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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
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Wet hairs nanotubes forest Chakrapani et al. 2004 artificial gecko 1 m 2 m photoresist Geim et al. 2003Tanaka et al. 1993
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Macroscopic brushes 1 mm with Loïc Moulin, Benoît Roman & Arezki Boudaoud Nature 2004
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2-lamellae d L wet L total L wet [mm] L total [mm] L stick h Jurin = 22 gd plastic transparency, d = 1 mm, h = 100 m silicone oil L stick
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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
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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 3 2 2 4
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Self-similar distributions N/N max (N/N max ) N max 2 (N/N max ) n (N )n (N ) N total = 2 3 4 5 … 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
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Fibres ? ?or Elementary sticking
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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. 2007 Eb 3
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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
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Post-buckling continuous transition discontinuous transition H b /L crit L/L crit L HbHb Sébastien Neukirch's talk
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Capillary origami with Lionel Doppler, Paul Reverdy, Benoît Roman, Charles Baroud & Charlotte Py Flexible sheet L 3d ? folds ? crumpling ? singularities ? Phys. Rev. Lett. 2007
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Pyramids 1 mm
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Encapsulation (L >> L EC ) 1 mm
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Closes ?... S /LS /L 2 /L /L / R/ R R L EC = Eh 3 L > 3.5 L EC S 2d simulation
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... or reopens ? S /LS /L 2 /L /L L < 3.5 L EC / R/ R R L EC = Eh 3 S 2d simulation
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Measuring L EC liquidair 0.89 L EC elastica + B.C. angle = 0 curvaturture = √2/L EC
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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
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Open questions role of edges, 3D model "ridge" ? sealing
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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:
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2D origami with Aline Delbos, Benoît Roman & Anne Juel oil lense L < L crit L > L crit
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Conclusion: elasto-capillarity bending + capillarity elastocapillary length L EC = Eh 3 dominant at small scales h h 3/2
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Prospects: delamination ingredients : elasticity / adhesion biaxial compression with Benoît Roman, Denis Bartolo & Pedro Reis 200 nm C on SiO 2, Gille & Rau 1984 50 µm 5 mm
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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
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