 1000 time (s) Bentonite (colloidal gel), 5% Coussot et al., PRL 2002 The phenomenonThe phenomenon is general!is general!

4 10 7 6 stress (Pa) 10 10 stress (Pa) 26 105 1000 20 62 16 6 64 12 10 68 4 9 70 10 8 100 6.5 72 6 1000 5 105 10 100

4

10 viscosity (Pas) 10 1 viscosity (Pas) viscosity

viscosity (Pas) 1 0.1 1000 0,1

0.01 0,01 100 0 500 1000 1500 2000 2500 3000 1 10 100 1000 1 10 100 1000 time (s) time (s) time (s) Colloidal gel Polymer gel Colloidal glass (Bentonite) (hairgel) (Laponite)

101 Foam Polystyrene beads 101 QUESTION: WHAT Stress (Pa): Torque (mNm):

190 4.24 HAPPENS IF A 4.1 0 185 10 180 3.98 3.87 175 0 SHEAR RATE 10 3.72 150 3.66 3.61 -1 10 3.59 IS IMPOSED THAT IS Shear (1/s) rate 3.58 3.55 Rotation velocity (rad/s) 3.5 NOT ACCESSIBLE WHEN 3.2 -2 10 2.1 FIXING THE STRESS? -1 0 1 2 10 10 10 10 100 101 102 Time (s) Time (s) Foam Granular matter Coussot et al., PRL 2002 (shaving foam) (polystyrene beads) Da Cruz et al PRE 2003 Vertical MRI, 40cm borehole, 0.5-2.4T Inserted rheometer

Controlled rotation velocity

r1 2 cm gap

r2

vθ ω Material

12 cm

Tangential velocity measured in a central fluid portion MRI velocity profile measurement in a Couette cell

Deformation of fictive lines within the material in a Couette geometry MRI measurements of the velocity profile Under imposed shear rate (unstable region)

Série1

Position Speed

Competition between aging and shear rejuvenation naturally leads to the viscosity bifurcation, which in turn implies SHEAR BANDING! Velocity profiles: shear localization

QuickTime™ et un décompresseur TIFF (LZW) sont requis pour visionnerIncreasing cette image. speed Simplest possible model

e.g. η λ =η + λn Instantaneous state of structure λ ( ) 0 (1 ) (degree of jamming) dλ 1 ∝ λ = −αγÝλ E τ 3 dt 10 Stress:

0.1 1 102 1.5 1.85 1.98 2.02 2.5 1

Viscosity 10 4 10

100 Coussot et al., PRL 2002 10-2 10-1 100 101 102 J. Rheol. 2002 Time γ & ‘real’ fluid Herschel-Bulkley Coussot et al., PRL 2002, PRL 2002, et al., Coussot J. Rheol.2002 c τ σ «Unstable flow curve » τ σ

τ σ ‘real’ fluid Herschel-Bulkley c τ σ No flow

η Yield stress, shear rejuvenation & aging Applications in geophysics: Quicksand and Quickclay

Three Quicksand Myths: 1) once in, don't move 2) once in, hard to get out 3) once in, one drowns

A. Khaldoun, E. Eiser, G. Wegdam, Daniel Bonn (van der Waals-ZeemanJulie Insitute DRAPPIER, 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

Gypsum Quartz Cristobali Hematite Swelling te Clays

50% 25% 15% 3% 7 %

Results of X-ray analysis

Size of the sand particles 20-50µm Fig.1 Rheology of quicksand

105 105 (a) 104 104

103 1Pa 103

102 102 1.3Pa 1 10 101 1.35Pa 0 10 1.4Pa 1.5Pa 100

-1 10 10-1 1.6Pa -2 10 10-2 0 200 400 600 800 1000 0 50 100 150

5 salinity10 10-1 mole/l salinity >2.10-2 mole/l

By mixing sand104 and clay (bentonite) in salt water, “laboratory quicksand” can be created. Viscosity increase: aging Aging: increase of the viscosity at rest, and at zero (or very low) shear: characteristic of clays

1000 clay gel Bentonite 5% 100 “house of cards” structure

10

1 complex viscosity (Pas) viscosity complex 0,1

0,01 0 5000 10000 15000 aging time (s) ..combined with liquefaction under shear

“house of cards” Structure is destroyed

number of connections E ∝ ∝σ volume c Fig.1 ….and phase separation

Phase separation: 105 sedimented105 sand (a) ω 104 with104 a very high

103 1Pa viscosity:103 φ ≈ 0.8 You’re stuck! 102 102 water 1.3Pa 1 10 101 1.35Pa sand 0 10 1.4Pa 1.5Pa 100

-1 10 To10-1 get your foot out you have to 1.6Pa -2 10 introduce10-2 water in the sand packing: 0 200 400 600 800 1000 0at 1 50cm/s : F=10 1004 N! 150 5 From salt lake: salinity10 10-1 mole/l

Salt is essential104 for the collapse: salinity needs to be >2.10-2 mole/l for the laboratory quicksand 1.4Pa 1.5Pa 10

10-1 1.6Pa Elastic modulus10 -2from rheology 200 400 600 800 1000 0 50 100 150

105

104

103

102

101

5 1015202530354045

Quicksand can support the weight of an adult person at φ=0.4! 2 F 50kg *10m /s 4 = = 5⋅10 Pa ≈ E (supposing normal and shear forces to be similar) A 10−2 m2 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 of cards 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 un décompresseur DVCPRO - PAL sont requis pour visionner cette image. Sinking away in quicksand

Sinking ball 4 10 (aluminum) on a 2.37m/s2 Bead stops shaker 3.16 3.63 4.74 5.05 5.53 103 Viscosity (Pa.s)

6.32 7.11

012345678910 Distance (cm) Clay: ball sinks immediately; sand: ball doesn’t move Ball of density 1 floats! You cannot drown in quicksand ! Density 1 g/cm3

QuickTime™ et un décompresseur DVCPRO - PAL sont requis pour visionner cette image.

Density of quicksand: approximately 2g/cm3 Quicksand

Three Quicksand Myths: 1) once in, don't move: TRUE 2) once in, hard to get out: TRUE 3) once in, one drowns: FALSE

……but what is the difference with Quick clay???? Julie DRAPPIER What is quickclay?

Natural quickclay From Trondheim-Norway ) water + non-swelling CLAY+sand NO SALT!

Illite Chlorite sand

50% 50% A few %

Results of X-ray analysis

Size of the sand particles 5-30µm Quick clay landslides

QuickTime™ et un décompresseur Cinepak-kodek fra Radius sont requis pour visionner cette image. Quick clay landslides (the Rissa raset)

QuickTime™ et un décompresseur Cinepak-kodek fra Radius sont requis pour visionner cette image. Laboratory landslides

QuickTime™ et un décompresseur sont requis pour visionner cette image. Laboratory landslides

10

liquid regime 55w% 8 yield stress regime 59w% land slid regime 61w%

6

4

2

0 0 1020304050607080 Quick clay: viscosity bifurcation Natural quick clay Trondheim, norway Sand+water + clay (Illite/Clorite), NO SALT 106

105

104

1000 1% difference

100 In water content

viscosity (Pas) 10

1

0,1

0,01 0 500 1000 1500 2000 2500 3000

time (s) Quick clay

Particle (sand+clay) suspension NO house of cards Too much water: Yield stress disappears

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

Aging and shear rejuvenation (thixotropy) are GENERAL for structured 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

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]