fluid avalanches: from hairgel to quicksand and...
TRANSCRIPT
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
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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
“house of cards”structure
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!
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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
“house of cards”structure
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….
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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
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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
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Quick clay landslides (the Rissa raset)
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Laboratory landslides
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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]