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From Hairgel to Quicksand and Landslides 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 stress (Pa) 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 Yield stress, shear rejuvenation & aging η «Unstable flow curve » τσ No ‘real’ fluid flow Herschel-Bulkley στ c ‘real’ fluid Herschel-Bulkley τ τ γ σc σ & Coussot et al., PRL 2002, J. Rheol. 2002 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.
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