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Fluctuations and power-law scaling of dry, frictionless granular rheology near the hard-particle limit

A. P. Santos1,*, Ishan Srivastava2, Leonardo E. Silbert3, Jeremy B. Lechman1,†, and Gary S. Grest1

  • 1Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
  • 2Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 3School of Math, Science and Engineering, Central New Mexico Community College, Albuquerque, New Mexico 87106, USA

  • *Present address: AMA Inc., Thermal Protection Materials Branch, NASA Ames Research Center, Moffett Field, CA 94035, USA.
  • †jblechm@sandia.gov
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Phys. Rev. Fluids 7, 084303 – Published 19 August, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.084303

Abstract

The flow of frictionless granular particles is studied with stress-controlled discrete element modeling simulations for systems varying in size from 300 to 100 000 particles. The volume fraction and shear-stress ratio μ are relatively insensitive to system size for a wide range of inertial numbers I. Second-order effects in strain rate, such as normal stress differences, require large system sizes to accurately extract meaningful results, notably a nonmonotonic dependence in the first normal stress difference with strain rate. The rheological response represented by the μ(I) scalar model works well at describing the lower-order aspects of the rheology, except near the quasistatic limit of these stress-controlled flows. The pressure is varied over five decades, and a pressure dependence of the coordination number is observed, which is not captured by the inertial number. Large fluctuations observed for small systems N≤1000 near the quasistatic limit can lead to the arrest of flow resulting in challenges to fitting the data to rheological relationships. The inertial number is also insufficient for capturing the pressure-dependent behavior of property fluctuations. Fluctuations in the flow and microstructural properties are measured in both the quasistatic and inertial regimes, including shear stress, pressure, strain rate, normal stress differences, volume fraction, coordination number, and contact fabric anisotropy. The fluctuations in flow properties scale self-similarly with pressure and system size. A transition in the scaling of fluctuations of stress properties and contact fabric anisotropy are measured and proposed as a quantitative identification of the transition from inertial to quasistatic flow.

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Phys. Rev. Fluids 7, 084303– Published 19 August, 2022
  • Received 12 January 2022
  • Accepted 22 July 2022
Article part of CHORUS
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