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Length and time scales of a liquid drop impact and penetration into a granular layer

Published online by Cambridge University Press:  11 May 2011

HIROAKI KATSURAGI
HIROAKI KATSURAGI*
Affiliation:
Department of Applied Science for Electronics and Materials, Kyushu University, 6-1 Kasugakoen, Kasuga, Fukuoka 816-8580, Japan
*
†Current address: Graduate School of Environmental Studies, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan. Email address for correspondence: [email protected]
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Abstract

Liquid drop impact and penetration into a granular layer are investigated with diverse liquids and granular materials. We use various sizes of SiC abrasives and glass beads as a target granular material. We also employ ethanol and glycerol aqueous solutions as well as distilled water to make a liquid drop. The liquid drop impacts the granular layer with a low speed (~ms−1). The drop deformation and penetration are captured by a high-speed camera. From the video data, characteristic time scales are measured. Using a laser profilometry system, resultant crater morphology and its characteristic length scales are measured. Static strength of the granular layer is also measured by the slow pillar penetration experiment to quantify the cohesive force effect. We find that the time scales are almost independent of impact speed, but they depend on liquid drop viscosity. In particular, the penetration time is proportional to the square root of the liquid drop viscosity. In contrast, the crater radius is independent of the liquid drop viscosity. The crater radius is scaled by the same form as the previous paper, Katsuragi (Phys. Rev. Lett., vol. 104, 2010, art. 218001).

JFM classification

Drops and Bubbles: Drops Granular media: Granular media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 675 , 25 May 2011 , pp. 552 - 573
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Amato, J. C. & Williams, R. E. 1998 Crater formation in the laboratory: An introductory experiment in error analysis. Am. J. Phys. 66, 141–143.CrossRefGoogle Scholar
Ambroso, M. A., Kamien, R. D. & Durian, D. J. 2005 a Dynamics of shallow impact cratering. Phys. Rev. E 72 (4), 041305.CrossRefGoogle ScholarPubMed
Ambroso, M. A., Santore, C. R., Abate, A. R. & Durian, D. J. 2005 b Penetration depth for shallow impact cratering. Phys. Rev. E 71 (5), 051305.CrossRefGoogle ScholarPubMed
Aranson, I. S. & Tsimring, L. S. 2006 Patterns and collective behavior in granular media: theoretical concepts. Rev. Mod. Phys. 78, 641–692.CrossRefGoogle Scholar
Bergmann, R., Mikkelsen, R., zeilstra, C., van der Meer, D., Versluis, M., van der Weele, K., van der Hoef, M., Kuipers, H. & Lohse, D. 2005 Impact on soft sand: void collapse and jet formation. In Powders and Grains 2005 (ed. Garcia-Rojo, R., Herrmann, H. J. & McNamara, S.), pp. 1211–1214. Balkema.Google Scholar
Bhola, R. & Chandra, S. 1999 Parameters controlling solidification of molten wax droplets falling on a solid surface. J. Mater. Sci. 34, 4883–4894.CrossRefGoogle Scholar
Biance, A.-L., Chevy, F., Clanet, C., Lagubeau, G. & Quéré, D. 2006 On the elasticity of an inertial liquid shock. J. Fluid. Mech. 554, 47–66.CrossRefGoogle Scholar
Boudet, J. F., Amarouchene, Y. & Kellay, H. 2006 Dynamics of impact cratering in shallow sand layers. Phys. Rev. Lett. 96 (15), 158001.CrossRefGoogle ScholarPubMed
Caballero, G., Bergmann, R., van der Meer, D., Prosperetti, A. & Lohse, D. 2007 Role of air in granular jet formation. Phys. Rev. Lett. 99 (1), 018001.CrossRefGoogle ScholarPubMed
Clanet, C., Béguin, C., Richard, D. & Quéré, D. 2004 Maximal deformation of an impacting drop. J. Fluid. Mech. 517, 199–208.CrossRefGoogle Scholar
Dalziel, S. B. & Seaton, M. D. 2003 Resuspension by droplets. In Sedimentation and Sediment Transport (ed. Gyr, A. & Kinzelbach, W.), pp. 101–104. Kluwer.CrossRefGoogle Scholar
Deboeuf, S., Gondret, P. & Rabaud, M. 2009 Dynamics of grain ejection by sphere impact on a granular bed. Phys. Rev. E 79 (4), 041306.CrossRefGoogle ScholarPubMed
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 1997 Capillary flow as the cause of ring stains from dried liquid drop. Nature 389, 827–829.CrossRefGoogle Scholar
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 2000 Contact line deposits in an evaporating drop. Phys. Rev. E 62 (1), 756–765.CrossRefGoogle Scholar
Delon, G., Dorbolo, S., Vandewalle, N. & Caps, H. 2009 Drop impact on sand: from donut to pie. In 62nd Annual Meeting of the APS Division of Fluid Dynamics, vol. 54, AH.00006.Google Scholar
Desor, E. 1850 On fossil rain drops. Edin. New Phil. J. 49, 246–248.Google Scholar
Duran, J. 2000 Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials. Springer.CrossRefGoogle Scholar
de Gennes, P. G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer.CrossRefGoogle Scholar
Goldman, D. I. & Umbanhowar, P. 2008 Scaling and dynamics of sphere and disk impact into granular media. Phys. Rev. E 77, 021308.CrossRefGoogle ScholarPubMed
Hapgood, K. P., Litster, J. D., Biggs, S. R. & Howes, T. 2002 Drop penetration into porous powder beds. J. Colloid Interface Sci. 253 (2), 353–366.CrossRefGoogle ScholarPubMed
Hou, M., Peng, Z., Liu, R., Lu, K. & Chan, C. K. 2005 Dynamics of a projectile penetrating in granular systems. Phys. Rev. E 72 (6), 062301.CrossRefGoogle ScholarPubMed
Jaeger, H. M., Nagel, S. R. & Behringer, R. P. 1996 Granular solids, liquids, and gases. Rev. Mod. Phys. 68, 1259–1273.CrossRefGoogle Scholar
von Kann, S., Joubaud, S., Caballero-Robledo, G. A., Lohse, D. & vander Meer, D. der Meer, D. 2010 Effect of finite container size on granular jet formation. Phys. Rev. E 81 (4), 041306.CrossRefGoogle ScholarPubMed
Katsuragi, H. 2010 Morphology scaling of drop impact onto a granular layer. Phys. Rev. Lett. 104 (21), 218001.CrossRefGoogle ScholarPubMed
Katsuragi, H. & Durian, D. J. 2007 Unified force law for granular impact cratering. Nature Phys. 3, 420–423.CrossRefGoogle Scholar
Lohse, D., Bergmann, R., Mikkelsen, R., Zeilstra, C., van der Meer, D., Versluis, M., van der Weele, K., van der Hoef, M. & Kuipers, H. 2004 Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93, 198003.CrossRefGoogle ScholarPubMed
Lohse, D., Rauhé, R., Bergmann, R. & van der Meer, D. 2001 Creating a dry variety of quicksand. Nature 432, 689–690.CrossRefGoogle Scholar
Marmanis, H. & Thoroddsen, S. T. 1996 Scaling of the fingering pattern of an impacting drop. Phys. Fluids 8, 1344–1346.CrossRefGoogle Scholar
Melosh, H. J. 1989 Impact Cratering. Oxford University Press.Google Scholar
Metz, R. 1981 Why not raindrop impressions? J. Sedim. Petrol. 51, 265–268.Google Scholar
Mizoue, T., Aoki, Y., Tokita, M., Honjo, H., Barraza, H. J. & Katsuragi, H. 2010 Control of polymer gel surface pattern formation and its three dimensional measurement method. J. Polym. Engng 30, 523–534.CrossRefGoogle Scholar
Nefzaoui, E. & Skurtys, O. R. 2010 Impact of a liquid drop on a granular-medium: inertia, viscosity and surface tension effects on the drop deformation. arXiv:1009.1806v1.Google Scholar
Nelson, E. L., Katsuragi, H., Mayor, P. & Durian, D. J. 2008 Projectile interactions in granular impact cratering. Phys. Rev. Lett. 101, 068001.CrossRefGoogle ScholarPubMed
Okumura, K., Chevy, F., Richard, D., Quéré, D. & Clanet, C. 2003 Water spring: a model for bouncing drops. Europhys. Lett. 62, 237–243.CrossRefGoogle Scholar
Pica Ciamarra, M., Lara, A. H., Lee, A. T., Goldman, D. I., Vishik, I. & Swinney, H. L. 2004 Dynamics of drag and force distributions for projectile impact in a granular medium. Phys. Rev. Lett. 92 (19), 194301.CrossRefGoogle Scholar
Range, K. & Feuillebois, F. 1998 Influence of surface roughness on liquid drop impact. J. Colloid Interface Sci. 203, 16–30.CrossRefGoogle Scholar
Reyssat, M., Yeomans, J. M. & Quéré, D. 2008 Impalement of fakir drops. Europhys. Lett. 81, 26006.CrossRefGoogle Scholar
Richard, D. & Quéré, D. 2000 Bouncing water drops. Europhys. Lett. 50, 769–775.CrossRefGoogle Scholar
Rioboo, R., Marengo, M. & Tropea, C. 2002 Time evolution of liquid drop impact onto solid, dry surfaces. Exp. Fluids 33, 112–124.CrossRefGoogle Scholar
Roller, P. S. 1930 The bulking properties of microscopic particles. Ind. Engng Chem. 22, 1206–1208.CrossRefGoogle Scholar
Royer, J. R., Corwin, E. I., Eng, P. J. & Jaeger, H. M. 2007 Gas-mediated impact dynamics in fine-grained granular materials. Phys. Rev. Lett. 99 (3), 038003.CrossRefGoogle ScholarPubMed
Royer, J. R., Corwin, E. I., Flior, A., Cordero, M.-L., Rivers, M. L., Eng, P. J. & Jaeger, H. M. 2005 Formation of granular jets observed by high-speed x-ray radiography. Nature Phys. 1, 164–167.CrossRefGoogle Scholar
Stone, M. B., Barry, R., Bernstein, D. P., Pelc, M. D., Tsui, Y. K. & Schiffer, P. 2004 a Local jamming via penetration of a granular medium. Phys. Rev. E 70, 041301.CrossRefGoogle ScholarPubMed
Stone, M. B., Bernstein, D. P., Barry, R., Pelc, M. D., Tsui, Y. K. & Schiffer, P. 2004 b Getting to the bottom of a granular medium. Nature 427, 503–504.CrossRefGoogle Scholar
Suzuki, M., Sato, H., Hasegawa, M. & Hirota, M. 2001 Effect of size distribution on tapping properties of fine powder. Powder Technol. 118, 53–57.CrossRefGoogle Scholar
The Japan Society of Mechanical Engineers, ed. 1983 JSME Data Book: Thermophysical Properties of Fluids. JSME (in Japanese).Google Scholar
Thoroddsen, S. T. & Sakakibara, J. 1998 Evolution of the fingering pattern of an impact drop. Phys. Fluids 10, 1359–1374.CrossRefGoogle Scholar
Thoroddsen, S. T. & Shen, A. Q. 2001 Granular jets. Phys. Fluids 13, 4–6.CrossRefGoogle Scholar
Tsimring, L. S. & Volfson, D. 2005 Modeling of impact cratering in granular media. In Powders and Grains 2005 (ed. Garcia-Rojo, R., Herrmann, H. J. & McNamara, S.), pp. 1215–1218. Balkema.Google 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
de Vet, S. J. & de Bruyn, J. R. 2007 Shape of impact craters in granular media. Phys. Rev. E 76, 041306.CrossRefGoogle ScholarPubMed
Wada, K., Senshu, H. & Matsui, T. 2006 Numerical simulation of impact cratering on granular material. Icarus 180 (2), 528–545.CrossRefGoogle Scholar
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
Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17 (3), 273–283.CrossRefGoogle Scholar
Xu, L. 2010 Instability development of a viscous liquid drop impacting a smooth substrate. Phys. Rev. E 82 (2), 025303.CrossRefGoogle ScholarPubMed
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159–192.CrossRefGoogle Scholar