Transcript Document

Capillary origami
José Bico
PMMH-ESPCI, Paris
with
Charlotte Py, Charles Baroud, Benoît Roman, Sébastien Neukirch, Arezki Boudaoud
Loïc Moulin, Renaud Bastien, Lionel Doppler, Paul Reverdy, Aline Delbos, Ariane Calvar
PMMH-ESPCI, LadHyx, LPS-ENS, LMM-Paris6
Wet hairs
nanotubes forest
2 mm
1 mm
photoresist
Chakrapani et al. 2004
Tanaka et al. 1993
artificial gecko
Geim et al. 2003
Macroscopic brushes
1 mm
with Loïc Moulin, Benoît Roman & Arezki Boudaoud
Nature 2004
2-lamellae
Lwet [mm]
40
Ltotal
30
Lstick
20
d
Lstick
Lwet
10
hJurin = 2g
rgd
0
0
10
20
30
40
Ltotal [mm]
plastic transparency, d = 1 mm, h = 100 mm
silicone oil
Fracture
2
Lstick / LEC
g Lstick ~ E h d2 Lstick
Lstick
3
Griffith, 1921
3 1/4
Lstick ~ Eh
g
d
d
1
Lstick
1/2
1/2
~ LEC d
1/2
0.1
Elasto-capillary length
LEC =

170 mm

100 mm

50 mm
Eh3
g
0.01
0.0001
0.001
0.01
0.1
1
d / LEC
Multi-lamellae
3 2 2
4
d
Lstick ~ N d LEC
d N/2
Lstick [mm]
100
Eh3N/2
80
Lstick
60
40
N lamellae
20
0
0
5
10
15
20
25
30
N lamellae
Self-similar distributions
coalescence
f (N/Nmax) =
Nmax
2
3
n(N ) 2
N
Ntotal max
f (N/Nmax)
4






4
3
5
…
Nmax = 6
Nmax = 7
Nmax = 8
Nmax = 9
Nmax = 10
Nmax = 11
2
1
fragmentation
actual brush ≠ 2 p
0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
N/Nmax
 Arezki Boudaoud's talk
Fibres
Elementary sticking
?
or
?
Fibre bundles
Lstick ~ N
d
N/2
3/8 1/2 1/2
3
LEC = Eb
g
d LEC
N/2
1/2 1/2
d N/2
Lstick /d LEC
10
Eb3N/2
Lsec
1
1
10
100
N
with Renaud Bastien, Benoît Roman, Arezki Boudaoud & Charlotte Py
Europhys. Lett. 2007
Piercing an interface
F
Hb
Euler buckling
F = 2pbg
L
?
Lcrit =
p
2
EI
~
F
Eb3
g
with Benoît Roman & Sébastien Neukirch
JMPS 2007
Post-buckling
Hb /Lcrit
1
L
0.8
Hb
0.6
0.4
0.2
0
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
L/Lcrit
continuous transition
discontinuous transition
 Sébastien Neukirch's talk
Capillary origami
3d ?
Flexible sheet
L
folds ?
crumpling ?
singularities ?
with Lionel Doppler, Paul Reverdy, Benoît Roman, Charles Baroud & Charlotte Py
Phys. Rev. Lett. 2007
Pyramids
1 mm
Encapsulation (L >> LEC)
1 mm
Closes ? ...
2d simulation
d /L
3
Eh
LEC =
g
QuickTime™ and a
Motion JPEG B decompressor
are needed to see this picture.
L > 3.5 LEC
S/L2
g
g
d
g /R
S
R
... or reopens ?
2d simulation
d /L
3
Eh
LEC =
g
L < 3.5 LEC
S/L2
g
g
d
g /R
S
R
QuickTime™ and a
Motion JPEG B decompressor
are needed to see this picture.
Measuring LEC
air
liquid
0.89 LEC
elastica + B.C.
angle = 0
curvaturture = √2/LEC
Closing conditions (3d)
3
Eh
LEC =
g
Lcrit [mm]
L
Lcrit  7 LEC
2D model:
Lcrit  3,5 LEC
L
LEC [mm]
Open questions
role of edges,
3D model
"ridge" ?
sealing
Compressed ring
surfactant
g-
QuickTime™ and a
MPEG-4 V ideo decompressor
are needed to see this picture.
g+
1 cm
A/A0
0.8
buckling:
Dg
R2
1
EI
~ 2R
R
0.6
0.4
0.2
0
0
5
10
Dg R`3 /EI
15
20
with Aline Delbos, Ariane Calvar, Benoît Roman, Denis Bartolo & Anne Juel
2D origami
oil lense
L < Lcrit
L > Lcrit
with Aline Delbos, Benoît Roman & Anne Juel
Conclusion: elasto-capillarity
bending + capillarity  elastocapillary length
3
Eh
LEC =
g
 h3/2
 dominant at small scales
Prospects: delamination
ingredients :
elasticity / adhesion
biaxial compression
50 µm
200 nm C on SiO2, Gille & Rau 1984
5 mm
with Benoît Roman, Denis Bartolo & Pedro Reis
Acknowledgments
Benoît Roman
Arezki Boudaoud
Loïc Moulin
Renaud Bastien
Sébastien Neukirch
Charlotte Py
Charles Baroud
Lionel Doppler
Fabien Closa
Aline Delbos
Denis Bartolo
Ariane Calvar
Anne Juel
Pedro Reis
Société de Amis de l'ESPCI
ACI jeunes chercheurs - CNRS