Английская Википедия:Inertial number

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The Inertial number <math>I</math> 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.[1][2][3][4] It is given by:

<math>I = \frac{\dot\gamma d}{\sqrt{P/\rho}},</math>

where <math>\dot\gamma</math> is the shear rate, <math>d</math> the average particle diameter, <math>P</math> is the pressure and <math>\rho</math> is the density.

Generally three regimes are distinguished:

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

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