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Theoretical analysis on capillary adhesion of microsized plates with a substrate

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Abstract

The stiction of a thin plate induced by the capillary force has attracted much attention in the broad range of applications. A novel method is presented to calculate the capillary adhesion problem of the plate through analytical method. The expressions of the surface energy, the strain energy and the total potential energy of the plate–substrate system have been analyzed and delineated. By means of continuum mechanics and the principle of minimum potential energy, the governing equation of the plate with an arbitrary shape and the corresponding transversality boundary condition due to the moving bound have been derived. Then the critical adhesion radius of the circular plate has been solved according to the supplementary transversality condition. Thus the deflections of the plates are analytically calculated with different critical adhesion radii. The results may be beneficial to the engineering application and the micro/nano-measurement.

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References

  1. Palasantzas G.: Contact angle influence on the pull-in voltage of microswitches in the presence of capillary and quantum vacuum effects. J. Appl. Phys. 101, 053512 (2007)

    Article  Google Scholar 

  2. Zhang L.X., Zhao Y.P.: Adhesion of rough surfaces with plastic deformation. J. Adhesion Sci. Technol. 18, 715–729 (2005)

    Article  Google Scholar 

  3. 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  Google Scholar 

  4. 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 

  5. Hui C.Y., Jagota A., Lin Y.Y., Kramer E.J.: Constraints on microcontact printing imposed by stamp deformation. Langmuir 18, 1394–1407 (2002)

    Article  Google Scholar 

  6. Gao H.J., Wang X., Yao H.M., Gorb S., Arzt E.: Mechanics of hierarchical adhesion structures of geckos. Mech. Mater. 37, 275–285 (2005)

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Liu J.L., Feng X.Q., Wang G.F., Yu S.W.: Mechanisms of superhydrophobic states on a hydrophilic substrate. J. Phys. Condens. Matter 19, 356002 (2007)

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. 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  Google Scholar 

  11. Lei Z.K., Kang Y.L., Qiu Y., Hu M., Cen H.: Experimental study of capillary effect in porous silicon using micro-raman spectroscopy and X-ray diffraction. Chin. Phys. Lett. 21, 1377–1380 (2004)

    Article  Google Scholar 

  12. Bico, J., Roman, Moulin, L., Boudaoud, A.: Adhesion: elastocapillary coalescence in wet hair. Nature 432, 690 (2004)

  13. Liu J.L., Feng X.Q., Xia R., Zhao H.P.: Hierarchical capillary adhesion of micro-cantilevers or hairs. J. Phys. D Appl. Phys. 40, 5564–5570 (2007)

    Article  Google Scholar 

  14. Boudaoud A., Bico J., Roman B.: Elastocapillary coalescence: aggregation and fragmentation with a maximal size. Phys. Rev. E 76, 060102 (2007)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  17. de Boer M.P.: Capillary adhesion between elastically hard rough surfaces. Exp. Mech. 47, 171–183 (2007)

    Article  Google Scholar 

  18. 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 

  19. 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  Google Scholar 

  20. Maboudian R., Howe R.T.: Critical review: adhesion in surface micromechanical structures. J. Vac. Sci. Technol. B 15, 1–19 (1997)

    Article  Google Scholar 

  21. Tas N., Sonnenberg T., Jansen H., Legtenberg R., Elwenspoek M.: Stiction in surface micromachining. J. Micromech. Microeng. 6, 385–397 (1996)

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. Rymuza Z.: Control tribological and mechanical properties of MEMS surface. Part 1. Critical review. Microsyst. Technol. 5, 173–180 (1999)

    Article  Google Scholar 

  24. Ren S., Yang S., Zhao Y.: Nano-tribological study on a super-hydrophobic film formed on rough aluminum substrates. Acta Mech. Sin. 20, 159–164 (2004)

    Article  Google Scholar 

  25. 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 

  26. 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 

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

    Article  Google Scholar 

  28. Journet C., Moulinet S., Ybert C., Purcell S.T., Bocquet L.: Contact angle measurements on superhydrophobic carbon nanotube forest: effect of fluid pressure. Europhys. Lett. 71, 104–109 (2005)

    Article  Google Scholar 

  29. Wei B.Q., Vajtai R., Jung Y., Ward J., Zhang R., Ramanath G., Ajayan P.M.: Organized assembly of carbon nanotubes: cunning refinements help to customize the architecture of nanotube structures. Nature 416, 495–496 (2002)

    Article  Google Scholar 

  30. Lu C.H., Qi L.M., Yang J.H., Tang L., Zhang D.Y., Ma J.M.: 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 

  31. Lachut M.J., Sader J.E.: Effect of surface stress on the stiffness of cantilever plates. Phys. Rev. Lett. 99, 206102 (2007)

    Article  Google Scholar 

  32. Bonaccurso E., Butt H.: Microdrops on atomic force microscope cantilevers: evaporation of water and spring constant calibration. J. Phys. Chem. B 209, 253–263 (2005)

    Article  Google Scholar 

  33. Chen S.H., Soh A.K.: The capillary force in micro- and nano-indentation with different indenter shapes. Int. J. Solids Struct. 45, 3122–3137 (2008)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Mechanics, China University of Petroleum, 266555, Qingdao, China

    Jian Lin Liu

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  1. Jian Lin Liu
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Correspondence to Jian Lin Liu.

Additional information

The project was supported by Scientific Research Foundation of China University of Petroleum (Y081513), National Natural Science Foundation of China (10802099) and Doctoral Fund of Ministry of Education of China (200804251520).

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Liu, J.L. Theoretical analysis on capillary adhesion of microsized plates with a substrate. Acta Mech Sin 26, 217–223 (2010). https://doi.org/10.1007/s10409-009-0318-7

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  • DOI: https://doi.org/10.1007/s10409-009-0318-7

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