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Capillary Adhesion of Micro-beams and Plates: A Review

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Advances in Soft Matter Mechanics
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Abstract

A review is presented for the capillary adhesion of micro-beams and plates, and this phenomenon exists widely in MEMS, animal hairs, carbon nanotubes or nanowires. Although the capillary force is usually negligible at the macroscopic scale of human buildings, bridges or vehicles, it becomes dominant at small scales since the surface/volume ratio increases as smaller objects are considered. In this review, we show the fundamental theory and analysis method for general problems of capillary adhesion. Firstly, for the adhesion of micro-beam or micro-plate, the existing investigation deals with the cases of both infinitesimal and finite deformation. In use of the principle of minimum total potential energy, the critical adhered length and deflection of the micro-structure can be derived. Furthermore, the mechanism of the hierarchical structure in adhesion can be elucidated by means of energy theory. The method adopted in this chapter can also be developed to solve other adhesion problems associated with van der Waals force or electrostatic force. These findings may provide inspirations for the design of micro-devices, MEMS, micro-sensor and non-wetting materials from different aspects (e.g., geometric shape, characteristic size, surface microstructure and elasticity).

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References

  1. Neinhuis C, Barthlott W. Characterization and distribution of water-repellent, self-cleaning plant surfaces. Ann Bot, 79: 667–677, 1997.

    Article  Google Scholar 

  2. Otten A, Herminghaus S. How plants keep dry: A physicist’s point of view. Langmuir, 20: 2405–2408, 2004.

    Article  Google Scholar 

  3. Liu J L, Feng X Q, Wang G F, et al. Mechanisms of superhydrophobicity on hydrophilic substrates. J Phys: Condens Matter, 19: 356002, 2007.

    Article  Google Scholar 

  4. Hu D L, Chan B, Bush J W M. The hydrodynamics of water strider locomotion. Nature, 424: 663–666, 2004.

    Article  ADS  Google Scholar 

  5. Liu J L, Feng X Q, Wang G F. Buoyant force and sinking conditions of a hydrophobic thin rod floating on water. Phys Rev E, 76: 066103, 2007.

    Article  ADS  Google Scholar 

  6. Stewart D. The quest to quench. Nat Wildlife, 42: 52–56, 2004.

    Google Scholar 

  7. Hu D L, Bush J W M. Meniscus-climbing insects. Nature, 437: 733–736, 2005.

    Article  ADS  Google Scholar 

  8. Prakash M, Quere D, Bush J W M. Surface tension transport of prey by feeding shorebirds: The capillary ratchet. Science, 320: 931–934, 2008.

    Article  ADS  Google Scholar 

  9. Whitesides G M, Grzybowski B. Self-assembly at all scales. Science, 295: 2418–2421, 2002.

    Article  ADS  Google Scholar 

  10. Blossey R. Self-cleaning surfaces: Virtual realities. Nature Mater, 2: 301–306, 2003.

    Article  ADS  Google Scholar 

  11. Liu J L, Xia R, Li B W, et al. Directional motion of droplets in a conical tube or on a conical fibre. Chin Phys Lett, 24: 3210–3213, 2007.

    Article  ADS  Google Scholar 

  12. Zhao Y P, Wang L S, Yu T X. Mechanics of adhesion in MEMS: A review. J Adhesion Sci Technol, 17: 519–546, 2003.

    Article  ADS  Google Scholar 

  13. Israelachvili J N. Intermolecular and Surface Forces. 2nd ed. Academic, San Diego, CA, 1992.

    Google Scholar 

  14. Mastrangelo C H, Hsu C H. Mechanical stability and adhesion of microstructures under capillary forces, part I: Basic theory. J Microelectromech Syst, 2: 33–43, 1993.

    Article  Google Scholar 

  15. Mastrangelo C H, Hsu C H. Mechanical stability and adhesion of microstructures under capillary forces, part II: Experiments. J Microelectromech Syst, 2: 44–55, 1993.

    Article  Google Scholar 

  16. Tang T, Hui C Y, Glassmaker N J. Can a fibrillar interface be stronger and tougher than a non — fibrillar one? J R Soc Interface, 2: 505–516, 2005.

    Article  Google Scholar 

  17. Hui C Y, Jagota A, Lin Y Y, et al. Constraints on microcontact printing imposed by stamp deformation. Langmuir, 18: 1394–1407, 2002.

    Article  Google Scholar 

  18. Capovilla R, Guven J. Geometry of lipid vesicle adhesion. Phys Rev E, 66: 041604, 2002.

    Article  ADS  Google Scholar 

  19. Gruhn T, Lipowsky R. Temperature dependence of vesicle adhesion. Phys Rev E, 71: 011903, 2005.

    Article  ADS  Google Scholar 

  20. Seifert U. Dynamics of a bound membrane. Phys. Rev. E, 49: 3124–3127, 1994.

    Article  ADS  Google Scholar 

  21. Gorb S, Scherge M. Biological microtribology: Anisotropy in frictional forces of orthopteran attachment pads reflects the ultrastructure of a highly deformable material. Proc R Soc Lond B, 267: 1239–1244, 2000.

    Article  Google Scholar 

  22. Geim A K, Dubonos S V, Grigorieva I V, et al. Microfabricated adhesive mimicking gecko foot-hair. Nature Mater, 2: 461–463, 2003.

    Article  ADS  Google Scholar 

  23. Gao H J, Wang X, Yao H M, et al. Mechanics of hierarchical adhesion structures of geckos. Mech Mater, 37: 275–285, 2005.

    Article  Google Scholar 

  24. Yao H M, Gao H J. Shape insensitive optimal adhesion of nanoscale fibrillar structures. P Natl Acad Sci USA, 101: 7851–7856, 2004.

    Article  ADS  Google Scholar 

  25. Williams J A, Le H R. Tribology and MEMS. J Phys D: Appl Phys, 39: R201–R214, 2006.

    Article  ADS  Google Scholar 

  26. Li Q W, DePaula R, Zhang X F, et al. Drying induced upright sliding and reorganization of carbon nanotube arrays. Nanotechnology, 17: 4533–4536, 2006.

    Article  ADS  Google Scholar 

  27. Wei B Q, Vajtai R, Jung Y, et al. Microfabrication technology: Organized assembly of carbon nanotubes. Nature, 416: 495–496, 2002.

    Article  ADS  Google Scholar 

  28. Lu C H, Qi L M, Yang J H, et al. Hydrothermal growth of large-scale micropatterned arrays of ultralong ZnO nanowires and nanobelts on zinc substrate. Chem Commun, 33: 3551–3553, 2006.

    Article  Google Scholar 

  29. Bico J, Roman B, Moulin L, et al. Adhesion: Elastocapillary coalescence in wet hair. Nature, 432: 690, 2004.

    Article  ADS  Google Scholar 

  30. Zhu J, Ru C Q, Mioduchowski A. Surface energy-driven adhesion of two opposing microcantilevers. Acta Mech, 184: 33–45, 2006.

    Article  MATH  Google Scholar 

  31. de Boer M P, Michalske T A. Accurate method for determining adhesion of cantilever beams. J Appl Phys, 86: 817–827, 1999.

    Article  ADS  Google Scholar 

  32. Li X, Peng Y. Investigation of capillary adhesion between the microcantilever and the substrate with electronic speckle pattern interferometry. Appl Phys Lett, 89: 234104, 2006.

    Article  ADS  Google Scholar 

  33. Kwon H M, Kim H Y, Puell J, et al. Equilibrium of an elastically confined liquid drop. J Appl Phys, 103: 093519, 2008.

    Article  ADS  Google Scholar 

  34. Kim H Y, Mahadevan L. Capillary rise between elastic sheets. J Fluid Mech, 548: 141–150, 2006.

    Article  ADS  Google Scholar 

  35. Liu J L, Feng X Q, Xia R, et al. Hierarchical capillary adhesion of microcantilevers or hairs. J Phys D: Appl Phys, 40: 5564–5570, 2007.

    Article  ADS  Google Scholar 

  36. Journet C, Moulinet S, Ybert C, et al. Contact angle measurements on superhydrophobic carbon nanotube forest: Effect of fluid pressure. Europhys Lett, 71: 104–109, 2005.

    Article  ADS  Google Scholar 

  37. Liu J L, Feng X Q. Capillary adhesion of micro-beams: Finite deformation analyses. Chin Phys Lett, 8: 2349–2352, 2007.

    ADS  Google Scholar 

  38. Liu J L. Analogies between a meniscus and a cantilever. Chin Phys Lett, 26: 116803, 2009.

    Article  ADS  Google Scholar 

  39. Py C, Bastien R, Bico J, et al. 3D aggregation of wet fibers. Europhys Lett, 77: 44005, 2007.

    Article  ADS  Google Scholar 

  40. Boudaoud A, Bico J, Roman B. Elastocapillary coalescence: Aggregation and fragmentation with a maximal size. Phys Rev E, 76: 060102, 2007.

    Article  ADS  Google Scholar 

  41. Lin M J, Chen R. Sticking effect on center-anchored circular plates in microstructures. IEEE T Compon Pack T, 24: 645–649, 2001.

    Article  Google Scholar 

  42. Py C, Reverdy P, Doppler L, et al. Capillarity induced folding of elastic sheets. Eur Phys J Special Topics, 166: 67–71, 2009.

    Article  ADS  Google Scholar 

  43. Py C, Reverdy P, Doppler L, et al. Capillary origami: Spontaneous wrapping of a droplet with an elastic sheet. Phys Rev Lett, 98: 156103, 2007.

    Article  ADS  Google Scholar 

  44. Liu J L. Theoretical analysis on capillary adhesion of microsized plates with a substrate. Acta Mechanica Sinica, 26: 217–223, 2010.

    Article  MathSciNet  ADS  Google Scholar 

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© 2012 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg

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Liu, J., Xia, R. (2012). Capillary Adhesion of Micro-beams and Plates: A Review. In: Advances in Soft Matter Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19373-6_9

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