Acta Mechanica Solida Sinica

, Volume 23, Issue 5, pp 428–436 | Cite as

Abnormal Bending of Micro-Cantilever Plate Inducecd by a Droplet

  • Jianlin Liu
  • Xueyan Zhu
  • Xinkang Li
  • Zhiwei Li


The abnormal bending of a micro-cantilever plate induced by a droplet is of great interest and of significance in micro/nano-manipulations. In this study, the physical mechanism of this abnormal phenomenon induced by an actual droplet is elucidated. Firstly, the morphologies of 2D and 3D droplets are solved analytically or numerically. Then the Laplace pressure difference acting on the cantilever plate caused by the droplet is presented. Finally, the deflections of the micro-cantilever plates driven by the capillary forces are quantitatively analyzed. These analytical results may be beneficial to some engineering applications, such as micro-sensors, MEMS and the micro/nano-measurement.

Key words

micro-cantilever plate surface tension Laplace pressure difference abnormal bending deflection 


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  1. [1]
    Neinhuis, C. and Barthlott, W., Characterization and distribution of water-repellent, self-cleaning plant surfaces. Annuals of Botany, 1997, 79: 667–677.CrossRefGoogle Scholar
  2. [2]
    Otten, A. and Herminghaus, S., How plants keep dry: A physicists point of view. Langmuir, 2004, 20: 2405–2408.CrossRefGoogle Scholar
  3. [3]
    Liu, J.L., Feng, X.Q., Wang, G.F. and Yu, S.W., Mechanisms of superhydrophobicity on hydrophilic substrates. Journal of Physics: Condensed Matter, 2007, 19: 356002.Google Scholar
  4. [4]
    Hu, D.L., Chan, B. and Bush, J.W., The hydrodynamics of water strider locomotion. Nature, 2004, 424: 663–666.CrossRefGoogle Scholar
  5. [5]
    Liu, J.L., Feng, X.Q. and Wang, G.F., Buoyant force and sinking conditions of a hydrophobic thin rod floating on water. Physical Review E, 2007, 76: 066103.CrossRefGoogle Scholar
  6. [6]
    Feng, X.Q., Gao, X.F., Wu, Z.N., Jiang, L. and Zheng, Q.S., Superior water repellency of water strider legs with hierarchical structures: Experiments and analysis. Langmuir, 2007, 23: 4892–4896.CrossRefGoogle Scholar
  7. [7]
    Whitesides, G.M. and Grzybowski, B., Self-assembly at all scales. Science, 2002, 295: 2418–2421.CrossRefGoogle Scholar
  8. [8]
    Liu, J.L., Xia, R., Li, B.W. and Feng, X.Q., Directional motion of droplets in a conical tube or on a conical fibre. Chinese Physics Letters, 2007, 24: 3210–3213.CrossRefGoogle Scholar
  9. [9]
    Blossey, R., Self-cleaning surfaces: Virtual realities. Nature Materials, 2003, 2: 301–306.CrossRefGoogle Scholar
  10. [10]
    Wei, Z. and Zhao, Y.P., Growth of liquid bridge in AFM. Journal of Physics D: Applied Physics, 2007, 40: 4368–4376.CrossRefGoogle Scholar
  11. [11]
    Liu, J.L., 2D analytical solutions of the liquid bridge surrounding a punch. International Journal of Nanosystem, 2008, 1: 109–113.Google Scholar
  12. [12]
    Zhao, Y.P., Wang, L.S. and Yu, T.X., Mechanics of adhesion in MEMS: A review. Journal of Adhesion Science, 2003, 17: 519–546.CrossRefGoogle Scholar
  13. [13]
    Mastrangelo, C.H. and Hsu, C.H., Mechanical stability and adhesion of microstructures under capillary forces—Part I: Basic theory. Journal of Microelectromechanical System, 1993, 2: 33–43.CrossRefGoogle Scholar
  14. [14]
    Journet, C., Moulinet, S., Ybert, C., Purcell, S.T. and Bocquet, L., Contact angle measurements on superhydrophobic carbon nanotube forests: Effect of fluid pressure. Europhysics Letters, 2005, 71: 104–109.CrossRefGoogle Scholar
  15. [15]
    Bico, J., Roman, B., Moulin, L. and Boudaoud, A., Adhesion: Elastocapillary coalescence in wet hair. Nature, 2004, 432: 690.CrossRefGoogle Scholar
  16. [16]
    Kim, H.Y. and Mahadevan, L., Capillary rise between elastic sheets. Journal of Fluid Mechanics, 2006, 548: 141–150.CrossRefGoogle Scholar
  17. [17]
    Liu, J.L., Feng, X.Q., Xia, R. and Zhao, H.P., Hierarchical capillary adhesion of micro-cantileversor hairs. Journal of Physics D: Applied Physics, 2007, 40: 5564–5570.CrossRefGoogle Scholar
  18. [18]
    Lu, C.H., Qi, L.M., Yang, J.H., Tang, L., Zhang, D.Y. and Ma, J.M., Hydrothermal growth of large-scale micropatterned arrays of ultralong ZnO nanowires and nanobelts on zinc substrate. Chemical Communications, 2006, 33: 3551–3553.CrossRefGoogle Scholar
  19. [19]
    Wei, B.Q., Vajtai, R., Jung, Y., Ward, J., Zhang, R., Ramanath, G. and Ajayan, P.M., Organized assembly of carbon nanotubes. Nature, 2002, 416: 495–496.CrossRefGoogle Scholar
  20. [20]
    Grotberg, J.B. and Jensen, O.E., Biofluid mechanics in flexible tubes. Annual Review of Fluid Mechanics, 2004, 36: 121–147.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Spaepen, F., Substrate curvature resulting from the capillary forces of a liquid drop. Journal of Mechanics and Physics of Solid, 1996, 44: 675–681.CrossRefGoogle Scholar
  22. [22]
    Liu, J.L., Nie, Z.X. and Jiang, W.G., Deformation field of soft substrate induced by capillary force. Physica B, 2009, 404: 1195–1199.CrossRefGoogle Scholar
  23. [23]
    Butt, H. and Bonaccurso, E., Microdrops on Atomic Force Microscope cantilevers: Evaporation of water and spring constant calibration. Journal of Physical Chemistry B, 2005, 109: 253–263.CrossRefGoogle Scholar
  24. [24]
    Haschke, T., Bonaccurso, E. and Butt, H., Sessile-drop-induced bending of atomic force microscope cantilevers: A model system for monitoring microdrop evaporation. Journal of Micromechanics and Microengineering, 2006, 16: 2273–2280.CrossRefGoogle Scholar
  25. [25]
    Yu, Y.S. and Zhao, Y.P., Elastic deformation of soft membrane with finite thickness induced by a sessile liquid droplet. Journal of Colloid and Interface Science, 2009, 339: 489–494.CrossRefGoogle Scholar
  26. [26]
    Yu, Y.S. and Zhao, Y.P., Deformation of PDMS membrane and microcantilever by a water droplet: Comparison between Mooney-Rivlin and linear elastic constitutive models. Journal of Colloid and Interface Science, 2009, 332: 467–476.CrossRefGoogle Scholar
  27. [27]
    Zheng, X.P., Zhao, H.P., Gao, L.T., Liu, J.L., Yu, S.W. and Feng, X.Q., Elasticity-driven droplet movement on a microbeam with gradient stiffness: A biomimetic self-propelling mechanism. Journal of Colloid and Interface Science, 2008, 323: 133–140.CrossRefGoogle Scholar
  28. [28]
    Yu, Y.S., Yang, Z.Y. and Zhao, Y.P., Role of vertical component of surface tension of the droplet on the elastic deformation of PDMS membrane. Journal of Adhesion Science and Technology, 2008, 22: 687–698.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2010

Authors and Affiliations

  • Jianlin Liu
    • 1
  • Xueyan Zhu
    • 1
  • Xinkang Li
    • 1
  • Zhiwei Li
    • 1
  1. 1.Department of Engineering MechanicsChina University of PetroleumQingdaoChina

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