Inertial number explained

The Inertial number

I 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:I = (• \gamma d)/(\sqrt{P/\rho) },

where

• \gamma is the shear rate, d the average particle diameter, P is the pressure and \rho is the density.

Generally three regimes are distinguished:

I< 10 ^{-3} : quasi static flow10 ^{-3} <I< 10 ^{-1} : dense flowI> 10 ^{-1} : 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.

Notes and References

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