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Hydrogel sphere impact cratering, spreading and bouncing on granular media

Published online by Cambridge University Press:  27 October 2021

Xiaoyan Ye Open the ORCID record for Xiaoyan Ye [Opens in a new window]  and
Devaraj van der Meer Open the ORCID record for Devaraj van der Meer [Opens in a new window]
Xiaoyan Ye*
Affiliation:
Key Laboratory of Mechanics on Disaster and Environment in Western China attached to the Ministry of Education of China, Department of Mechanics and Engineering Science, School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, 730000 Gansu, PR China Physics of Fluids Group and Max Planck Center Twente for Complex Fluid Dynamics, Faculty of Science and Technology, MESA+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands
Devaraj van der Meer
Affiliation:
Physics of Fluids Group and Max Planck Center Twente for Complex Fluid Dynamics, Faculty of Science and Technology, MESA+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

The impact of a hydrogel sphere onto a granular target results in both the deformation of the sphere and the formation of a prominent topographic feature known as an impact crater on the granular surface. We investigate the crater formation and scaling, together with the spreading diameter and post-impact dynamics of spheres by performing a series of experiments, varying the Young's modulus $Y$ and impact speed $U_{0}$ of the hydrogel spheres, and the packing fraction and grain size of the granular target. We determine how the crater diameter and depth depend on $Y$ and show the data to be consistent with those from earlier experiments using droplets and hard spheres. Most specifically, we find that the crater diameter data are consistent with a power law, where the power exponent changes more sharply when $Y$ becomes less than 200 Pa. Next, we introduce an estimate for the portion of the impact kinetic energy that is stored as elastic energy during impact, and thus correct the energy that remains available for crater formation. Subsequently, we determine the deformation of the hydrogel spheres and find that the normalized spreading diameter data are well collapsed introducing an equivalent velocity from an energy balance of the initial kinetic energy against surface and elastic energy. Finally, we observe that under certain intermediate values for the Young's modulus and impact velocities, the particles rebound from the impact crater. We determine the phase diagram and explain our findings from a comparison of the elastocapillary spreading time and the impact duration.

JFM classification

Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 929 , 25 December 2021 , A24
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Arora, S., Fromental, J.M., Mora, S., Phou, T., Ramos, L. & Ligoure, C. 2018 Impact of beads and drops on a repellent solid surface: a unified description. Phys. Rev. Lett. 120, 148003.CrossRefGoogle ScholarPubMed
Chantelot, P., Coux, M., Clanet, C. & Quéré, D. 2018 Drop trampoline. Europhys. Lett. 124 (2), 1–4.CrossRefGoogle Scholar
Clanet, C., Béguin, C., Richard, D. & Quéré, D. 2004 Maximal deformation of an impacting drop. J. Fluid Mech. 517, 199–208.CrossRefGoogle Scholar
Delon, G., Terwagne, D., Dorbolo, S., Vandewalle, N. & Caps, H. 2011 Impact of liquid droplets on granular media. Phys. Rev. E 84, 046320.CrossRefGoogle ScholarPubMed
Goldman, D.I. & Umbanhowar, P. 2008 Scaling and dynamics of sphere and disk impact into granular media. Phys. Rev. E 77, 021308.CrossRefGoogle ScholarPubMed
Holsapple, K.A. 1993 The scaling of impact processes in planetary sciences. Annu. Rev. Earth Planet. Sci. 21, 333–373.CrossRefGoogle Scholar
Holsapple, K.A. & Schmidt, R.M. 1987 Point source solutions and coupling parameters in cratering mechanics. J. Geophys. Res.: Solid Earth 92, 6350–6376.CrossRefGoogle Scholar
de Jong, R., Zhao, S.-C., Garcia-Gonzalez, D., Verduijn, G. & van der Meer, D. 2021 Impact cratering in sand: comparing solid and liquid intruders. Soft Matt. 17, 120–125.CrossRefGoogle ScholarPubMed
de Jong, R., Zhao, S.C. & van der Meer, D. 2017 Crater formation during raindrop impact on sand. Phys. Rev. E 95, 042901.CrossRefGoogle ScholarPubMed
Josserand, C. & Thoroddsen, S.T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48 (1), 365–391.CrossRefGoogle Scholar
Katsuragi, H. 2011 Length and time scales of a liquid drop impact and penetration into a granular layer. J. Fluid Mech. 675, 552–573.CrossRefGoogle Scholar
Katsuragi, H. 2016 Physics of Soft Impact and Cratering. Springer.CrossRefGoogle Scholar
Katsuragi, H. & Durian, D.J. 2007 Unified force law for granular impact cratering. Nat. Phys. 3, 420–423.CrossRefGoogle Scholar
Liu, D.D., Tan, H.W. & Tran, T. 2018 Droplet impact on heated powder bed. Soft Matt. 14, 9967–9972.CrossRefGoogle ScholarPubMed
Lohse, D., Rauhe, R., Bergmann, R. & van der Meer, D. 2003 Creating a dry variety of quicksand. Nature 91, 104301.Google Scholar
Marston, J., Thoroddsen, S.T., Ng, W. & Tan, R. 2010 Experimental study of liquid drop impact onto a powder surface. Powder Technol. 203, 223–236.CrossRefGoogle Scholar
Matsuda, Y., Fukui, S., Kamiya, R., Yamaguchi, H. & Niimi, T. 2019 Impact cratering on a granular bed by hydrogel spheres having intermediate property between solid and liquid. Phys. Rev. E 99, 032906.CrossRefGoogle Scholar
van der Meer, D. 2017 Impact on granular beds. Annu. Rev. Fluid Mech. 49, 463–484.CrossRefGoogle Scholar
Miranda, C.S. & Dowling, D.R. 2019 Mach number scaling of impact craters in unconsolidated granular materials. Icarus 325, 84–93.CrossRefGoogle Scholar
Nefzaoui, E. & Skurtys, O. 2012 Impact of a liquid drop on a granular medium: inertia, viscosity and surface tension effects on the drop deformation. Exp. Therm. Fluid Sci. 41, 43–50.CrossRefGoogle Scholar
Pacheco-Vázquez, F. 2019 Ray systems and craters generated by the impact of nonspherical projectiles. Phys. Rev. Lett. 122, 164501.CrossRefGoogle ScholarPubMed
Pacheco-Vázquez, F. & Ruiz-Suárez, J.C. 2011 Impact craters in granular media: grains against grains. Phys. Rev. Lett. 107, 218001.CrossRefGoogle ScholarPubMed
Richard, D. & Quéré, D. 2000 Bouncing water drops. Europhys. Lett. 50 (6), 769–775.CrossRefGoogle Scholar
Ruiz-Suárez, J.C. 2013 Penetration of projectiles into granular targets. Rep. Prog. Phys. 76 (6), 066601.CrossRefGoogle ScholarPubMed
Tanaka, Y. 2005 Impact of gel balls beyond the hertzian regime. Eur. Phys. J. E 18 (1), 95–103.CrossRefGoogle ScholarPubMed
Tanaka, Y., Yamazaki, Y. & Okumura, K. 2003 Bouncing gel balls: impact of soft gels onto rigid surface. Europhys. Lett. 63 (1), 146–153.CrossRefGoogle Scholar
Uehara, J.S., Ambroso, M.A., Ojha, R.P. & Durian, D.J. 2003 Low-speed impact craters in loose granular media. Phys. Rev. Lett. 90, 194301.CrossRefGoogle ScholarPubMed
Walsh, A.M., Holloway, K.E., Habdas, P. & de Bruyn, J.R. 2003 Morphology and scaling of impact craters in granular media. Phys. Rev. Lett. 91, 104301.CrossRefGoogle ScholarPubMed
Worthington, A.M. 1908 A Study of Splashes. Longmans, Green, and Co.Google Scholar
Yarin, A.L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing$\ldots$. Annu. Rev. Fluid Mech. 38, 159–192.CrossRefGoogle Scholar
Zhang, Q.Y., Gao, M., Zhao, R.C. & Cheng, X. 2015 Scaling of liquid-drop impact craters in wet granular media. Phys. Rev. E 92, 042205.CrossRefGoogle ScholarPubMed
Zhao, R., Zhang, Q., Tjugito, H. & Cheng, X. 2015 a Granular impact cratering by liquid drops: understanding raindrop imprints through an analogy to asteroid strikes. Proc. Natl Acad. Sci. 112 (2), 342–347.CrossRefGoogle ScholarPubMed
Zhao, S.C., de Jong, R. & van der Meer, D. 2015 b Raindrop impact on sand: a dynamic explanation of crater morphologies. Soft Matt. 11, 6562–6568.CrossRefGoogle ScholarPubMed
Zhao, S.C., de Jong, R. & van der Meer, D. 2017 Liquid-grain mixing suppresses droplet spreading and splashing during impact. Phys. Rev. Lett. 118, 054502.CrossRefGoogle ScholarPubMed
Zhao, S.C., de Jong, R. & van der Meer, D. 2019 Formation of a hidden cavity below droplets impacting on a granular substrate. J. Fluid Mech. 880, 59–72.CrossRefGoogle Scholar
Zheng, X.J., Wang, Z.T. & Qiu, Z.G. 2004 Impact craters in loose granular media. Eur. Phys. J. E 13, 321–324.CrossRefGoogle ScholarPubMed