Capillary origami
description
Transcript of Capillary origami
Capillary origami
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
José BicoPMMH-ESPCI, Paris
Wet hairs
nanotubes forest Chakrapani et al. 2004
artificial gecko
1 m 2 m
photoresist Geim et al. 2003Tanaka et al. 1993
Macroscopic brushes
1 mmwith Loïc Moulin, Benoît Roman & Arezki Boudaoud
Nature 2004
40
30
20
10
0403020100
2-lamellae
d
Lwet
Ltotal
Lwet [mm]
Ltotal [mm]
Lstick
hJurin =2gd
plastic transparency, d = 1 mm, h = 100 msilicone oil
Lstick
0.01
0.1
1
0.0001 0.001 0.01 0.1 1
Fracture
d
Lstick
Lstick ~ dLstick
2
2LstickE h3 Lstick / LEC
d / LEC
170 m 100 m 50 m
Elasto-capillary length
LEC =
~
1/4
d 1/2Eh3Lstick ~ LEC d 1/2 1/2
Griffith, 1921
Eh3
302520151050
100
80
60
40
20
0
Multi-lamellae
N lamellae
Eh3N/2
dd N/2
Lstick
Lstick [mm]
N lamellae
Lstick ~ N d LEC3 2 24
4
3
2
1
01.21.00.80.60.40.20.0
Self-similar distributions
N/Nmax
(N/Nmax)
Nmax2(N/Nmax)
n (N )Ntotal
=
23
4
5
…
Nmax
Nmax = 6 Nmax = 7 Nmax = 8 Nmax = 9 Nmax = 10 Nmax = 11
fragmentation
coalescence
actual brush ≠ 2p
Arezki Boudaoud's talk
Fibres
? ?or
Elementary sticking
Fibre bundles
Eb3N/2
Lsec
N/2 N/2
d N/2
d
1
10
1 10 100N
Lstick ~ N d LEC
3/8 1/2 1/2
Lstick /d LEC1/2 1/2
LEC =
with Renaud Bastien, Benoît Roman, Arezki Boudaoud & Charlotte PyEurophys. Lett. 2007
Eb3
Piercing an interface
?L
HbEuler buckling
F = 2b
F
Lcrit =2 F
EI ~ Eb3
with Benoît Roman & Sébastien NeukirchJMPS 2007
Post-buckling
1
0.8
0.6
0.4
0.2
0
-0.2
1.61.41.210.80.60.40.20
continuous transitiondiscontinuous transition
Hb /Lcrit
L/Lcrit
L Hb
Sébastien Neukirch's talk
Capillary origami
with Lionel Doppler, Paul Reverdy, Benoît Roman, Charles Baroud & Charlotte Py
Flexible sheet
L
3d ?
folds ?crumpling ?singularities ?
Phys. Rev. Lett. 2007
Pyramids
1 mm
Encapsulation (L >> LEC)
1 mm
Closes ? ...
S /L2
/L
/ R
R
LEC = Eh3
L > 3.5 LEC
S
QuickTime™ and aMotion JPEG B decompressor
are needed to see this picture.
2d simulation
... or reopens ?
S /L2
/L
L < 3.5 LEC
/ R
R
LEC = Eh3
S
2d simulation
QuickTime™ and aMotion JPEG B decompressor
are needed to see this picture.
Measuring LEC
liquidair
0.89 LEC
elastica + B.C. angle = 0curvaturture = √2/LEC
Closing conditions (3d)
LEC [mm]
Lcrit [mm]
L
LLcrit 7 LEC
2D model:Lcrit 3,5 LEC
LEC = Eh3
Open questions
role of edges, 3D model
"ridge" ?
sealing
1
0.8
0.6
0.4
0.2
020151050
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
Compressed ring
with Aline Delbos, Ariane Calvar, Benoît Roman, Denis Bartolo & Anne Juel
surfactant
A/A0
R` /EI3
1 cm
R2 ~EI RR2
buckling:
2D origami
with Aline Delbos, Benoît Roman & Anne Juel
oil lense
L < Lcrit L > Lcrit
Conclusion: elasto-capillarity
bending + capillarity elastocapillary length
LEC = Eh3
dominant at small scales h3/2
Prospects: delamination
ingredients :
elasticity / adhesion
biaxial compression
with Benoît Roman, Denis Bartolo & Pedro Reis
200 nm C on SiO2, Gille & Rau 1984
50 µm
5 mm
Acknowledgments
Loïc MoulinSociété de Amis de l'ESPCI
Arezki Boudaoud
Charlotte PyCharles Baroud
Renaud Bastien ACI jeunes chercheurs - CNRS
Lionel Doppler
Aline Delbos
Sébastien Neukirch
Benoît Roman
Denis BartoloAriane CalvarAnne Juel
Pedro Reis
Fabien Closa