The impact of an object on a granular solid is an ubiquitous phenomenon in nature, the scale of which ranges from the impact of a raindrop onto sand all the way to that of a large asteroid on a planet. Despite the obvious relevance of these impact events, the study of the underlying physics mechanisms that guide them is relatively young, with most work concentrated in the past decade. Upon impact, an object starts to interact with a granular bed and experiences a drag force from the sand. This ultimately leads to phenomena such as crater formation and the creation of a transient cavity that upon collapse may cause a jet to appear from above the surface of the sand. This review provides an overview of research that targets these phenomena, from the perspective of the analogous but markedly different impact of an object on a liquid. It successively addresses the drag an object experiences inside a granular bed, the expansion and collapse of the cavity created by the object leading to the formation of a jet, and the remarkable role played by the air that resides within the pores between the grains.


Article metrics loading...

Loading full text...

Full text loading...


Literature Cited

  1. Aguilar J, Goldman DI. 2016. Robophysical study of jumping dynamics on granular media. Nat. Phys. 12:278–83 [Google Scholar]
  2. Albert I, Sample JG, Morss AJ, Rajagopalan S, Barabási AL, Schiffer P. 2001. Granular drag on a discrete object: shape effects on jamming. Phys. Rev. E 64:061303 [Google Scholar]
  3. Allen WA, Mayfield EB, Morrison HL. 1957. Dynamics of a projectile penetrating sand. J. Appl. Phys. 28:370–76 [Google Scholar]
  4. Altshuler E, Torres H, González Pita A, Sánchez Colina G, Pérez Penichet C. et al. 2014. Settling into dry granular media in different gravities. Geophys. Res. Lett. 41:3032–37 [Google Scholar]
  5. Amato JC, Williams RE. 1998. Crater formation in the laboratory: an introductory experiment in error analysis. Am. J. Phys. 66:141–43 [Google Scholar]
  6. Ambroso MA, Kamien RD, Durian DJ. 2005a. Dynamics of shallow impact cratering. Phys. Rev. E 72:041305 [Google Scholar]
  7. Ambroso MA, Santore CR, Abate AR, Durian DJ. 2005b. Penetration depth for shallow impact cratering. Phys. Rev. E 71:051305 [Google Scholar]
  8. Anghel DV, Strauss M, McNamara S, Flekkøy EG, Måløy KJ. 2006. Erratum: Grains and gas flow: molecular dynamics with hydrodynamic interactions. Phys. Rev. E 74:029906 [Google Scholar]
  9. Aranson IS, Tsimring LS. 2006. Patterns and collective behavior in granular media: theoretical concepts. Rev. Mod. Phys. 78:641–92 [Google Scholar]
  10. Backman ME, Goldsmith W. 1978. The mechanics of penetration of projectiles into targets. Int. J. Eng. Sci. 16:1–99 [Google Scholar]
  11. Bartali R, Rodriguez-Liñán GM, Nahmad-Molinari Y, Sarocchi D, Ruiz-Suárez JC. 2013. Role of the granular nature of meteoritic projectiles in impact crater morphogenesis. arXiv:1302.0259 [astro-ph.EP]
  12. Ben-Dor G, Dubinsky A, Elperin T. 2009. Modeling of penetration by rigid impactors. Mech. Res. Commun. 36:625–29 [Google Scholar]
  13. Bergmann R, Stijnman M, Sandtke M, van der Meer D, Prosperetti A, Lohse D. 2006. Giant bubble collapse. Phys. Rev. Lett. 96:154505 [Google Scholar]
  14. Bergmann R, van der Meer D, Gekle S, van der Bos A, Lohse D. 2009. Controlled impact of a disk on a water surface: cavity dynamics. J. Fluid Mech. 633:381–409 [Google Scholar]
  15. Boguslavskii Y, Drabkin S, Juran I, Salman A. 1996a. Theory and practice of projectile's penetration in soils. J. Geotechnol. Eng. 122:806–10 [Google Scholar]
  16. Boguslavskii Y, Drabkin S, Salman A. 1996b. Analysis of vertical projectile penetration in granular soils. J. Phys. D 29:905–16 [Google Scholar]
  17. Boudet JF, Amarouchene Y, Kellay H. 2006. Dynamics of impact cratering in shallow sand layers. Phys. Rev. Lett. 96:158001 [Google Scholar]
  18. Brzinski TA. Durian DJ. III, 2010. Characterization of the drag force in an air-moderated granular bed. Soft Matter 6:3038–43 [Google Scholar]
  19. Brzinski TA. Mayor P, Durian DJ. III, 2013. Depth-dependent resistance of granular media to vertical penetration. Phys. Rev. Lett. 111:168002 [Google Scholar]
  20. Brzinski TA. Schug J, Mao K, Durian DJ. III, 2015. Penetration depth scaling for impact into wet granular packings. Phys. Rev. E 91:022202 [Google Scholar]
  21. Caballero G, Bergmann R, van der Meer D, Prosperetti A, Lohse D. 2007. Role of air in granular jet formation. Phys. Rev. Lett. 99:018001 [Google Scholar]
  22. Caballero-Robledo GA, Kelly KP, Homan TAM, Weijs JH, van der Meer D, Lohse D. 2012. Suction of splash after impact on dry quick sand. Granul. Matter 14:179–84 [Google Scholar]
  23. Carman PC. 1956. Flow of Gases Through Porous Media London: Butterworths Sci.
  24. Ciamarra MP, Lara AH, Lee AT, Goldman DI, Vishik I, Swinney HL. 2004. Dynamics of drag and force distributions for projectile impact in a granular medium. Phys. Rev. Lett. 92:194301 [Google Scholar]
  25. Clark AH, Behringer RP. 2013. Granular impact model as an energy-depth relation. Eur. Phys. Lett. 101:64001 [Google Scholar]
  26. Clark AH, Kondic L, Behringer RP. 2012. Particle scale dynamics in granular impact. Phys. Rev. Lett. 109:238302 [Google Scholar]
  27. Clark AH, Petersen AJ, Behringer RP. 2014. Collisional model for granular impact dynamics. Phys. Rev. E 89:012201 [Google Scholar]
  28. Clément R, Courrech du Pont S, Ould-Hamouda M, Duveau D, Douady S. 2011. Penetration and blown air effect in granular media. Phys. Rev. Lett. 106:098001 [Google Scholar]
  29. Daniels KE, Coppock JE, Behringer RP. 2004. Dynamics of meteor impacts. Chaos 14:S4 [Google Scholar]
  30. Darcy HPG. 1856. Les fontaines publiques de la ville de Dijon Paris: Victor Dalmont
  31. de Bruyn JR, Walsh AM. 2004. Penetration of spheres into loose granular media. Can. J. Phys. 82:439–46 [Google Scholar]
  32. de Gennes PG. 1999. Granular matter: a tentative view. Rev. Mod. Phys. 71:S374 [Google Scholar]
  33. Deboeuf S, Gondret P, Rabaud M. 2009. Dynamics of grain ejection by sphere impact on a granular bed. Phys. Rev. E 79:041306 [Google Scholar]
  34. Delon G, Terwagne D, Dorbolo S, Vandewalle N, Caps H. 2011. Impact of liquid droplets on granular media. Phys. Rev. E 84:046320 [Google Scholar]
  35. Duclaux V, Caillé F, Duez C, Ybert C, Bocquet L, Clanet C. 2007. Dynamics of transient cavities. J. Fluid Mech. 591:1–19 [Google Scholar]
  36. Dwivedi SK, Teeter RD, Felice CW, Gupta YM. 2008. Two dimensional mesoscale simulations of projectile instability during penetration in dry sand. J. Appl. Phys. 104:083502 [Google Scholar]
  37. Emady HN, Kayrak-Talay D, Schwerin WC, Litster JD. 2012. A regime map for granule formation by drop impact on powder beds. Powder Technol. 212:69–79 [Google Scholar]
  38. Gekle S, Gordillo JM, van der Meer D, Lohse D. 2009. High-speed jet formation after solid object impact. Phys. Rev. Lett. 102:034502 [Google Scholar]
  39. Goldman DI, Umbanhowar P. 2008. Scaling and dynamics of sphere and disk impact into granular media. Phys. Rev. E 77:021308 [Google Scholar]
  40. González Gutiérrez J, Carrillo Estrada JL, Ruiz Suárez JC. 2014. Penetration of granular projectiles into a water target. Sci. Rep. 4:6762 [Google Scholar]
  41. Gutman RG, Davidson JF. 1975. Darcy's law for oscillatory flow. Chem. Eng. Sci. 30:89–95 [Google Scholar]
  42. Hinch J. 2014. Particles impacting on a granular bed. J. Eng. Math. 84:41–48 [Google Scholar]
  43. Holsapple KA. 1993. The scaling of impact processes in planetary science. Annu. Rev. Earth Planet. Sci. 21:333–73 [Google Scholar]
  44. Holsapple KA, Giblin I, Housen K, Nakamura A, Ryan E. 2002. Asteroid impacts: laboratory experiments and scaling laws. Asteroid III W Bottke, A Cellino, P Paolicchi, RP Binzel 443–62 Tucson: Univ. Ariz. Press [Google Scholar]
  45. Homan TAM, Gjaltema C, van der Meer D. 2014. Collapsing granular beds: the role of interstitial air. Phys. Rev. E 89:052204 [Google Scholar]
  46. Homan TAM, Mudde R, Lohse D, van der Meer D. 2015. High-speed X-ray imaging of a ball impacting on loose sand. J. Fluid Mech. 777:690–706 [Google Scholar]
  47. Homan TAM, van der Meer D. 2016. Giant drag reduction due to interstitial air in sand. arXiv:1607.07774 [cond-mat.soft]
  48. Hou M, Peng Z, Liu R, Lu K, Chan CK. 2005a. Dynamics of a projectile penetrating in granular systems. Phys. Rev. E 72:062301 [Google Scholar]
  49. Hou M, Peng Z, Liu R, Wu Y, Tian Y. et al. 2005b. Projectile impact and penetration in loose granular bed. Sci. Technol. Adv. Mater. 6:855–59 [Google Scholar]
  50. Jaeger HM, Nagel SR, Behringer RP. 1996a. Granular solids, liquids, and gases. Rev. Mod. Phys. 68:1259–73 [Google Scholar]
  51. Jaeger HM, Nagel SR, Behringer RP. 1996b. The physics of granular materials. Phys. Today 49:32–39 [Google Scholar]
  52. Janssen HA. 1895. Versuche uber getreidedruck in silozellen. Dtsch. Ing. 39:1045 [Google Scholar]
  53. Joubaud S, Homan TAM, Gasteuil Y, Lohse D, van der Meer D. 2014. Forces encountered by a sphere during impact into sand. Phys. Rev. E 90:060201 [Google Scholar]
  54. Kadanoff LP. 1999. Built upon sand: theoretical ideas inspired by granular flows. Rev. Mod. Phys. 71:435–44 [Google Scholar]
  55. Katsuragi H. 2010. Morphology scaling of drop impact onto a granular layer. Phys. Rev. Lett. 104:218001 [Google Scholar]
  56. Katsuragi H. 2011. Length and time scales of a liquid drop impact and penetration into a granular layer. J. Fluid Mech. 675:552–73 [Google Scholar]
  57. Katsuragi H. 2016. Physics of Soft Impact and Cratering New York: Springer
  58. Katsuragi H, Durian DJ. 2007. Unified force law for granular impact cratering. Nat. Phys. 3:420–23 [Google Scholar]
  59. Katsuragi H, Durian DJ. 2013. Drag force scaling for penetration into granular media. Phys. Rev. E 87:052208 [Google Scholar]
  60. Kondic L, Fang X, Losert W, O'Hern CS, Behringer RP. 2012. Microstructure evolution during impact on granular matter. Phys. Rev. E 85:011305 [Google Scholar]
  61. Lohse D, Bergmann R, Mikkelsen R, Zeilstra C, van der Meer D. et al. 2004a. Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93:198003 [Google Scholar]
  62. Lohse D, Rauhé R, Bergmann R, van der Meer D. 2004b. Creating a dry variety of quicksand. Nature 432:689–90 [Google Scholar]
  63. Long EJ, Hargrave GK, Cooper JR, Kitchener BGB, Parsons AJ. et al. 2014. Experimental investigation into the impact of a liquid droplet onto a granular bed using three-dimensional, time-resolved, particle tracking. Phys. Rev. E 89:032201 [Google Scholar]
  64. Loranca-Ramos FE, Carrillo-Estrada JL, Pacheco-Vázquez F. 2015. Craters and granular jets generated by underground cavity collapse. Phys. Rev. Lett. 115:028001 [Google Scholar]
  65. Marston JO, Li EQ, Thoroddsen ST. 2012a. Evolution of fluid-like granular ejecta generated by sphere impact. J. Fluid Mech. 704:5–36 [Google Scholar]
  66. Marston JO, Seville JPK, Cheun YV, Ingram A, Decent SP, Simmons MJH. 2008. Effect of packing fraction on granular jetting from solid sphere entry into aerated and fluidized beds. Phys. Fluids 20:023301 [Google Scholar]
  67. Marston JO, Thoroddsen S, Ng W, Tan R. 2010. Experimental study of liquid drop impact onto a powder surface. Powder Technol. 203:223–36 [Google Scholar]
  68. Marston JO, Vakarelski IU, Thoroddsen ST. 2012b. Sphere impact and penetration into wet sand. Phys. Rev. E 86:020301 [Google Scholar]
  69. Marston JO, Zhu Y, Vakarelski IU, Thoroddsen ST. 2012c. Drop spreading and penetration into pre-wetted powders. Powder Technol. 228:424–28 [Google Scholar]
  70. McNamara S, Flekkøy EG, Måløy KJ. 2000. Grains and gas flow: molecular dynamics with hydrodynamic interactions. Phys. Rev. E 61:4054–59 [Google Scholar]
  71. Melosh HJ. 1989. Impact Cratering: A Geological Process Oxford, UK: Oxford Univ. Press
  72. Melosh HJ, Ivanov BA. 1999. Impact crater collapse. Annu. Rev. Earth Planet. Sci. 27:385–415 [Google Scholar]
  73. Mikkelsen R, Versluis M, Koene E, Bruggert GW, van der Meer D. et al. 2002. Granular eruptions: void collapse and jet formation. Phys. Fluids 14:S14 [Google Scholar]
  74. Möbius ME, Cheng X, Eshuis P, Karczmar GS, Nagel SR, Jaeger HM. 2005. Effect of air on granular size separation in a vibrated granular bed. Phys. Rev. E 72:011304 [Google Scholar]
  75. Möbius ME, Lauderdale BE, Nagel SR, Jaeger HM. 2001. Brazil-nut effect: size separation of granular particles. Nature 414:270 [Google Scholar]
  76. 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 [Google Scholar]
  77. Nelson EL, Katsuragi H, Mayor P, Durian DJ. 2008. Projectile interactions in granular impact cratering. Phys. Rev. Lett. 101:068001 [Google Scholar]
  78. Newhall KA, Durian DJ. 2003. Projectile-shape dependence of impact craters in loose granular media. Phys. Rev. E 68:060301 [Google Scholar]
  79. Nishida M, Okumura M, Tanaka K. 2010. Effects of density ratio and diameter ratio on critical incident angles of projectiles impacting granular media. Granul. Matter 12:337–44 [Google Scholar]
  80. Nordstrom K, Lim E, Harrington M, Losert W. 2014. Granular dynamics during impact. Phys. Rev. Lett. 112:228002 [Google Scholar]
  81. Pacheco-Vázquez F, Caballero-Robledo GA, Solano-Altamirano JM, Altshuler E, Batista-Leyva AJ, Ruiz-Suárez JC. 2011. Infinite penetration of a projectile into a granular medium. Phys. Rev. Lett. 106:218001 [Google Scholar]
  82. Pacheco-Vázquez F, Ruiz-Suárez JC. 2009. Sliding through a superlight granular medium. Phys. Rev. E 80:060301 [Google Scholar]
  83. Pacheco-Vázquez F, Ruiz-Suárez JC. 2010. Cooperative dynamics in the penetration of a group of intruders in a granular medium. Nat. Commun. 1:123 [Google Scholar]
  84. Pacheco-Vázquez F, Ruiz-Suárez JC. 2011. Impact craters in granular media: grains against grains. Phys. Rev. Lett. 107:218001 [Google Scholar]
  85. Pak HK, van Doorn E, Behringer RP. 1995. Effects of ambient gases on granular materials under vertical vibration. Phys. Rev. Lett. 74:4643–46 [Google Scholar]
  86. Pastenes JC, Géminard JC, Melo F. 2014. Interstitial gas effect on vibrated granular columns. Phys. Rev. E 89:062205 [Google Scholar]
  87. Pierazzo E, Collins G. 2004. A brief introduction to hydrocode modeling of impact cratering. Cratering in Marine Environments and on Ice H Dypvik, MJ Burchell, P Claeys 323–40 New York: Springer [Google Scholar]
  88. Poncelet JV. 1829. Cours de mécanique industrielle Metz
  89. Royer JR, Conyers B, Corwin EI, Eng PJ, Jaeger HM. 2011. The role of interstitial gas in determining the impact response of granular beds. Europhys. Lett. 93:28008 [Google Scholar]
  90. Royer JR, Corwin EI, Conyers B, Flior A, Rivers ML. et al. 2008. Birth and growth of a granular jet. Phys. Rev. E 78:011305 [Google Scholar]
  91. Royer JR, Corwin EI, Flior A, Cordero ML, Rivers ML. et al. 2005. Formation of granular jets observed by high-speed X-ray radiography. Nat. Phys. 1:164–67 [Google Scholar]
  92. Royer JR, Corwin EI, Rivers ML, Eng PJ, Jaeger HM. 2007. Gas-mediated impact dynamics in fine-grained granular materials. Phys. Rev. Lett. 99:038003 [Google Scholar]
  93. Ruiz Suárez JC. 2013. Penetration of projectiles into granular targets. Rep. Prog. Phys. 76:066601 [Google Scholar]
  94. Schofield AN, Wroth CP. 1968. Critical State Soil Mechanics London: McGraw-Hill
  95. Schröter M, Nägle S, Radin C, Swinney HL. 2007. Phase transition in a static granular system. Eur. Phys. Lett. 78:44004 [Google Scholar]
  96. Seguin A, Bertho Y, Gondret P, Crassous J. 2009. Sphere penetration by impact in a granular medium: a collisional process. Eur. Phys. Lett. 88:44002 [Google Scholar]
  97. Solano-Altamirano JM, Caballero-Robledo GA, Pacheco-Vázquez F, Kamphorst V, Ruiz-Suárez JC. 2013. Flow-mediated coupling on projectiles falling in a superlight granular medium. Phys. Rev. E 88:032206 [Google Scholar]
  98. Sperl M. 2006. Experiments on corn pressure in silo cells: translation and comment of Janssen's paper from 1895. Granul. Matter 8:59–65 [Google Scholar]
  99. Stone MB, Barry R, Bernstein DP, Pelc MD, Tsui YK, Schiffer P. 2004. Local jamming via penetration of a granular medium. Phys. Rev. E 70:041301 [Google Scholar]
  100. Thoroddsen ST, Etoh TG, Takehara K. 2008. High-speed imaging of drops and bubbles. Annu. Rev. Fluid Mech. 40:257–85 [Google Scholar]
  101. Thoroddsen ST, Shen AQ. 2001. Granular jets. Phys. Fluids 13:4–6 [Google Scholar]
  102. Tiwari M, Krishna Mohan TR, Sen S. 2014. Penetration depth scaling for impact into wet granular packings. Phys. Rev. E 90:062202 [Google Scholar]
  103. Tsimring LS, Volfson D. 2005. Modeling of impact cratering in granular media. Powders Grains 2:1215–23 [Google Scholar]
  104. Uehara JS, Ambroso MA, Ojha RP, Durian DJ. 2003. Low-speed impact craters in loose granular media. Phys. Rev. Lett. 90:194301 Erratum. 2003 Phys. Rev. Lett. 91:149902 [Google Scholar]
  105. Umbanhowar P, Goldman DI. 2010. Granular impact and the critical packing state. Phys. Rev. E 82:010301 [Google Scholar]
  106. van der Hoef MA, van Sint Annaland M, Deen NG, Kuipers JAM. 2008. Numerical simulation of dense gas-solid fluidized beds: a multiscale modeling strategy. Annu. Rev. Fluid Mech. 40:47–70 [Google Scholar]
  107. van Gerner HJ, Caballero-Robledo GA, van der Meer D, van der Weele K, van der Hoef MA. 2009. Coarsening of Faraday heaps: experiment, simulation, and theory. Phys. Rev. Lett. 103:028001 [Google Scholar]
  108. van Gerner HJ, van der Hoef MA, van der Meer D, van der Weele K. 2007. The interplay of air and sand: Faraday heaping unravelled. Phys. Rev. E 76:051305 [Google Scholar]
  109. van Gerner HJ, van der Weele K, van der Hoef MA, van der Meer D. 2011. Air-induced inverse Chladni patterns. J. Fluid Mech. 689:203–20 [Google Scholar]
  110. van Gerner HJ, van der Weele K, van der Meer D, van der Hoef MA. 2015. Scaling behavior of coarsening Faraday heaps. Phys. Rev. E 92:042203 [Google Scholar]
  111. Versluis M. 2013. High-speed imaging in fluids. Exp. Fluids 54:1458 [Google Scholar]
  112. Volfson D, Tsimring LS, Aranson IS. 2003. Partially fluidized shear granular flows: continuum theory and molecular dynamics simulations. Phys. Rev. E 68:021301 [Google Scholar]
  113. von Kann S, Joubaud S, Caballero-Robledo GA, Lohse D, van der Meer D. 2010. Effect of finite container size on granular jet formation. Phys. Rev. E 81:041306 [Google Scholar]
  114. Walsh AM, Holloway KE, Habdas P, de Bruyn JR. 2003. Morphology and scaling of impact craters in granular media. Phys. Rev. Lett. 91:104301 [Google Scholar]
  115. Worthington AM. 1908. A Study of Splashes London: Longmans, Green & Co.
  116. Xu Y, Padding JT, Kuipers JAM. 2014. Numerical investigation of the vertical plunging force of a spherical intruder into a prefluidized granular bed. Phys. Rev. E 90:062203 [Google Scholar]
  117. Xu Y, Padding JT, van der Hoef MA, Kuipers JAM. 2013. Detailed numerical simulation of an intruder impacting on a granular bed using a hybrid discrete particle and immersed boundary (DP-IB) method. Chem. Eng. Sci. 104:201–7 [Google Scholar]
  118. Zhao R, Zhang Q, Tjugito H, Cheng X. 2015. Drop spreading and penetration into pre-wetted powders. PNAS 112:342–47 [Google Scholar]
  119. Zhao SC, de Jong R, van der Meer D. 2015. Raindrop impact on sand: a dynamic explanation of crater morphologies. Soft Matter 11:6562–68 [Google Scholar]
  120. Zheng XJ, Wang ZT, Qiu ZG. 2004. Impact craters in loose granular media. Eur. Phys. J. 13:321–24 [Google Scholar]

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error