Drying of complex fluids: fractures L. Pauchard F luides, A - PowerPoint PPT Presentation

Drying of complex fluids: fractures L. Pauchard F luides, A utomatique, S ystèmes T hermiques Université d’Orsay, FRANCE Cargèse, Corsica, 28/07-08/08 2008

II. fractures Some motivations... - growth patterns cracks venation Couder, Pauchard, Allain, Douady EPJB (2002)

II. fractures Interests to study crack patterns... - restoration, judging authenticity and knowledge of techniques in Paintings ANR « Morphologies » L. Pauchard, B. Abou, V. Lazarus, K. Sekimoto C. Lahanier, G. Aitken (Centre de Recherche et de Restauration des Musées de France - Musée du Louvre) “ la Belle Ferronnière ” De Vinci large variety of craquelures

Interests to study crack patterns... cracking due to a physical impact “ Saint Matthias ” Georges de La Tour

Exemple of craquelures linked to the support la Joconde: Painting on a poplar panel « la Joconde: essai scientfique» ouvrage collectif (2007)

500µm

500µm

II. fractures Model: drying colloidal suspensions concentrated suspensions of colloidal particles (nanolatex ∅ ~15nm, φ V0 ~ 30%) 5 10 -6 mass variations of the layer 0 10 -5 10 -6 drying rate m (mg) -1 10 -5 -1,5 10 -5 9 -2 10 -5 -2,5 10 -5 air -3 10 -5 8 2 10 4 4 10 4 6 10 4 8 10 4 1 10 5 1,2 10 5 1,4 10 5 time substrate Constant Rate Period φ ~ 60%

II. fractures Drying colloidal suspensions Mechanical stress induced by desiccation P = − 2 γ solvent/air .cos θ evaporation  high capillary pressure ∼ − 10 7 Pa r pore shrinkage limited by adhesion

II. fractures Model: drying colloidal suspensions concentrated suspensions of colloidal particles ( φ V0 ~ 30%) 5 10 -6 mass variations of the layer 0 10 -5 10 -6 drying rate m (mg) -1 10 -5 -1,5 10 -5 9 -2 10 -5 -2,5 10 -5 air -3 10 -5 8 2 10 4 4 10 4 6 10 4 8 10 4 1 10 5 1,2 10 5 1,4 10 5 time drying process substrate Constant Rate Period Falling Rate Period φ ~ 60%

II. fractures Drying colloidal suspensions Mechanical stress induced by desiccation Drying stress due to: * shrinkage induced by capillary pressure limited by adhesion * shrinkage-resistance by the compressibility modulus of the gel mechanical stress ➙ elastic energy stored in the consolidating layer

II. fractures Drying colloidal suspensions Mechanical stress induced by desiccation V E = D ˙ flux balance at the drying surface: Darcy’law η ∇ P | surface D ∝ ( porosity ) × ( pore radius ) 2 σ ∼ η h ˙ V E drying stress depends on transport parameters: D mechanical stress depend on: * permeability of porous matrix * elasticity of porous matrix * drying kinetics * presence of surfactants (diminishing capillary pressure)

II. fractures Drying colloidal suspensions Mechanical stress induced by desiccation mechanical stress σ ➙ elastic energy stored in the consolidating layer ij Griffith criterion recovery of elastic energy = cost of surface energy Griffith Trans. R. Soc. London (1920) Xia, Hutchinson J. Mech. Phys. Solids (2000)

II. fractures Drying colloidal suspensions Mechanical stress induced by desiccation

QUIZ #1 II. fractures What is the angles distribution in a cracks pattern ? in the plane ? in 3D ?

QUIZ #1 II. fractures What is the angles distribution in a cracks pattern ? in the plane ? - 90° due to connection between cracks crack - 120° due to nucleation process in certain conditions in 3D ?

QUIZ #1 II. fractures What is the angles distribution in a cracks pattern ? in the plane ? - 90° due to connection between cracks crack - 120° due to nucleation process in certain conditions in 3D ? more complex: depends on the growth kinetics

II. fractures Directional propagation of cracks directional opened geometries suspension gel substrate silica sols or latex particles ferrofluid liquid liquid thickness gradient gel gel Pauchard, Adda-Bedia, Allain, Couder Phys. Rev. E (2002) Pauchard, Elias, Boltenhagen, Bacri Phys. Rev. E (2008)

II. fractures directional magnetic liquid colloidal particles gel

II. fractures directional magnetic liquid colloidal particles − → B → − B − → B − → B → − B gel

II. fractures Directional propagation of cracks directional confined geometries Hele Shaw cell capillary tube fractures glass slides lames de verres air suspension gel y z x cales de mylar Allain, Limat Phys. Rev. Lett. (1995) Gauthier et al. Langmuir (2007) Dufresne et al. Phys. Rev. Lett. (2003)

objectif microscope II. fractures Isotropic crack patterns isotropic suspension paroi circulaire final patterns for layers of different thicknesses susbtrat crack free isolated junctions sinuous paths connected networks hf ( µ m) h c 8 12 15 3 15 µ m 30 µ m ⎛ ⎞ porous matrix elasticity 120° ⎜ ⎟ A cell = f 2 adhesion . h f surface area: ⎜ ⎟ ⎜ ⎟ dying rate ⎝ ⎠ drying rate Atkinson et al J. Mat. Sc. (1991) Hutchinson et al Advances in Applied Mechanics (1992)

II. fractures Hierarchical formation of cracks network isotropic consolidation e c d Bohn, Pauchard, Couder Phys Rev E (2005)

II. fractures isotropic Drying kinectics 5 10 -6 0 mass variations of the layer 10 -5 10 -6 drying rate m (mg) -1 10 -5 -1,5 10 -5 9 -2 10 -5 -2,5 10 -5 -3 10 -5 8 2 10 4 4 10 4 6 10 4 8 10 4 1 10 5 1,2 10 5 1,4 10 5 time t(s)

II. fractures Delamination process isotropic rate × 5 50 µ m

II. fractures Delamination process isotropic rate × 5 50 µ m

II. fractures Delamination process isotropic layer h substrate C : delamination front rate × 5 50 µ m

II. fractures Delamination process isotropic measuring A adh /A cell A adh ?  A cell adhesion energy gel/substrate

II. fractures Delamination process isotropic measuring A adh /A cell A adh ?  A cell adhesion energy gel/substrate 5/2 ⎛ ⎞ h f h f U buckl = 2 C r 3 3/4 Y Competition between elastic energy : ⎜ ⎟ R ≪ 1 R ⎝ ⎠ ⎡ ⎤ 3 12(1 − ν 2 ) ⎢ ⎥ ⎣ ⎦ pli

II. fractures Delamination process isotropic measuring A adh /A cell A adh ?  A cell adhesion energy gel/substrate 5/2 ⎛ ⎞ h f h f U buckl = 2 C r 3 3/4 Y Competition between elastic energy : ⎜ ⎟ R ≪ 1 R ⎝ ⎠ ⎡ ⎤ 3 12(1 − ν 2 ) ⎢ ⎥ ⎣ ⎦ pli ( ) U crack = 2 Γ gel / substrat A cell − A adh and interfacial crack energy : � 5 / 2 � h f  Γ gel/substrat ∝ Y A 1 / 2 adh R

thickness gradient II. fractures isotropic RH = 46% Y = 5±1 × 10 7 N.m -2 R ≈ 85.A cell 0.44 A cell ≈ 1.8 h 2 Γ gel/sub = 70±23N.m -1 adhering area polygonal cell area Pauchard Europhys. Lett. (2006)

thickness gradient II. fractures isotropic RH = 46% RH = 70% Y = 5±1 × 10 7 N.m -2 Y = 8 ± 2 × 10 7 N.m -2 R ≈ 85.A cell 0.44 R ≈ 100.A cell 0.44 A cell ≈ 1.8 h 2 A cell ≈ 2.6 h 2 Γ gel/sub = 70±23N.m -1 adhering area Γ gel/sub = 62 ± 28N.m -1 polygonal cell area Pauchard Europhys. Lett. (2006)

thickness gradient II. fractures isotropic RH = 46% RH = 46% RH = 70% Y = 30 ± 2 × 10 7 N.m -2 Y = 5±1 × 10 7 N.m -2 Y = 8 ± 2 × 10 7 N.m -2 R ≈ 85.A cell 0.44 R ≈ 202.A cell 0.44 R ≈ 100.A cell 0.44 A cell ≈ 1.8 h 2 A cell ≈ 1.2 h 2 A cell ≈ 2.6 h 2 Γ gel/sub = 70±23N.m -1 Γ gel/sub = 30 ± 25N.m -1 adhering area Γ gel/sub = 62 ± 28N.m -1 hypothesis solvent particle capillary bridge substrate polygonal cell area Pauchard Europhys. Lett. (2006)

II. fractures isotropic Drying kinectics 5 10 -6 0 mass variations of the layer 10 -5 10 -6 drying rate m (mg) -1 10 -5 -1,5 10 -5 9 -2 10 -5 -2,5 10 -5 -3 10 -5 8 2 10 4 4 10 4 6 10 4 8 10 4 1 10 5 1,2 10 5 1,4 10 5 time t(s)

Residual stress

II. fractures isotropic A new generation of cracks inside the adhering region of gel 100 µ m rate × 5

II. fractures isotropic A new generation of cracks inside the adhering region of gel 100 µ m rate × 5

II. fractures isotropic A new generation of cracks inside the adhering region of gel 100 µ m rate × 5

II. fractures isotropic A new generation of cracks inside the adhering region of gel 100 µ m rate × 5 Archimedian spiral hf side view hm conical spiral 0 substrat

II. fractures isotropic Drying kinectics 5 10 -6 0 mass variations of the layer 10 -5 10 -6 drying rate m (mg) -1 10 -5 -1,5 10 -5 9 -2 10 -5 -2,5 10 -5 -3 10 -5 8 2 10 4 4 10 4 6 10 4 8 10 4 1 10 5 1,2 10 5 1,4 10 5 time t(s)

II. fractures Influence of the porous matrix stiffness isotropic on the crack patterns Latex particles suspension of hard particles high Tg particles T amb < Tg suspension of soft particle low Tg particles Tg < T amb binary mixtures ?

II. fractures Influence of the porous matrix stiffness on the crack patterns room temperature

II. fractures Influence of the porous matrix stiffness isotropic on the crack patterns Mechanical characterization of gels made of binary mixtures: 1. mean stress measurements during bending of desiccating gelled layer/flexible plate cracks+delamination