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

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

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Drying of complex fluids: fractures L. Pauchard F luides, A utomatique, S ystmes T hermiques Universit dOrsay, FRANCE Cargse, Corsica, 28/07-08/08 2008 II. fractures Some motivations... - growth patterns cracks venation Couder,

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SLIDE 1

Drying of complex fluids: fractures

  • L. Pauchard

Fluides, Automatique, Systèmes Thermiques Université d’Orsay, FRANCE

Cargèse, Corsica, 28/07-08/08 2008

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SLIDE 2

Some motivations...

  • II. fractures
  • growth patterns

Couder, Pauchard, Allain, Douady EPJB (2002)

cracks venation

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SLIDE 3
  • 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)

large variety of craquelures

“la Belle Ferronnière” De Vinci

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SLIDE 4

cracking due to a physical impact

“Saint Matthias” Georges de La Tour

Interests to study crack patterns...

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SLIDE 5

« la Joconde: essai scientfique»

  • uvrage collectif (2007)

la Joconde: Painting on a poplar panel

Exemple of craquelures linked to the support

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SLIDE 6

500µm

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SLIDE 7

500µm

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SLIDE 8

Model: drying colloidal suspensions

concentrated suspensions of colloidal particles (nanolatex ∅~15nm, φV0 ~ 30%) φ ~ 60%

  • II. fractures

8 9 10

  • 3 10-5
  • 2,5 10-5
  • 2 10-5
  • 1,5 10-5
  • 1 10-5
  • 5 10-6

5 10 -6 2 104 4 104 6 104 8 104 1 105 1,2 105 1,4 105

m (mg) mass variations of the layer time drying rate

Constant Rate Period air substrate

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SLIDE 9

evaporation  high capillary pressure shrinkage limited by adhesion

Mechanical stress induced by desiccation

  • II. fractures

Drying colloidal suspensions

P = −2γsolvent/air.cosθ rpore ∼ −107Pa

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SLIDE 10

Model: drying colloidal suspensions

concentrated suspensions of colloidal particles (φV0 ~ 30%) drying process φ ~ 60%

  • II. fractures

8 9 10

  • 3 10-5
  • 2,5 10-5
  • 2 10-5
  • 1,5 10-5
  • 1 10-5
  • 5 10-6

5 10 -6 2 104 4 104 6 104 8 104 1 105 1,2 105 1,4 105

m (mg) mass variations of the layer time drying rate

Constant Rate Period Falling Rate Period air substrate

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SLIDE 11
  • II. fractures

* 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

Mechanical stress induced by desiccation Drying colloidal suspensions

Drying stress due to:

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SLIDE 12

˙ VE = D η ∇P |surface

σ ∼ ηh ˙ VE D

Darcy’law flux balance at the drying surface:

D ∝ (porosity) × (pore radius)2

drying stress depends on transport parameters: mechanical stress depend on: * permeability of porous matrix * elasticity of porous matrix * drying kinetics * presence of surfactants (diminishing capillary pressure)

  • II. fractures

Mechanical stress induced by desiccation Drying colloidal suspensions

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SLIDE 13
  • II. fractures

mechanical stress σ ➙ elastic energy stored in the consolidating layer

Mechanical stress induced by desiccation Drying colloidal suspensions

recovery of elastic energy cost of surface energy Griffith criterion

Griffith Trans. R. Soc. London (1920) Xia, Hutchinson J. Mech. Phys. Solids (2000)

=

ij

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SLIDE 14
  • II. fractures

Mechanical stress induced by desiccation Drying colloidal suspensions

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SLIDE 15

QUIZ #1 What is the angles distribution in a cracks pattern ?

in the plane ? in 3D ?

  • II. fractures
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SLIDE 16

QUIZ #1 What is the angles distribution in a cracks pattern ?

  • 90° due to connection between cracks
  • 120° due to nucleation process in certain conditions

crack

in the plane ? in 3D ?

  • II. fractures
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SLIDE 17

QUIZ #1 What is the angles distribution in a cracks pattern ?

  • 90° due to connection between cracks
  • 120° due to nucleation process in certain conditions

crack

more complex: depends on the growth kinetics in the plane ? in 3D ?

  • II. fractures
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SLIDE 18

Directional propagation of cracks

  • II. fractures

directional

gel liquid

substrate suspension gel

liquid gel

Pauchard, Adda-Bedia, Allain, Couder Phys. Rev. E (2002) Pauchard, Elias, Boltenhagen, Bacri Phys. Rev. E (2008)

ferrofluid silica sols or latex particles thickness gradient

  • pened geometries
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SLIDE 19

gel liquid magnetic colloidal particles

  • II. fractures

directional

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SLIDE 20

gel liquid magnetic colloidal particles

  • II. fractures

directional

− → B − → B − → B − → B − → B

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SLIDE 21

fractures cales de mylar suspension air lames de verres gel y x z

Directional propagation of cracks

confined geometries

Gauthier et al. Langmuir (2007)

glass slides

Allain, Limat Phys. Rev. Lett. (1995) Dufresne et al. Phys. Rev. Lett. (2003)

Hele Shaw cell capillary tube

  • II. fractures

directional

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SLIDE 22

hc

Atkinson et al J. Mat. Sc. (1991) Hutchinson et al Advances in Applied Mechanics (1992)

Isotropic crack patterns

crack free

suspension susbtrat

  • bjectif microscope

paroi circulaire

connected networks isolated junctions

15µm 30µm

hf (µm)

3

8 12 15

  • II. fractures

isotropic

sinuous paths

Acell = f porous matrix elasticity adhesion dying rate ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ .hf

2

final patterns for layers of different thicknesses

drying rate

120°

surface area:

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SLIDE 23

Hierarchical formation of cracks network

Bohn, Pauchard, Couder Phys Rev E (2005)

c d e consolidation

  • II. fractures

isotropic

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SLIDE 24

8 9 10

  • 3 10-5
  • 2,5 10-5
  • 2 10-5
  • 1,5 10-5
  • 1 10-5
  • 5 10-6

5 10 -6 2 104 4 104 6 104 8 104 1 105 1,2 105 1,4 105

m (mg)

Drying kinectics

t(s)

  • II. fractures

isotropic

mass variations of the layer drying rate time

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SLIDE 25

Delamination process

50µm

rate ×5

  • II. fractures

isotropic

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SLIDE 26

Delamination process

50µm

rate ×5

  • II. fractures

isotropic

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SLIDE 27

Delamination process

50µm

layer h substrate

C : delamination front rate ×5

  • II. fractures

isotropic

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SLIDE 28

Aadh Acell measuring Aadh/Acell adhesion energy gel/substrate

?  Delamination process

  • II. fractures

isotropic

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SLIDE 29

Aadh Acell measuring Aadh/Acell adhesion energy gel/substrate

?  Delamination process

hf R ≪ 1

Ubuckl =

2C 3 12(1−ν2 ) ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 3/4 Y

hf R ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

5/2

r3

pli

Competition between elastic energy :

  • II. fractures

isotropic

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SLIDE 30

Aadh Acell measuring Aadh/Acell adhesion energy gel/substrate

?  Delamination process

hf R ≪ 1

Ubuckl =

2C 3 12(1−ν2 ) ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 3/4 Y

hf R ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

5/2

r3

pli

Competition between elastic energy : Ucrack = 2Γ gel/substrat Acell − Aadh

( )

Γgel/substrat ∝ Y A1/2

adh

hf R 5/2 and interfacial crack energy :

  • II. fractures

isotropic

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SLIDE 31

RH = 46% Y = 5±1×107 N.m-2 R ≈ 85.Acell

0.44

Acell ≈ 1.8 h2 Γgel/sub = 70±23N.m-1 thickness gradient

Pauchard Europhys. Lett. (2006)

  • II. fractures

isotropic

adhering area polygonal cell area

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SLIDE 32

RH = 46% Y = 5±1×107 N.m-2 R ≈ 85.Acell

0.44

Acell ≈ 1.8 h2 Γgel/sub = 70±23N.m-1 RH = 70% Y = 8±2×107 N.m-2 R ≈ 100.Acell

0.44

Acell ≈ 2.6 h2 Γgel/sub = 62±28N.m-1 thickness gradient

Pauchard Europhys. Lett. (2006)

  • II. fractures

isotropic

adhering area polygonal cell area

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SLIDE 33

RH = 46% Y = 5±1×107 N.m-2 R ≈ 85.Acell

0.44

Acell ≈ 1.8 h2 Γgel/sub = 70±23N.m-1 RH = 70% Y = 8±2×107 N.m-2 R ≈ 100.Acell

0.44

Acell ≈ 2.6 h2 Γgel/sub = 62±28N.m-1 thickness gradient RH = 46% Y = 30±2×107 N.m-2 R ≈ 202.Acell

0.44

Acell ≈ 1.2 h2 Γgel/sub = 30±25N.m-1

substrate particle solvent capillary bridge hypothesis

Pauchard Europhys. Lett. (2006)

  • II. fractures

isotropic

adhering area polygonal cell area

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SLIDE 34

8 9 10

  • 3 10-5
  • 2,5 10-5
  • 2 10-5
  • 1,5 10-5
  • 1 10-5
  • 5 10-6

5 10 -6 2 104 4 104 6 104 8 104 1 105 1,2 105 1,4 105

m (mg)

t(s)

Drying kinectics

  • II. fractures

isotropic

mass variations of the layer drying rate time

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SLIDE 35

Residual stress

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SLIDE 36

A new generation of cracks inside the adhering region of gel

100µm

rate ×5

  • II. fractures

isotropic

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SLIDE 37

A new generation of cracks inside the adhering region of gel

100µm

rate ×5

  • II. fractures

isotropic

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SLIDE 38

A new generation of cracks inside the adhering region of gel

100µm

rate ×5

  • II. fractures

isotropic

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SLIDE 39

A new generation of cracks inside the adhering region of gel

100µm

rate ×5

  • II. fractures

isotropic

conical spiral

hm

hf

substrat

Archimedian spiral

side view

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SLIDE 40

8 9 10

  • 3 10-5
  • 2,5 10-5
  • 2 10-5
  • 1,5 10-5
  • 1 10-5
  • 5 10-6

5 10 -6 2 104 4 104 6 104 8 104 1 105 1,2 105 1,4 105

m (mg)

t(s)

Drying kinectics

  • II. fractures

isotropic

mass variations of the layer drying rate time

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SLIDE 41

suspension of hard particles suspension of soft particle binary mixtures

Influence of the porous matrix stiffness

  • n the crack patterns

?

  • II. fractures

isotropic

Latex particles high Tg particles Tamb < Tg low Tg particles Tg < Tamb

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SLIDE 42
  • II. fractures

Influence of the porous matrix stiffness on the crack patterns

room temperature

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SLIDE 43

Influence of the porous matrix stiffness

  • n the crack patterns
  • II. fractures

isotropic

Mechanical characterization of gels made of binary mixtures:

  • 1. mean stress measurements during bending of desiccating gelled layer/flexible plate

cracks+delamination

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SLIDE 44

5 10 15 20 25 30 35 50 100 150 200 250 300 350 400

change in depth (µm)

time (s) φ=1.0 φ=0 φ=0.5 φ=0.8

Influence of the porous matrix stiffness

  • n the crack patterns

cst applied force depth layer

  • II. fractures

isotropic

Mechanical characterization of gels made of binary mixtures:

  • 2. creep measurements by micro-indention process
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SLIDE 45

∆U =

  • i,j

σijǫij

Influence of the porous matrix stiffness

  • n the crack patterns
  • II. fractures

isotropic

Recovery of elastic energy in the film:

F ∼ −a2

  • G

2(1 − ν) + η d dt

  • ǫ3/2

F

Matthews (1980)

Model for 1D-film formation:

Man, Russel Phys. Rev. Lett. (2008)

viscoelastic behaviour

(G, η)

micro-indentation measurements ⇒ cracks crack-free

∆U

⇒

deformation of the porous matrix

∆U

⇒

cracks formation

G

Kelvin-Voigt model

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SLIDE 46

hard

Influence of the layer thickness and porous matrix stiffness

  • n crack patterns
  • II. fractures

isotropic

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SLIDE 47

network of connected cracks layer thickness~100µm “rigid” particles dense network of isolated cracks layer thickness~10µm “rigid” particles low density of isolated cracks layer thickness~100µm “soft” particles

Craquelures related to the composition of the painting layer

experiments series of « les Apôtres » Georges de La Tour

20µm

equivalent thicknesses

1cm