Acta Mechanica Sinica

, Volume 33, Issue 1, pp 40–61 | Cite as

Effects of hysteresis of static contact angle (HSCA) and boundary slip on the hydrodynamics of water striders

  • J. Zheng
  • B. S. Wang
  • W. Q. Chen
  • X. Y. Han
  • C. F. Li
  • J. Z. Zhang
  • K. P. Yu
Research Paper


It is known that contact lines keep relatively still on solids until static contact angles exceed an interval of hysteresis of static contact angle (HSCA), and contact angles keep changing as contact lines relatively slide on the solid. Here, the effects of HSCA and boundary slip were first distinguished on the micro-curvature force (MCF) on the seta. Hence, the total MCF is partitioned into static and dynamic MCFs correspondingly. The static MCF was found proportional to the HSCA and related with the asymmetry of the micro-meniscus near the seta. The dynamic MCF, exerting on the relatively sliding contact line, is aroused by the boundary slip. Based on the Blake–Haynes mechanism, the dynamic MCF was proved important for water walking insects with legs slower than the minimum wave speed \(23\,\hbox {cm}\cdot \hbox {s}^{-1}\). As insects brush the water by laterally swinging legs backwards, setae on the front side of the leg are pulled and the ones on the back side are pushed to cooperatively propel bodies forward. If they pierce the water surface by vertically swinging legs downwards, setae on the upside of the legs are pulled, and the ones on the downside are pushed to cooperatively obtain a jumping force. Based on the dependency between the slip length and shear rate, the dynamic MCF was found correlated with the leg speed U, as \(F\sim C_{1}U+C_{2} U^{2+\varepsilon }\), where \(C_{1}\) and \(C_{2}\) are determined by the dimple depth. Discrete points on this curve could give fitted relations as \(F\sim U^{b}\) (Suter et al., J. Exp. Biol. 200, 2523–2538, 1997). Finally, the axial torque on the inclined and partially submerged seta was found determined by the surface tension, contact angle, HSCA, seta width, and tilt angle. The torque direction coincides with the orientation of the spiral grooves of the seta, which encourages us to surmise it is a mechanical incentive for the formation of the spiral morphology of the setae of water striders.


Seta Water strider Hysteresis of static contact angle (HSCA) Boundary slip 



The project was supported by the National Natural Science Foundation of China (Grant 11502097), the Nature and Science Foundation of Jiangsu Province (Grant BK20130478), and the Foundation of Senior Talent of Jiangsu University (Grant 1281130025). We thank the profound questions of the reviewers of this paper. Speculations on their questions further enhanced the quality and completeness of this paper.


  1. 1.
    Hu, D.L., Bush, J.W.M.: The hydrodynamics of water-walking arthropods. J. Fluid Mech. 644, 5–33 (2010)CrossRefMATHGoogle Scholar
  2. 2.
    Hu, D.L.: The hydrodynamics of water-walking insects and spiders. [Ph.D. Thesis], Massachusetts Institute of Technology, America (2006)Google Scholar
  3. 3.
    Bush, J.W.M., Hu, D.L., Prakash, M.: The integument of water-walking arthropods: form and function. Adv. Insect Physiol. 34, 117–192 (2008)CrossRefGoogle Scholar
  4. 4.
    Bush, J.W.M., Hu, D.L.: Walking on water: biolocomotion at interface. Ann. Rev. Fluid Mech. 38, 339–369 (2006)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Gao, P., Feng, J.J.: A numerical investigation of the propulsion of water walker. J. Fluid Mech. 668, 363–383 (2011)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Koh, J.S., Yang, E., Jung G.P., Jumping on water: surface tension-dominated jumping of water striders and robotic insects. Science 349, 517–521 (2015). (Supplementary material:
  7. 7.
    Prakash, M., Bush, J.W.M.: Interfacial propulsion by directional adhesion. Int. J. Non-linear Mech. 46, 607–615 (2011)CrossRefGoogle Scholar
  8. 8.
    Xu, L., Yao, X., Zheng, Y.: Direction-dependent adhesion of water strider’s legs for water walking. Solid State Sci. 14, 1146–1151 (2012)CrossRefGoogle Scholar
  9. 9.
    Wei, P.J., Chen, S.C., Lin, J.F.: Adhesion forces and contact angles of water strider legs. Langmuir 25, 1526–1528 (2009)Google Scholar
  10. 10.
    Suter, R.B., Rosenerg, O., Loeb, S., et al.: Locomotion on the water surface: propulsive mechanisms of the fisher spider Dolomedes triton. J. Exp. Biol. 200, 2523–2538 (1997)Google Scholar
  11. 11.
    Song, Y.S., Sitti, M.: Surface-tension-driven biologically inspired water strider robots: theory and experiments. IEEE Trans. Robot. 23, 578–588 (2007)CrossRefGoogle Scholar
  12. 12.
    Hu, D.L., Prakash, M., Chan, B., et al.: Water-walking devices. Exp. Fluids 43, 769–778 (2007)CrossRefGoogle Scholar
  13. 13.
    Blake, T.D., Haynes, J.M.: Kinetics of liquid /liquid displacement. J. Colloid Interface Sci. 30, 421–423 (1969)CrossRefGoogle Scholar
  14. 14.
    Snoeijer, J.H., Andreotti, B.: Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45, 269–292 (2013)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Petrov, P.G., Petrov, J.G.: Comparison of the static and dynamic contact angle hysteresis at low velocities of the three-phase contact line. Colloid Surf. 61, 227–240 (1991)CrossRefGoogle Scholar
  16. 16.
    Dussan, V.E.B.: On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371–400 (1997)CrossRefGoogle Scholar
  17. 17.
    Perlin, M., Schultz, W.W., Liu, Z.: High Reynolds number oscillating contact lines. Wave Motion 40, 41–56 (2004)CrossRefMATHGoogle Scholar
  18. 18.
    Sedev, R.V., Petrov, J.G., Neumann, A.W.: Effect of swelling of a polymer surface on advancing and receding contact angles. J. Colloid Interface Sci. 180, 36–42 (1996)CrossRefGoogle Scholar
  19. 19.
    Watson, G.S., Cribb, B.W., Watson, J.A.: Experimental determination of the efficiency of nanostructuring on non-wetting legs of the water strider. Acta Biomat. 6, 4060–4064 (2010)CrossRefGoogle Scholar
  20. 20.
    Feng, X.Q., Gao, X.F., Wu, Z.N., et al.: Superior water repellency of water strider legs with hierarchical structures: experiments and analysis. Langmuir 23, 4892–4896 (2007)CrossRefGoogle Scholar
  21. 21.
    Wang, Q.B., Yao, X., Liu, H., et al.: Self-removel of condensed water on the legs of water striders. PNAS 112, 9247–9252 (2015)CrossRefGoogle Scholar
  22. 22.
    Byung, D., Honh, J.: Saputra, : Wetting characteristics of insect wing surfaces. J. Bionic Eng. 6, 63–70 (2009)CrossRefGoogle Scholar
  23. 23.
    Dupont, J.B., Legendre, D.: Numerical simulation of static and sliding drop with contact angle hysteresis. J. Comput. Phys. 229, 2453–2478 (2010)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Keller, J.B.: Surface tension force on a partly submerged body. Phys. Fluids 10, 3009–3010 (1998)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    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)CrossRefGoogle Scholar
  26. 26.
    Priezjev, N.V.: Rate dependent slip boundary conditions for simple fluids. Phys. Rev. E 75, 051605(1-7) (2007)Google Scholar
  27. 27.
    Craig, V.S.J., Neto, C., Williams, D.R.M.: Shear dependent boundary slip in an aqueous Newtonian liquid. Phys. Rev. Lett. 87, 054504(1-4) (2001)Google Scholar
  28. 28.
    Suter, R.B., Wildman, H.: Locomotion on the water surface: hydrodynamic constraints on rowing velocity require a gait change. J. Exp. Biol. 202, 2771–2785 (1999)Google Scholar
  29. 29.
    Su, Y., He, S., Ji, B., et al.: More evidence of the crucial roles of surface superhydrophobicity in free and safe maneuver of water strider. Appl. Phys. Lett. 99, 263704 (2011)CrossRefGoogle Scholar
  30. 30.
    Liu, J., Sun, J., Mei, Y.: Biomimetic mechanics behaviors of the strider leg vertically pressing water. Appl. Phys. Lett. 104, 231607 (2014)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • J. Zheng
    • 1
  • B. S. Wang
    • 2
  • W. Q. Chen
    • 2
  • X. Y. Han
    • 1
  • C. F. Li
    • 1
  • J. Z. Zhang
    • 3
  • K. P. Yu
    • 3
  1. 1.School of Energy and Power EngineeringJiangsu UniversityZhenjiangChina
  2. 2.China Ship Scientific Research CenterWuxiChina
  3. 3.School of AstronauticsHarbin Institute of TechnologyHarbinChina

Personalised recommendations