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- Julie Amsterdam) DRAPPIER P. Coussot, G. Ovarlez, F. Bertrand (LCPC, Paris)
Viscosity x F T Stress : σ xy = F T A shear rate :. γ = x v y V 0 y Viscosity : η = σ Ý γ viscosity σ η = σ Ý γ. γ
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 and Julie solid DRAPPIER at the same time!
η Yield stress fluids Simple yield stress fluids: Herschel-Bulkley model σ = σ y + ký γ n τ σ No flow σ y «Flow curve» σ y σ γ&
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)
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 10 2 Stress increase Bentonite suspension Stress decrease 10 2 Emulsion (Mayonnaise) Shear stress (Pa) 10 1 Shear stress (Pa) 10 1 10 0 10-3 10-2 10-1 10 0 10 1 10 2 10 3 10 4 Shear rate (1/s) 10 0 10-4 10-3 10-2 10-1 10 0 10 1 10 2 Shear rate (1/s) Stress increase Stress decrease
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 complex viscosity (Pas) 1000 100 10 1 Bentonite 5% clay gel house of cards structure 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 ) 10 4 1000 viscosity (Pas) 100 10 stress 4Pa stress 6Pa stress 10Pa 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 Bentonite avalanche on an inclined plane σ y = ρghsin(α)
Sand avalanches McDonald and Anderson, 1988
Aging/shear rejuvenation of a clay gel house of cards structure E number of connections σ c volume
RHEOLOGY: VISCOSITY BIFURCATION viscosity (Pas) 10 4 1000 100 10 1 0.1 stress (Pa) 26 20 16 12 9 8 6.5 6 5 Aging Shear 0.01 1 10 100 1000 rejuvenation time (s) Bentonite (colloidal gel), 5% Coussot et al., PRL 2002
The phenomenon The is general! is general! viscosity (Pas) 10 4 1000 100 10 1 0.1 stress (Pa) 26 20 16 12 9 8 6.5 6 5 viscosity (Pas) 10 7 10 6 10 5 10 4 1000 stress (Pa) 62 64 68 70 72 viscosity (Pas) 10 6 10 5 10 4 1000 100 10 1 0,1 0.01 1 10 100 1000 time (s) Colloidal gel (Bentonite) 100 1 10 100 1000 time (s) Polymer gel (hairgel) 0,01 0 500 1000 1500 2000 2500 3000 time (s) Colloidal glass (Laponite) Shear rate (1/s) 10 1 Stress (Pa): 10 0 10-1 10-2 Foam 10 0 10 1 10 2 Time (s) Foam (shaving foam) 190 185 180 175 150 Rotation velocity (rad/s) 10 1 Polystyrene beads 10 0 10-1 Torque (mnm): 10 0 10 1 10 2 Time (s) Granular matter (polystyrene beads) 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: WHAT HAPPENS IF A SHEAR RATE IS IMPOSED THAT IS NOT ACCESSIBLE WHEN FIXING THE STRESS? Coussot et al., PRL 2002 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 visionner cette image. Increasing speed
Instantaneous state of structure (degree of jamming) E λ Simplest possible model 10 3 Stress: e.g. n λ η ( λ) = η0(1 + λ ) dλ dt = 1 τ α Ý γ λ Viscosity 10 2 10 1 0.1 1 1.5 1.85 1.98 2.02 2.5 4 10 10 0 10-2 10-1 10 0 10 1 10 2 Time Coussot et al., PRL 2002 J. Rheol. 2002
Yield stress, shear rejuvenation & aging η No flow Herschel-Bulkley «Unstable flow curve» τ σ real fluid real fluid στ c Herschel-Bulkley στ c τ σ Coussot et al., PRL 2002, J. Rheol. 2002 γ&
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-Zeeman Julie 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 te Hematite Swelling Clays 50% 25% 15% 3% 7 % Results of X-ray analysis Size of the sand particles 20-50µm
Fig.1 Rheology of quicksand 10 5 10 4 10 3 (a) 1Pa 10 5 10 4 10 3 10 2 10 1 10 0 1.3Pa 1.35Pa 1.4Pa 1.5Pa 10 2 10 1 10 0 10-1 10-2 0 200 400 600 800 1000 10 salinity 10 5-1 mole/l 1.6Pa 10-1 10-2 0 50 100 150 salinity >2.10-2 mole/l By mixing sand 10 4 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 complex viscosity (Pas) 1000 100 10 1 Bentonite 5% clay gel house of cards structure 0,1 0,01 0 5000 10000 15000 aging time (s)
..combined with liquefaction under shear house of cards Structure is destroyed E number of connections σ c volume
Fig.1.and phase separation 10 5 10 4 10 3 10 2 10 1 10 0 10-1 10-2 (a) 1Pa 1.3Pa 1.35Pa 1.4Pa 1.5Pa 1.6Pa 0 200 400 600 800 1000 10 5 From salt lake: salinity 10-1 mole/l Phase separation: 10 sedimented 5 sand with 10 a very high 4 10 2 10 1 10 0 φ 0.8 viscosity: 10 3 You re stuck! ω water sand To 10-1 get your foot out you have to introduce 10 water in the sand packing: -2 0 50 100 150 at 1 cm/s : F=10 4 N! Salt is essential 10 4 for the collapse: salinity needs to be >2.10-2 mole/l for the laboratory quicksand
1.4Pa 1.5Pa 10 10-1 Elastic modulus 1.6Pa from rheology 10-2 200 400 600 800 1000 10 5 0 50 100 150 10 4 10 3 10 2 10 1 5 10 15 20 25 30 35 40 45 F A Quicksand can support the weight of an adult person at φ=0.4! = 50kg *10m /s2 10 2 m 2 = 5 10 4 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 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 (aluminum) on a shaker 10 4 2.37m/s 2 Bead stops 3.16 Viscosity (Pa.s) 10 3 3.63 4.74 5.05 5.53 6.32 7.11 0 1 2 3 4 5 6 7 8 9 10 Distance (cm) Clay: ball sinks immediately; sand: ball doesn t move Ball of density 1 floats! You cannot drown in quicksand!
Density 1 g/cm 3 QuickTime et un décompresseur DVCPRO - PAL sont requis pour visionner cette image. Density of quicksand: approximately 2g/cm 3
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 8 liquid regime 55w% yield stress regime 59w% land slid regime 61w% 6 4 2 0 0 10 20 30 40 50 60 70 80
Quick clay: viscosity bifurcation 10 6 10 5 Natural quick clay Trondheim, norway Sand+water + clay (Illite/Clorite), NO SALT viscosity (Pas) 10 4 1000 100 10 1 0,1 0,01 0 500 1000 1500 2000 2500 3000 time (s) 1% difference In water content
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: bonn@lps.ens.fr