Skip to main content
SpringerLink
Log in

The transient dynamics of dilation waves in granular phase transitions during silo discharge

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

Granular material has the unique ability to transition between solid and liquid-like phases, but quantitative observations of the dynamics involved in this process remain rare. We hypothesize that granular packing of the solid phase has a leading control on this transition. To test this, we visualize the flow transitions that occur during discharge from a grain-filled silo. X-ray fluoroscopy and high-speed video analysis are used to detect and characterize the kinematics of dilation waves that trigger the phase transitions. Wave velocities are shown to vary by an order of magnitude with strong dependence on the packing density of the initially static bed. The speed of dilation waves exceeds any granular flow velocity in the system, and a simple model based upon conservation of mass is presented to describe this phenomenon. Our results have major implications for the quantitative description and prediction of granular system behaviour in natural and industrial applications, particularly with regards to the onset of avalanche motion and the handling of powders and grains.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Ancey, C., Coussot, P., Evesque, P.: A theoretical framework for granular suspensions in a steady simple shear flow. J. Rheol. 43(6), 1673–1699 (1999)

    Article  ADS  Google Scholar 

  2. Balevičius, R., Kačianauskas, R., Mróz, Z., Sielamowicz, I.: Analysis and dem simulation of granular material flow patterns in hopper models of different shapes. Adv. Powder Technol. 22(2), 226–235 (2011)

    Article  Google Scholar 

  3. Baxter, G.W., Behringer, R., Fagert, T., Johnson, G.A.: Pattern formation in flowing sand. Phys. Rev. Lett. 62(24), 2825–2828 (1989)

    Article  ADS  Google Scholar 

  4. Brown, R., Richards, J.C.: Principles of Powder Mechanics. Pergamon Press, Oxford (1970)

    Google Scholar 

  5. Delaplaine, J.W.: Forces acting in flowing beds of solids. AIChE J. 2(1), 127–138 (1956)

    Article  Google Scholar 

  6. Faqih, A., Chaudhuri, B., Muzzio, F.J., Tomassone, M.S., Alexander, A., Hammond, S.: Flow-induced dilation of cohesive granular materials. AIChE J. 52(12), 4124–4132 (2006)

    Article  Google Scholar 

  7. Fickie, K.E., Mehrabi, R., Jackson, R.: Density variations in a granular material flowing from a wedge-shaped hopper. AIChE J. 35(5), 853–855 (1989)

    Article  Google Scholar 

  8. Fullard, L., Davies, C.: A brief investigation into ejection times from a conical mass flow hopper-coulomb and conical model difference. In: POWDERS AND GRAINS 2013: Proceedings of the 7th International Conference on Micromechanics of Granular Media, vol. 1542, pp. 1254–1257. AIP Publishing (2013)

  9. Fullard, L.A., Davies, C.E., Wake, G.C.: Modelling powder mixing in mass flow discharge: a kinematic approach. Adv. Powder Technol. 24(2), 499–506 (2013)

    Article  Google Scholar 

  10. Gravish, N., Goldman, D.I.: Effect of volume fraction on granular avalanche dynamics. Phys. Rev. E 90(3), 032202 (2014)

    Article  ADS  Google Scholar 

  11. Haw, M.: Jamming, two-fluid behavior, and self-filtration in concentrated particulate suspensions. Phys. Rev. Lett. 92(18), 185506 (2004)

    Article  ADS  Google Scholar 

  12. Henann, D.L., Kamrin, K.: A predictive, size-dependent continuum model for dense granular flows. Proc. Natl. Acad. Sci. 110(17), 6730–6735 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Hunt, M., Zenit, R., Campbell, C., Brennen, C.: Revisiting the 1954 suspension experiments of RA Bagnold. J. Fluid Mech. 452, 1–24 (2002)

    Article  ADS  MATH  Google Scholar 

  14. Johanson, K.: Predicting cone-in-cone blender efficiencies from key material properties. Powder Technol. 170(3), 109–124 (2006)

    Article  Google Scholar 

  15. Johanson, K., Eckert, C., Ghose, D., Djomlija, M., Hubert, M.: Quantitative measurement of particle segregation mechanisms. Powder Technol. 159(1), 1–12 (2005)

    Article  Google Scholar 

  16. Jyotsna, R., Kesava Rao, K.: A frictional-kinetic model for the flow of granular materials through a wedge-shaped hopper. J. Fluid Mech. 346, 239–270 (1997)

    Article  ADS  MATH  Google Scholar 

  17. Kamrin, K., Bazant, M.Z.: Stochastic flow rule for granular materials. Phys. Rev. E 75(4), 041301 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  18. Kulkarni, S.D., Metzger, B., Morris, J.F.: Particle-pressure-induced self-filtration in concentrated suspensions. Phys. Rev. E 82(1), 010402 (2010)

    Article  ADS  Google Scholar 

  19. Lube, G., Huppert, H.E., Sparks, R.S.J., Freundt, A.: Static and flowing regions in granular collapses down channels. Phys. Fluids 19(4), 043301 (2007)

    Article  ADS  MATH  Google Scholar 

  20. Mastbergen, D.R., Van Den Berg, J.H.: Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology 50(4), 625–637 (2003)

  21. Michalowski, R.: Flow of granular material through a plane hopper. Powder Technol. 39(1), 29–40 (1984)

    Article  Google Scholar 

  22. MiDi, GdR.: On dense granular flows. Eur. Phys. J. E 14(4), 341–365 (2004)

  23. Muite, B.K., Quinn, S.F., Sundaresan, S., Rao, K.K.: Silo music and silo quake: granular flow-induced vibration. Powder Technol. 145(3), 190–202 (2004)

    Article  Google Scholar 

  24. Nedderman, R.M.: Statics and Kinematics of Granular Materials. Cambridge University Press, Cambridge (2005)

    Google Scholar 

  25. Pailha, M., Nicolas, M., Pouliquen, O.: Initiation of underwater granular avalanches: influence of the initial volume fraction. Phys. Fluids 20(11), 111701 (2008)

    Article  ADS  MATH  Google Scholar 

  26. Pailha, M., Pouliquen, O.: A two-phase flow description of the initiation of underwater granular avalanches. J. Fluid Mech. 633, 115–135 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Sielamowicz, I., Błoñski, S., Kowalewski, T.A.: Digital particle image velocimetry (dpiv) technique in measurements of granular material flows, part 2 of 3-converging hoppers. Chem. Eng. Sci. 61(16), 5307–5317 (2006)

    Article  Google Scholar 

  28. Sigmund, W., El-Shall, H., Shah, D.O., Moudgil, B.M.: Particulate Systems in Nano-and Biotechnologies. CRC Press, London (2008)

    Google Scholar 

  29. Staron, L., Lagrée, P.Y., Popinet, S.: Continuum simulation of the discharge of the granular silo. Eur. Phys. J. E 37(1), 1–12 (2014)

    Article  Google Scholar 

  30. Taberlet, N., Richard, P., Jenkins, J., Delannay, R.: Density inversion in rapid granular flows: the supported regime. Eur. Phys. J. E 22(1), 17–24 (2007)

    Article  Google Scholar 

  31. Thielicke, W.: The flapping flight of birds-analysis and application. Ph.D. thesis, Rijksuniversiteit Groningen (2014)

  32. Thielicke, W., Stamhuis, E.J.: Pivlab-towards user-friendly, affordable and accurate digital particle image velocimetry in matlab. J. Open Res. Softw. 2(1), e30 (2014)

    Google Scholar 

  33. Thompson, P.A., Grest, G.S.: Granular flow: friction and the dilatancy transition. Phys. Rev. Lett. 67(13), 1751 (1991)

    Article  ADS  Google Scholar 

  34. Thorpe, R.: An experimental clue to the importance of dilation in determining the flow rate of a granular material from a hopper or bin. Chem. Eng. Sci. 47(17), 4295–4303 (1992)

    Article  Google Scholar 

  35. Vivanco, F., Melo, F., Fuentes, C.: Granular flow models and dilation front propagation applied to underground mining. Int. J. Bifurc. Chaos 19(10), 3533–3539 (2009)

    Article  MATH  Google Scholar 

  36. Weir, G.J.: A mathematical model for dilating, non-cohesive granular flows in steep-walled hoppers. Chem. Eng. Sci. 59(1), 149–161 (2004)

    Article  Google Scholar 

  37. Yaras, P., Kalyon, D., Yilmazer, U.: Flow instabilities in capillary flow of concentrated suspensions. Rheol. Acta 33(1), 48–59 (1994)

    Article  Google Scholar 

  38. Yukawa, S., Kikuchi, M.: Density fluctuations in traffic flow. J. Phys. Soc. Jpn. 65(4), 916–919 (1996)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge the Massey University Research Fund (MURF) for funding. We also thank Bronwen Comrie-Evans and John Edwards for the use of laboratory space, and Diane Orange for helpful discussions and access to the X-ray facilities. Finally, we thank the reviewers of this manuscript for their excellent suggestions for improvement during the first review of the manuscript.

Author information

Authors and Affiliations

  1. Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand

    L. A. Fullard

  2. School of Engineering and Advanced Technology, Massey University, Palmerston North, New Zealand

    C. E. Davies

  3. Volcanic Risk Solutions, Massey University, Palmerston North, New Zealand

    G. Lube, A. C. Neather & E. C. P. Breard

  4. Radiography Department, Palmerston North hospital, Palmerston North, New Zealand

    B. J. Shepherd

Authors
  1. L. A. Fullard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. E. Davies
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Lube
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. C. Neather
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. E. C. P. Breard
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. B. J. Shepherd
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. A. Fullard.

Ethics declarations

Conflict of interest

The authors acknowledge the Massey University research fund for providing funding for this project. The authors have no conflicts of interest to declare.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fullard, L.A., Davies, C.E., Lube, G. et al. The transient dynamics of dilation waves in granular phase transitions during silo discharge. Granular Matter 19, 6 (2017). https://doi.org/10.1007/s10035-016-0685-2

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1007/s10035-016-0685-2

Keywords

Search

Navigation