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.
the average particle diameter,
Generally three regimes are distinguished: 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.