The Inertial number

I

is a

dimensionless quantity Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...

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

granular material A granular material is a conglomeration of discrete solid, macroscopic scale, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when granulation, grains collide). T ...

. 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 In physics, mechanics and other areas of science, shear rate is the rate at which a progressive shear strain is applied to some material, causing shearing to the material. Shear rate is a measure of how the velocity changes with distance. Simple ...

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 eve ...

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 In granular mechanics, the ''μ''(''I'') rheology is one model of the rheology of a granular flow. Details The inertial number of a granular flow is a dimensionless quantity defined as I = \frac, where \dot\gamma is the shear rate tensor, , ...

, asserts that the

coefficient of friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of t ...

''μ'' of a granular material is a function of the inertial number only.

References

{{Reflist Granularity of materials