Granular Matter

, 21:25 | Cite as

Understanding the local flow rate peak of a hopper discharging discs through an obstacle using a Tetris-like model

  • Guo-Jie Jason GaoEmail author
  • Jerzy Blawzdziewicz
  • Michael C. Holcomb
  • Shigenobu Ogata
Original Paper


Placing a round obstacle above the orifice of a flat hopper discharging uniform frictional discs has been experimentally and numerically shown in the literature to create a local peak in the gravity-driven hopper flow rate. Using frictionless molecular dynamics simulations, we show that the local peak is unrelated to the interparticle friction, the particle dispersity, and the obstacle geometry. We then construct a probabilistic Tetris-like model, where particles update their positions according to prescribed rules rather than in response to forces, and show that Newtonian dynamics is also not responsible for the local peak. Finally, we propose that the local peak is caused by an interplay between the flow rate around the obstacle, greater than the maximum when the hopper contains no obstacle, and a slow response time, allowing the overflowing particles to achieve a higher local area packing fraction by converging well upon reaching the hopper orifice.


Granular hopper flow Adjustable obstacle Flow rate peak Tetris-like model Molecular Dynamics 



GJG gratefully acknowledges financial support from startup funding of Shizuoka University (Japan).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest. The research presented did not involve human participants and/or animals.


  1. 1.
    Zuriguel, I., Janda, A., Garcimartín, A., Lozano, C., Arévalo, R., Maza, D.: Phys. Rev. Lett. 107, 278001 (2011)ADSCrossRefGoogle Scholar
  2. 2.
    Zuriguel, I., Parisi, D.R., Hidalgo, R.C., Lozano, C., Janda, A., Gago, P.A., Peralta, J.P., Ferrer, L.M., Pugnaloni, L.A., Clément, E., Maza, D., Pagonabarraga, I., Garcimartn, A.: Sci. Rep. 4, 7324 (2014)CrossRefGoogle Scholar
  3. 3.
    Endo, K., Reddy, K.A., Katsuragi, H.: Phys. Rev. Fluids 2, 094302 (2018)ADSCrossRefGoogle Scholar
  4. 4.
    Lozano, C., Janda, A., Garcimartín, A., Maza, D., Zuriguel, I.: Phys. Rev. E 86, 031306 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    Alonso-Marroquin, F., Azeezullah, S.I., Galindo-Torres, S.A., Olsen-Kettle, L.M.: Phys. Rev. E 85, 020301 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    Pastor, J.M., Garcimartín, A., Gago, P.A., Martín-Gómez, J.P.P.amd César, Ferrer, L.M., Maza, D., Parisi, D.R., Pugnaloni, L.A., Zuriguel, I.: Phys. Rev. E 92, 062817 (2015)ADSCrossRefGoogle Scholar
  7. 7.
    Murray, A., Alonso-Marroquin, F.: Pap. Phys. 8, 080003 (2016)CrossRefGoogle Scholar
  8. 8.
    Caglioti, E., Loreto, V., Herrmann, H.J., Nicodemi, M.: Phys. Rev. Lett. 79, 1575 (1997)ADSCrossRefGoogle Scholar
  9. 9.
    Garcimartín, A., Pastor, J.M., Ferrer, L.M., Ramos, J.J., Martín-Gómez, C., Zuriguel, I.: Phys. Rev. E 91, 022808 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    Zuriguel, I., Olivares, J., Pastor, J.M., Martín-Gómez, C., Ferrer, L.M., Ramos, J.J., Garcimartín, A.: Phys. Rev. E 94, 032302 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    Gao, G.J.: J. Phys. Soc. Jpn. 87, 114401 (2018)ADSCrossRefGoogle Scholar
  12. 12.
    Gella, D., Zuriguel, I., Maza, D.: Phys. Rev. Lett. 121, 138001 (2018)ADSCrossRefGoogle Scholar
  13. 13.
    Endo, K., Katsuragi, H.: EPJ Web Conf. 140, 03004 (2017)CrossRefGoogle Scholar
  14. 14.
    Thomas, C.C., Durian, D.J.: Phys. Rev. E 87, 052201 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    Thomas, C., Durian, D.: Phys. Rev. Lett. 114, 178001 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    Gao, G.J., Blawzdziewicz, J., O’Hern, C.S., Shattuck, M.D.: Phys. Rev. E 80, 061304 (2009)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical and Systems EngineeringShizuoka UniversityHamamatsuJapan
  2. 2.Department of PhysicsTexas Tech UniversityLubbockUSA
  3. 3.Department of Mechanical EngineeringTexas Tech UniversityLubbockUSA
  4. 4.Department of Mechanical Science and BioengineeringOsaka UniversityToyonakaJapan
  5. 5.Center for Elements Strategy Initiative for Structural Materials (ESISM)Kyoto UniversitySakyoJapan

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