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Inertial number

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The Inertial number is a dimensionless quantity which quantifies the significance of dynamic effects on the flow of a granular material. It measures the ratio of inertial forces of grains to imposed forces: a small value corresponds to the quasi-static state, while a high value corresponds to the inertial state or even the "dynamic" state.[1][2][3][4] It is given by:

where is the shear rate, the average particle diameter, is the pressure and is the density.

Generally three regimes are distinguished:

  • : quasi static flow
  • : dense flow
  • : collisional flow

One model of dense granular flows, the μ(I) rheology, asserts that the coefficient of friction μ of a granular material is a function of the inertial number only.

References

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  1. ^ Combe, G.; Roux, J.-N. (22–24 September 2003). Discrete numerical simulation, quasistatic deformation and the origins of strain in granular materials. 3ème Symposium International sur le Comportement des sols et des roches tendres. Lyon. pp. 1071–1078 (2003). arXiv:0901.3842. Bibcode:2009arXiv0901.3842C.
  2. ^ Midi, G.D.R. (2004). "On dense granular flows". European Physical Journal E. 14 (4): 341–365 (2004). arXiv:cond-mat/0312502. Bibcode:2004EPJE...14..341M. doi:10.1140/epje/i2003-10153-0. PMID 15340859. S2CID 15206754.
  3. ^ Roux J.-N., Chevoir F. (2005). "Discrete numerical simulation and the mechanical behavior of granular materials". Bulletin des Laboratoires des Ponts et Chaussées - 254: 109–138.
  4. ^ Radjaï, F.; Dubois, F. (8 March 2011). "Chapter 8 - Dimensional Analysis and Control Parameters". Discrete-Element Modeling of Granular Materials. ISTE Ltd and John Wiley & Sons Inc. ISBN 978-1-84821-260-2.