Instabilités mécaniques et solidification directionnelle de dispersions colloïdales

Transcription

1 Instabilités mécaniques et solidification directionnelle de dispersions colloïdales François Boulogne, Marguerite Léang, Frédérique Giorgiutti, Ludovic Pauchard (FAST - Université Paris Sud) Bernard Cabane (PMMH - ESPCI) Lucas Goehring (MPI - Göttingen)

2 Drying colloidal gels

3 Drying colloidal gel: drying stress global elastic modulus: E p / 4 E2 0 a 1/3 V E p ϕ: particles volume fraction E0: elastic modulus particle a: particle size γ: particles interface energy Evaporation causes pressure gradient: Darcy law at the air/liquid interface Water pressure from Darcy flow: D p = 2 p 2 : diffusivity or consolidation coefficient V E z=h σ ij α pδ ij Mechanical stress local pressure: poroelasticity, Biot (1941)

4 Drying colloidal gels Stress build-up during colloidal film consolidation - Resistance - Cracking - Reorganization

5 I. Solidification colloidal dispersion in a Hele Shaw cell (gap=200µm) SAXS, SANS cracks air suspension dispersion gel v z x y V E solidification front velocity v = V E φ ~0.4µm/s 25mm

6 I. Solidification colloidal dispersion in a Hele Shaw cell SAXS, SANS air suspension dispersion gel v cracks z y (b) (c) z x (a) z Liquide (e) ( f ) x w Transition V E solidification front velocity v = V E φ (d) Solide (g) ~0.4µm/s 2 mm Evaporation Boulogne et al. EPL (2013)

7 I. Solidification onset of structural anisotropy (nm 1 ) position peak = 0.35 = 0.61 solidification of network q z, vertical q x, horizontal z (mm) 2! ~ (q x q z ) z (mm) shear thinning effect 100µm colloidal dispersion in a Hele Shaw cell Di Giuseppe et al. Rheologica Acta (2012) Boulogne et al. EPL (2013)

8 I. Solidification compression of the suspension 0.6 skin formation (part of a drop) fluorescent colloidal particles 0.4 z (mm) q x 2 q z fluorescence colorant (basic blue) théorie advection-diffusion t + r( v) =r(d( )r ) directional cracking (Hele Shaw cell) collective diffusion coefficient: D( )= D Z r( Giorgiutti, Pauchard J. Colloid Interface Science (2013)

9 I. Solidification Uniaxial compression of the particle network by the flow Structural anisotropy Local reorganizations particles are caged by their mutual interactions

10 II. Mechanical instabilities Wrinkles P 1 P2 apple 1 T h Cracks T = E p h : strain related to the change in surface area ) E p P/2apple Pa 80 3 mm shrinkage induced by capillary pressure limited by adhesion tensile stress 60 ( ) drying 1-RHrate

11 II. Mechanical instabilities Wrinkles P 1 P2 apple 1 T h Cracks T = E p h : strain related to the change in surface area ) E p P/2apple Pa Mechanical properties of two milk protein skins after drying Céline Sadek, Cécile Le Floch-Fouéré, Romain Jeantet shrinkage induced by capillary pressure limited by adhesion tensile stress équipe TIPIL, INRA Rennes Dynamics of shell formation during drying Hervé Tabuteau, Janine Emile, Olivier Emile IPR, Rennes

12 II. Mechanical instabilities Wrinkles P 1 P 2 apple 1 T h Cracks T = E p h : strain related to the change in surface area ) E p P/2apple Pa Mechanical properties of two milk protein skins after drying Céline Sadek, Cécile Le Floch-Fouéré, Romain Jeantet shrinkage induced by capillary pressure limited by adhesion tensile stress équipe TIPIL, INRA Rennes Dynamics of shell formation during drying Hervé Tabuteau, Janine Emile, Olivier Emile IPR, Rennes

13 II. Hierarchical formation of channeling cracks network successive generations c d e connection at right angles 50µm rate 5 Bohn, Pauchard, Couder Phys Rev E (2005)

14 II. Hierarchical formation of channeling cracks network crack opening in paintings Crignier Jeanne d Arc en prison (1824) thickness

15 II. Hierarchical formation of channeling cracks network δ d * opening (w) * cracks spacing (d) h w * thickness of cracks (h) * junctions or terminations of cracks (broken or connected network) (δ=0 or >0) * orientation * organization of cracks (ordered or random) * changes of direction : locally (smooth or jagged), globally (straight or curved)

16 II. Hierarchical formation of channeling cracks network crack opening effect w E p σ Y h generation 1 substrate α.v v = dw/dt w(t) =h 1 i g 1 e t.eh/ p (α<0) crack width (µm) w(tf) model painting film thickness (µm) Léang, Giorgiutti, Pauchard

17 II. Hierarchical formation of channeling cracks network crack opening effect substrate w v = dw/dt 10 1 w(t) =h 1 E α.v p i g σ Y h 1 e t.eh/ p (α<0) crack width (µm) w time (s) successive generations of cracks Léang, Giorgiutti, Pauchard

18 II. Hierarchical formation of channeling cracks network crack opening effect substrate w v = dw/dt w(t) =h 1 E α.v p i g σ Y h 1 e t.eh/ p (α<0) crack width (µm) w (t f )= Y time (s) drying stress (t) = E pv E h t yielding behaviour of aggregated colloidal dispersions: Y = g 9 MF max a 2 = M: coordination number, Fmax: interparticle force Léang, Giorgiutti, Pauchard

19 II. Hierarchical formation of channeling cracks network Measurements using indentation testing 4000 p indenter E F R η layer INDENTATION FORCE (mn) P max 3500mN S= µm h 0 s h c h max PENETRATION DEPTH ( m) print (top view) yielding behaviour of aggregated colloidal dispersions: Y = P max 2.8A 0 P cap = 10 7 Pa Y