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