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Fingering phenomena during grain–grain displacement

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Abstract

Spontaneous formation of fingered patterns during the displacement of dense granular assemblies was experimentally reported few years ago, in a radial Hele-Shaw cell. Here, by means of discrete element simulations, we have recovered the experimental findings and extended the original study to explore the control parameters space. In particular, using assemblies of grains with different geometries (monodisperse, bidisperse, or polydisperse), we measured the macroscopic stress tensor in the samples in order to confirm some conjectures proposed in analogy with Saffman–Taylor viscous fingering phenomena for immiscible fluids. Considering an axial setup which allows to control the discharge of grains and to follow the trajectory and the pressure gradient along the displacing interface, we have applied the Darcy law for laminar flow in fluids in order to measure an “effective viscosity” for each assembly combination, in an attempt to mimic variation of the viscosity ratio between the injected/displaced fluids in the Saffman–Taylor experiment. The results corroborate the analogy with the viscous fluids displacement, with the bidisperse assembly corresponding to the less viscous geometry. But, differently to fluid case, granular fingers only develop for a specific combination of displaced/injected geometries, and we have demonstrated that it is always related with the formation of a force chain network along the finger direction.

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Acknowledgments

We are indebted to E. Clèment and P. Claudin for fruitful discussions. APFA thanks FAPEMIG and CNPq funding brazilian agencies. NMPM thanks CAPES for funding and CEFET-MG and 3S-R Laboratory for the kind support for academic interchange. We thank the anonymous referees for the very detailed and constructive reports of our manuscript.

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Authors and Affiliations

  1. Post Graduation Program in Mathematical and Computer Modeling (PPGMMC), Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), Av. Amazonas 7675, Belo Horizonte, CEP 30510-000, Brazil

    Nathália M. P. Mello

  2. Departamento de Física e Matemática, CEFET-MG, Belo Horizonte, Brazil

    Humberto A. Paiva & A. P. F. Atman

  3. UJF-Grenoble 1, Grenoble-INP, CNRS UMR 5521, 3SR Lab, 38041, Grenoble, France

    G. Combe

  4. PPGMMC/CEFET-MG, Belo Horizonte, Brazil

    A. P. F. Atman

  5. National Institute of Science and Tecnology for Complex Systems - INCT-SC, Rio de Janeiro, Brazil

    A. P. F. Atman

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  1. Nathália M. P. Mello
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  2. Humberto A. Paiva
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  3. G. Combe
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  4. A. P. F. Atman
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Correspondence to A. P. F. Atman.

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Mello, N.M.P., Paiva, H.A., Combe, G. et al. Fingering phenomena during grain–grain displacement. Comp. Part. Mech. 4, 153–164 (2017). https://doi.org/10.1007/s40571-016-0113-8

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