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Tapped granular column dynamics: simulations, experiments and modeling

Abstract

This paper communicates the results of a synergistic investigation that initiates our long term research goal of developing a continuum model capable of predicting a variety of granular flows. We consider an ostensibly simple system consisting of a column of inelastic spheres subjected to discrete taps in the form of half sine wave pulses of amplitude a/d and period \(\tau \). A three-pronged approach is used, consisting of discrete element simulations based on linear loading-unloading contacts, experimental validation, and preliminary comparisons with our continuum model in the form of an integro-partial differential equation.

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Notes

  1. 1.

    The sharp gradient up to this peak is due to the scale of the horizontal axis.

  2. 2.

    The choice to utilize continuous vibration, as opposed to discrete taps, arises from the fact that as the number of particles in our system is altered, the motion of the oscillating base used to excite particles may be influenced by the varying mass, resulting in an unequal provision of energy to the different systems, and hence a lack of consistency in our results. The use of continuous vibrations allows feedback from an accelerometer to be used in order to ensure a driving strength which is consistent to within 0.1 % in all cases.

    Fig. 9
    figure9

    Schematic diagram of the PEPT system and a photo of the camera

  3. 3.

    The number of repeated runs for the three-dimensional systems was limited to this value due to the considerable amount of time required for the highest-N runs combined with the costs associated with the use of the PEPT facility. It should be noted, however, that the minimal variance observed in the data for our 3D systems (see Fig. 10) indicates that the number of runs conducted was indeed adequate to produce good statistics.

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Acknowledgments

The work of the NJIT group was supported in part by NSF Grant CMMI-1029809. Experiments conducted at the University of Birmingham were made possible through financial support provided by the Hawkesworth Scholarship, set up by the late Dr. Michael Hawkesworth.

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Correspondence to A. D. Rosato.

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Rosato, A.D., Zuo, L., Blackmore, D. et al. Tapped granular column dynamics: simulations, experiments and modeling. Comp. Part. Mech. 3, 333–348 (2016). https://doi.org/10.1007/s40571-015-0075-2

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Keywords

  • Granular column
  • Discrete element simulation
  • Positron emission tracking
  • Continuum model