Inertial number

The Inertial number relates the importance of inertia and confining stress and thus describes the speed of deformation in granular materials:

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

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:

• $I<10^{-3}$: quasi static flow
• $10^{-3}<I<10^{-1}$: dense flow
• $I>10^{-1}$: collisional flow