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 Bico PMMH-ESPCI, Paris

Wet hairs nanotubes forest Chakrapani et al artificial gecko 1  m 2  m photoresist Geim et al. 2003Tanaka et al. 1993

Macroscopic brushes 1 mm with Loïc Moulin, Benoît Roman & Arezki Boudaoud Nature 2004

2-lamellae d L wet L total L wet [mm] L total [mm] L stick h Jurin = 22  gd plastic transparency, d = 1 mm, h = 100  m silicone oil L stick

Fracture d L stick  ~ d 2 2 E hE h 3 L stick / L EC d / L EC 170  m 100  m  50  m Elasto-capillary length L EC =  ~  1/4 d 1/2 Eh 3 L stick ~ L EC d 1/2 Griffith, 1921 Eh 3

Multi-lamellae N lamellae Eh 3 N/2 d d N/2 L stick L stick [mm] N lamellae L stick ~ N d L EC

Self-similar distributions N/N max   (N/N max ) N max 2   (N/N max ) n (N )n (N ) N total = … N max  N max = 6  N max = 7  N max = 8  N max = 9  N max = 10  N max = 11 fragmentation coalescence actual brush ≠ 2 p  Arezki Boudaoud's talk

Fibres ? ?or Elementary sticking

Fibre bundles Eb 3 N/2 L sec N/2 d N/2 d N L stick ~ N d L EC 3/8 1/2 L stick /d L EC 1/2 L EC =  with Renaud Bastien, Benoît Roman, Arezki Boudaoud & Charlotte Py Europhys. Lett Eb 3

Piercing an interface ? L HbHb Euler buckling F = 2   b  F L crit =  2 F EI ~  Eb 3 with Benoît Roman & Sébastien Neukirch JMPS 2007

Post-buckling continuous transition discontinuous transition H b /L crit L/L crit L HbHb  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 >> L EC ) 1 mm

Closes ?... S /LS /L 2  /L /L    / R/ R R L EC =  Eh 3 L > 3.5 L EC  S 2d simulation

... or reopens ? S /LS /L 2  /L /L L < 3.5 L EC    / R/ R R L EC =  Eh 3  S 2d simulation

Measuring L EC liquidair 0.89 L EC elastica + B.C. angle = 0 curvaturture = √2/L EC

Closing conditions (3d) L EC [mm] L crit [mm] L L L crit  7 L EC 2D model: L crit  3,5 L EC L EC =  Eh 3

Open questions role of edges, 3D model "ridge" ? sealing

Compressed ring with Aline Delbos, Ariane Calvar, Benoît Roman, Denis Bartolo & Anne Juel surfactant   A/A0A/A0   R` /EI 3 1 cm  R 2 ~ EI R R2R2 buckling:

2D origami with Aline Delbos, Benoît Roman & Anne Juel oil lense L < L crit L > L crit

Conclusion: elasto-capillarity bending + capillarity  elastocapillary length L EC =  Eh 3  dominant at small scales  h h 3/2

Prospects: delamination ingredients : elasticity / adhesion biaxial compression with Benoît Roman, Denis Bartolo & Pedro Reis 200 nm C on SiO 2, Gille & Rau µm 5 mm

Acknowledgments Loïc Moulin Société de Amis de l'ESPCI Arezki Boudaoud Charlotte Py Charles Baroud Renaud Bastien ACI jeunes chercheurs - CNRS Lionel Doppler Aline Delbos Sébastien Neukirch Benoît Roman Denis Bartolo Ariane Calvar Anne Juel Pedro Reis Fabien Closa