- Editors' Suggestion
- Access by Xinjiang University
Propulsion by reciprocal motion into granular media
Phys. Rev. Fluids 6, 034604 – Published 5 March, 2021
DOI: https://doi.org/10.1103/PhysRevFluids.6.034604
Abstract
The force experienced by an object moving in a granular medium is a necessary input to describe locomotion problems in such a context. Towards this objective, resistive force theory (RFT) has been developed for granular flows inspired by previous developments in the case of viscous flows. In viscous fluids, a reciprocal motion does not lead to a net propulsion due to the kinematics reversibility of viscous flows that is included in the RFT. We show that, in a granular medium, a reciprocal motion allows for propulsion. We investigate the specific mechanisms underlying this propulsion and discuss how they differ from that of viscous flows. Understanding these phenomena permit both the accurate description of locomotion in sand and the refinement of the RFT for granular materials. These achievements provide opportunities towards the development of robots that are able to progress inside granular media and are suitable for controlling industrial processes.
Physics Subject Headings (PhySH)
Article Text
References (29)
- W. Baumgartner, F. Fidler, A. Weth, M. Habbecke, P. Jakob, C. Butenweg, and W. Böhme, Investigating the locomotion of the sandfish in desert sand using NMR-imaging, PloS ONE 3, e3309 (2008).
- 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).
- R. D. Maladen, Y. Ding, P. B. Umbanhowar, and D. I. Goldman, Undulatory swimming in sand: Experimental and simulation studies of a robotic sandfish, Int. J. Robot. Res. 30, 793 (2011).
- D. Goldman, H. Komsuoglu, and D. Koditschek, March of the sandbots, IEEE Spectrum 46, 30 (2009).
- C. Koch, Some aspects of abundant life in the vegetationless sand at the Namib Desert dunes, Sci. Papers Namib Desert Res. Station 1961, 9 (1961).
- E. Holm and E. B. Edney, Daily activity of Namib Desert arthropods in relation to climate, Ecology 54, 45 (1973).
- G. N. Louw, S. W. Nicolson, and M. K. Seely, Respiration beneath desert sand: Carbon dioxide diffusion and respiratory patterns in a tenebrionid beetle, J. Exp. Biol. 120, 443 (1986).
- J. Lighthill, Flagellar hydrodynamics, SIAM Rev. 18, 161 (1976).
- 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).
- C. Li, T. Zhang, and D. I. Goldman, A terradynamics of legged locomotion on granular media, Science 339, 1408 (2013).
- T. Zhang and D. I. Goldman, The effectiveness of resistive force theory in granular locomotion, Phys. Fluids 26, 101308 (2014).
- H. Askari and K. Kamrin, Intrusion rheology in grains and other flowable materials, Nat. Mater. 15, 1274 (2016).
- E. M. Purcell, Life at low Reynolds number, Am. J. Phys. 45, 3 (1977).
- E. Lauga, Life around the scallop theorem, Soft Matter 7, 3060 (2011).
- O. S. Pak, T. Normand, and E. Lauga, Pumping by flapping in a viscoelastic fluid, Phys. Rev. E 81, 036312 (2010).
- T. Qiu, T.-C. Lee, A. G. Mark, K. I. Morozov, R. Münster, O. Mierka, S. Turek, A. M. Leshansky, and P. Fischer, Swimming by reciprocal motion at low Reynolds number, Nat. Commun. 5, 5119 (2014).
- E. Lauga and D. Bartolo, No many-scallop theorem: Collective locomotion of reciprocal swimmers, Phys. Rev. E 78, 030901(R) (2008).
- A. Seguin, Y. Bertho, and P. Gondret, Influence of confinement on granular penetration by impact, Phys. Rev. E 78, 010301(R) (2008).
- Y. Forterre and O. Pouliquen, Flows of dense granular media, Annu. Rev. Fluid Mech. 40, 1 (2008).
- F. Guillard, Y. Forterre, and O. Pouliquen, Depth-Independent Drag Force Induced by Stirring in Granular Mediac, Phys. Rev. Lett. 110, 138303 (2013).
- F. Guillard, Y. Forterre, and O. Pouliquen, Origin of a depth-independent drag force induced by stirring in granular media, Phys. Rev. E 91, 022201 (2015).
- B. Darbois Texier, A. Ibarra, and F. Melo, Helical Locomotion in a Granular Medium, Phys. Rev. Lett. 119, 068003 (2017).
- J.-C. Géminard, J. C. Pastenes, and F. Melo, Foam rheology at large deformation, Phys. Rev. E 97, 042601 (2018).
- A. Seguin, Hysteresis of the drag force of an intruder moving into a granular medium, Eur. Phys. J. E 42, 13 (2019).
- K. Walton, The effective elastic moduli of a random packing of spheres, J. Mech. Phys. Solids 35, 213 (1987).
- J. Boschan, S. Luding, and B. P. Tighe, Jamming and irreversibility, Granular Matter 21, 58 (2019).
- 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).
- E. E. B. White, M. Chellamuthu, and J. P. Rothstein, Extensional rheology of a shear-thickening cornstarch and water suspension, Rheol. Acta 49, 119 (2010).
- P. C. F. Møller, J. Mewis, and D. Bonn, Yield stress and thixotropy: On the difficulty of measuring yield stresses in practice, Soft Matter 2, 274 (2006).
