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. 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.
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