The Inertial number I quantifies the significance of dynamic effects in 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.
I = γ ˙ d P / ρ , where γ ˙ is the shear rate, d the average particle diameter, P is the pressure and ρ is the density.
Generally three regimes are distinguished:
I < 10 − 3 : quasi static flow 10 − 3 < I < 10 − 1 : dense flow I > 10 − 1 : collisional flowOne 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.
