Skip to main content Accessibility help
×
Home

High-speed X-ray imaging of a ball impacting on loose sand

  • Tess Homan (a1) (a2), Rob Mudde (a3), Detlef Lohse (a1) and Devaraj van der Meer (a1)

Abstract

When a ball is dropped in fine very loose sand, a splash and subsequently a jet are observed above the bed, followed by a granular eruption. To directly and quantitatively determine what happens inside the sand bed, high-speed X-ray tomography measurements are carried out in a custom-made set-up that allows for imaging of a large sand bed at atmospheric pressures. Herewith, we show that the jet originates from the pinch-off point created by the collapse of the air cavity formed behind the penetrating ball. Subsequently, we measure how the entrapped air bubble rises through the sand, and show that this is consistent with bubbles rising in continuously fluidized beds. Finally, we measure the packing fraction variation throughout the bed. From this we show that there is (i) a compressed area of sand in front of and next to the ball while the ball is moving down, (ii) a strongly compacted region at the pinch-off height after the cavity collapse and (iii) a relatively loosely packed centre in the wake of the rising bubble.

Copyright

Corresponding author

Email address for correspondence: tesshoman@gmail.com

References

Hide All
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.
Bergmann, R., van der Meer, D., Stijnman, M., Sandtke, M., Prosperetti, A. & Lohse, D. 2006 Giant bubble pinch-off Phys. Rev. Lett. 96, 154505.
Boudet, J. F., Amarouchene, Y. & Kellay, H. 2006 Dynamics of impact cratering in shallow sand layers. Phys. Rev. Lett. 96, 158001.
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.
Cho, G., Dodds, J. & Santamarina, J. C. 2006 Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. J. Geotech. Geoenviron. Eng. 132, 591602.
Ciamarra, M. P., Lara, A. H., Lee, A. T., Goldman, D. I. & Vishik, I. 2004 Dynamics of drag and force distributions for projectile impact in a granular medium. Phys. Rev. Lett. 92, 194301.
Davidson, J. & Harrison, D. 1963 Fluidised Particles. Cambridge University Press.
Delaney, G. W., Hilton, J. E. & Cleary, P. W. 2011 Defining random loose packing for nonspherical grains. Phys. Rev. E 83, 051305.
Duclaux, V., Caillé, F., Duez, C., Ybert, C., Bocquet, L. & Clanet, C. 2007 Dynamics of transient cavities. J. Fluid Mech. 591, 119.
Eggers, J., Fontelos, M. A., Leppinen, D. & Snoeijer, J. H. 2007 Theory of the collapsing axisymmetric cavity. Phys. Rev. Lett. 98, 094502.
Gekle, S., Gordillo, J. M., van der Meer, D. & Lohse, D. 2009a High-speed jet formation after solid object impact. Phys. Rev. Lett. 102, 034502.
Gekle, S., Snoeijer, J. H., Lohse, D. & van der Meer, D. 2009b Approach to universality in axisymmetric inviscid bubble pinch-off. Phys. Rev. E 80, 036305.
Gordillo, J. M. & Pérez-Saborid, M. 2006 Axisymmetric breakup of bubbles at high Reynolds numbers. J. Fluid Mech. 562, 303312.
von Kann, S., Joubaud, S., Caballero-Robledo, G. A., Lohse, D. & van der Meer, D. 2010 Effect of finite container size on granular jet formation. Phys. Rev. E 81, 041306.
Katsuragi, H. & Durian, D. J. 2007 Unified force law for granular impact cratering. Nat. Phys. 3, 420423.
Lohse, D. 2003 Bubble puzzles. Phys. Today 56, 3642.
Lohse, D., Bergmann, R. P. H. M., Mikkelsen, R., Zeilstra, C., van der Meer, D., Versluis, A. M., van der Weele, J. P., van der Hoef, M. & Kuipers, J. A. M. 2004a Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93, 198003.
Lohse, D., Rauhe, R., Bergmann, R. P. H. M. & van der Meer, D. 2004b Dry quicksand. Nature 432, 689.
Marston, J. O., Seville, J. P. K., Cheun, Y.-V. & Ingram, A. 2008 Effect of packing fraction on granular jetting from solid sphere entry into aerated and fluidized beds. Phys. Fluids 20, 023301.
Melosh, H. J. 1989 Impact Cratering: A Geologic Process. Oxford University Press.
Mudde, R. F. 2010a Double X-ray tomography of a bubbling fluidized bed. Ind. Eng. Chem. Res. 49, 50615065.
Mudde, R. F. 2010b Time-resolved X-ray tomography of a fluidized bed. Powder Technol. 199, 5559.
Mudde, R. F., Alles, J. & van der Hagen, T. H. J. J. 2008 Feasibility study of a time-resolving X-ray tomographic system. Meas. Sci. Technol. 19, 085501.
Oguz, H. & Prosperetti, A. 1990 Bubble entrainment by the impact of drops on liquid surfaces. J. Fluid Mech. 219, 143179.
Pacheco-Vázquez, F., Caballero-Robledo, G. A., Solano-Altamirano, J. M., Altshuler, E., Batista-Leyva, A. J. & Ruiz-Suárez, J. C. 2011 Infinite penetration of a projectile into a granular medium. Phys. Rev. Lett. 106, 218001.
Royer, J. R., Conyers, B., Corwin, E. I., Eng, P. J. & Jaeger, H. M. 2011 The role of interstitial gas in determining the impact response of granular beds. Europhys. Lett. 93, 28008.
Royer, J. R., Corwin, E. I., Conyers, B., Flior, A., Rivers, M. L., Eng, P. J. & Jaeger, H. M. 2008 Birth and growth of a granular jet. Phys. Rev. E 78, 011305.
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, 038003.
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. Nat. Phys. 1, 164.
Ruiz-Suárez, J. C. 2013 Penetration of projectiles into granular targets. Rep. Prog. Phys. 76, 066601.
Seguin, A., Bertho, Y. & Gondret, P. 2008 Influence of confinement on granular penetration by impact. Phys. Rev. E 78, 010301R.
Thoroddsen, S. & Shen, A. 2001 Granular jets. Phys. Fluids 13, 46.
Umbanhowar, P. & Goldman, D. I. 2010 Granular impact and the critical packing state. Phys. Rev. E 82, 010301R.
Walsh, A., Holloway, K. E., Habdas, P. & de Bruyn, J. R. 2003 Morphology and scaling of impact craters in granular media. Phys. Rev. Lett. 91, 104301.
Worthington, A. M. 1908 A Study of Splashes. Longman and Green.
Yang, R. Y., Zou, R. P. & Yu, A. B. 2000 Computer simulation of the packing of fine particles. Phys. Rev. E 62, 39003908.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

High-speed X-ray imaging of a ball impacting on loose sand

  • Tess Homan (a1) (a2), Rob Mudde (a3), Detlef Lohse (a1) and Devaraj van der Meer (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed