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A numerical investigation of the propulsion of water walkers

Published online by Cambridge University Press:  30 November 2010

PENG GAO  and
JAMES J. FENG
PENG GAO
Affiliation:
Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada
JAMES J. FENG*
Affiliation:
Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
*
†Email address for correspondence: [email protected]
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Abstract

This paper presents a finite-element simulation of the interfacial flow during propulsion of water walkers such as fishing spiders and water striders. The unsteady stroke of the driving leg is represented by a two-dimensional cylinder moving on a specified trajectory. The interface and the moving contact lines are handled by a diffuse-interface model. We explore the mechanism of thrust generation in terms of the interfacial morphology and flow structures. Results show that the most important component of the thrust is the curvature force related to the deformation of the menisci and the asymmetry of the dimple. For water walkers with thick legs, the pressure force due to the inertia of the water being displaced by the leg is also important. The viscous force is negligible. An extensive parametric study is performed on the effect of leg velocity, stroke depth, leg diameter and surface wettability. The propulsive force is insensitive to the contact angle on the leg. However, the hydrophobicity of the leg helps it detach from the surface during the recovery stroke and thus decreases the resistance. It is also important for averting or delaying penetration of the interface at large rowing velocity and depth. In two dimensions, surface waves are more efficient than vortices in transferring the momentum imparted by the leg to the water.

JFM classification

Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Interfacial Flows (free surface) Biological Fluid Dynamics: Propulsion
Type
Papers
Information
Journal of Fluid Mechanics , Volume 668 , 10 February 2011 , pp. 363 - 383
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Anderson, N. M. 1976 A comparative study of locomotion on the water surface in semiaquatic bugs (Insects, Hemiptera, Gerromorpha). Vidensk. Meddr. Dansk. Naturh. Foren. 139, 337–396.Google Scholar
Batchelor, G. K. 2000 An Introduction to Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Bühler, O. 2007 Impulsive fluid forcing and water strider locomotion. J. Fluid Mech. 573, 211–236.CrossRefGoogle Scholar
Bush, J. W. M. & Hu, D. L. 2006 Walking on water: biolocomotion at the interface. Annu. Rev. Fluid Mech. 38, 339–369.Google Scholar
Bush, J. W. M., Hu, D. L. & Prakash, M. 2007 The integument of water-walking arthropods: form and function. Adv. Insect. Physiol.: Insect. Mech. Control 34, 117–192.CrossRefGoogle Scholar
Caginalp, G. & Chen, X. F. 1998 Convergence of the phase field model to its sharp interface limits. Eur. J. Appl. Maths 9, 417–445.Google Scholar
Cox, R. G. 1986 The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169–194.CrossRefGoogle Scholar
Denny, M. W. 1993 Air and Water: The Biology and Physics of Life's Media. Princeton University Press.Google Scholar
Denny, M. W. 2004 Paradox lost: answers and questions about walking on water. J. Expl Biol. 207, 1601–1606.Google Scholar
Dickinson, M. 2003 Animal locomotion: how to walk on water. Nature 424, 621–622.Google Scholar
Gao, X. F. & Jiang, L. 2004 Water-repellent legs of water striders. Nature 432, 36.CrossRefGoogle ScholarPubMed
de Gennes, P.-G., Quéré, D., Brochard-Wyart, F. & Reisinger, A. 2002 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls and Waves. Springer.Google Scholar
Goodwyn, P. P. & Fujisaki, K. 2007 Sexual conflicts, loss of flight, and fitness gains in locomotion of polymorphic water striders. Entomol. Exp. Appl. 124, 249–259.CrossRefGoogle Scholar
Hu, D. L. 2006 Thy hydrodynamics of water-walking insects and spiders. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
Hu, D. L. & Bush, J. W. M. 2010 The hydrodynamics of water-walking arthropods. J. Fluid Mech. pp. 5–33.Google Scholar
Hu, D. L., Chan, B. & Bush, J. W. M. 2003 The hydrodynamics of water strider locomotion. Nature 424, 663–666.CrossRefGoogle ScholarPubMed
Hu, D. L., Prakash, M., Chan, B. & Bush, J. W. M. 2007 Water-walking devices. Exp. Fluids 43, 769–778.Google Scholar
Jacqmin, D. 2000 Contact-line dynamics of a diffuse fluid interface. J. Fluid Mech. 402, 57–88.Google Scholar
Keller, J. B. 1998 Surface tension force on a partly submerged body. Phys. Fluids 10, 3009–3010.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Lee, D. G. & Kim, H. Y. 2008 Impact of a superhydrophobic sphere onto water. Langmuir 24, 142–145.CrossRefGoogle ScholarPubMed
Lee, D. G. & Kim, H. Y. 2009 The role of superhydrophobicity in the adhesion of a floating cylinder. J. Fluid Mech. 624, 23–32.Google Scholar
Liu, J. L., Feng, X. Q. & Wang, G. F. 2007 Buoyant force and sinking conditions of a hydrophobic thin rod floating on water. Phys. Rev. E 76, 066103.Google Scholar
Mansfield, E. H., Sepangi, H. R. & Eastwood, E. A. 1997 Equilibrium and mutual attraction or repulsion of objects supported by surface tension. Phil. Trans. R. Soc. Lond. A 355, 869–919.Google Scholar
Qian, T. Z., Wang, X. P. & Sheng, P. 2006 A variational approach to moving contact line hydrodynamics. J. Fluid Mech. 564, 333–360.CrossRefGoogle Scholar
Raphaël, E. & de Gennes, P. G. 1996 Capillary gravity waves caused by a moving disturbance: wave resistance. Phys. Rev. E 53, 3448–3455.Google Scholar
Song, Y. S. & Sitti, M. 2007 Surface-tension-driven biologically inspired water strider robots: theory and experiments. IEEE Trans. Robot. 23, 578–589.CrossRefGoogle Scholar
Sun, S. M. & Keller, J. B. 2001 Capillary–gravity wave drag. Phys. Fluids 13, 2146–2151.Google Scholar
Suter, R. B., Rosenberg, O., Loeb, S., Wildman, H. & Long, J. H. 1997 Locomotion on the water surface: propulsive mechanisms of the fisher spider Dolomedes triton. J. Expl Biol. 200, 2523–2538.Google Scholar
Suter, R. B. & Wildman, H. 1999 Locomotion on the water surface: hydrodynamic constraints on rowing velocity require a gait change. J. Expl Biol. 202, 2771–2785.Google Scholar
Vella, D., Lee, D. G. & Kim, H. Y. 2006 The load supported by small floating objects. Langmuir 22, 5979–5981.CrossRefGoogle ScholarPubMed
Yue, P. T., Zhou, C. F. & Feng, J. J. 2010 Sharp interface limit of the Cahn–Hilliard model for moving contact lines. J. Fluid Mech. 645, 279–294.CrossRefGoogle Scholar
Yue, P. T., Zhou, C. F., Feng, J. J., Ollivier-Gooch, C. F. & Hu, H. H. 2006 Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing. J. Comput. Phys. 219, 47–67.Google Scholar
Zhou, C. F., Yue, P. T. & Feng, J. J. 2010 3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids. J. Comput. Phys. 229, 498–511.CrossRefGoogle Scholar