Inertial number

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. It is given by:

I = \frac{\dot\gamma d}{\sqrt{P/\rho}},

where \dot\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: quasi static flow
• 10^{-3}: dense flow
• I10^{-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.