The Inertial number

I

is a

dimensionless quantity A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

which quantifies the significance of dynamic effects on the flow of a

granular material A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose gra ...

. 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,

where

\dot\gamma

is the shear rate,

d

the average particle diameter,

P

is the

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...

and

\rho

is the density. Generally three regimes are distinguished: *

I<10^

: quasi static flow *

10^: dense flow
* I>10^: 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.

References

{{Reflist Granularity of materials