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Self-propulsion of a helical swimmer in granular matter

Rogelio Valdés, Verónica Angeles, Elsa de la Calleja, and Roberto Zenit*

  • Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apartado Postal 70-360, Ciudad Universitaria, Distrito Federal 04510, México

  • *zenit@unam.mx
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Phys. Rev. Fluids 4, 084302 – Published 13 August, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.084302

Abstract

The motion of helicoidal swimmers moving in a pool filled with a granular medium is studied experimentally. The horizontal displacement through granular beads is measured considering geometrical modifications of the swimmer, the size, and frictional properties of the media. We found three main parameters which affect the swimming performance: the diameter, the wavelength, and the angle of the helix. The swimming speed scales with the rotation speed, ωR. The size of particles does not affect the swimming speed significantly; the swimming speed is reduced when the particle's angle of repose increases. It was found that a maximum swimming speed is achieved when the helix angle is close to 55∘. The experimental data are compared with predictions of the granular resistive force theory, which was extended to be applicable for a swimmer with a rigid helical tail, leading to good agreement.

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References (27)

  1. S. Childress, Mechanics of Swimming and Flying, Cambridge Studies in Mathematical Biology (Cambridge University Press, Cambridge, UK, 1981).
  2. T. Wei, R. Mark, and S. Hutchison, The fluid dynamics of competitive swimming, Annu. Rev. Fluid Mech. 46, 547 (2014).
  3. A. E. Hosoi and D. I. Goldman, Beneath our feet: Strategies for locomotion in granular media, Annu. Rev. Fluid Mech. 47, 431 (2015).
  4. T. Shimada, D. Kadau, T. Shinbrot, and H. J. Herrmann, Swimming in granular media, Phys. Rev. E 80, 020301(R) (2009).
  5. Y. Forterre and O. Pouliquen, Flows of dense granular media, Annu. Rev. Fluid Mech. 40, 1 (2008).
  6. K. Kamrin, Quantitative rheological model for granular materials: The importance of particle size, in Handbook of Materials Modeling: Applications: Current and Emerging Materials (Springer International, New York, 2018), Chap. 1, pp. 1–24.
  7. R. D. Maladen, Y. Ding, C. Li, and D. I. Goldman, Undulatory swimming in sand: Subsurface locomotion of the sandfish lizard, Science 325, 314 (2009).
  8. R. D. Maladen, Y. Ding, P. B. Umbanhowar, A. Kamor, and D. I. Goldman, Mechanical models of sandfish locomotion reveal principles of high performance subsurface sand-swimming, J. R. Soc. Interface 8, 1332 (2011).
  9. T. N. Zhang and D. I. Goldman, The effectiveness of resistive force theory in granular locomotion, Phys. Fluids 26, 101308 (2014).
  10. R. D. Maladen, P. B. Umbanhowar, Y. Ding, A. Masse, and D. I. Goldman, Granular lift forces predict vertical motion of a sand-swimming robot, in 2011 IEEE International Conference on Robotics and Automation (IEEE, Piscataway, NJ, 2011), pp. 1398–1403.
  11. Z. Peng, O. S. Pak, and G. J. Elfring, Characteristics of undulatory locomotion in granular media, Phys. Fluids 28, 031901 (2016).
  12. Z. Peng, Y. Ding, K. Pietrzyk, G. J. Elfring, and O. S. Pak, Propulsion via flexible flapping in granular media, Phys. Rev. E 96, 012907 (2017).
  13. J. Gray and G. J. Hancock, The propulsion of sea-urchin spermatozoa, J. Exp. Biol. 32, 802 (1955).
  14. B. Darbois Texier, A. Ibarra, and F. Melo, Helical Locomotion in a Granular Medium, Phys. Rev. Lett. 119, 068003 (2017).
  15. J. Slonaker, D. C. Motley, Q. Zhang, S. Townsend, C. Senatore, K. Iagnemma, and K. Kamrin, General scaling relations for locomotion in granular media, Phys. Rev. E 95, 052901 (2017).
  16. H. Askari and K. Kamrin, Intrusion rheology in grains and other flowable materials, Nat. Mater. 15, 1274 (2015).
  17. H. C. Berg, E. coli in Motion (Springer, New York, 2004).
  18. B. Rodenborn, C. H. Chen, H. L. Swinney, B. Liu, and H. P. Zhang, Propulsion of microorganisms by a helical flagellum, Proc. Natl. Acad. Sci. USA 110, E338 (2013).
  19. T. Atsumi, Y. Maekawa, T. Yamada, I. Kawagishi, Y. Imae, and M. Homma, Effect of viscosity on swimming by the lateral and polar flagella of Vibrio alginolyticus, J. Bacteriol. 178, 5024 (1996).
  20. M. Shigematsu, A. Umeda, S. Fujimoto, and K. Amako, Spirochaete-like swimming mode of Campylobacter jejuni in a viscous environment, J. Med. Microbiol. 47, 521 (1998).
  21. J. G. Mitchell, The energetics and scaling of search strategies in bacteria, Am. Nat. 160, 727 (2002).
  22. B. R. Robertson, J. L. O'Rourke, B. A. Neilan, P. Vandamme, S. L. On, J. G. Fox, and A. Lee, Mucispirillum schaedleri gen. nov., sp. nov., a spiral-shaped bacterium colonizing the mucus layer of the gastrointestinal tract of laboratory rodents, Int. J. Syst. Evol. Microbiol. 55, 1199 (2005).
  23. E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Prog. Phys. 72, 096601 (2009).
  24. S. Gomez, F. Godínez, E. Lauga, and R. Zenit, Helical propulsion in shear-thinning fluids, J. Fluid Mech. 812, R3 (2017).
  25. S. Riedel and B. Field, 2010 summary of grain entrapments in the United States, Technical report, Purdue University, 2011 (unpublished).
  26. F. A. Godínez, O. Chavez, and R. Zenit, Note: Design of a novel rotating magnetic field device, Rev. Sci. Instrum. 83, 066109 (2012).
  27. S. Chattopadhyay, R. Moldovan, C. Yeung, and X. L. Wu, Swimming efficiency of bacterium Escherichia coli, Proc. Natl. Acad. Sci. USA 103, 13712 (2006).

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Phys. Rev. Fluids 4, 084302– Published 13 August, 2019
  • Received 16 December 2018
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