Английская Википедия:Bagnold number

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The Bagnold number (Ba) is the ratio of grain collision stresses to viscous fluid stresses in a granular flow with interstitial Newtonian fluid, first identified by Ralph Alger Bagnold.

The Bagnold number is defined by

<math>\mathrm{Ba}=\frac{\rho d^2 \lambda^{1/2} \dot{\gamma}}{\mu}</math>,

where <math>\rho</math> is the particle density, <math>d</math> is the grain diameter, <math>\dot{\gamma}</math> is the shear rate and <math>\mu</math> is the dynamic viscosity of the interstitial fluid. The parameter <math>\lambda</math> is known as the linear concentration, and is given by

<math>\lambda=\frac{1}{\left(\phi_0 / \phi\right)^{\frac{1}{3}} - 1}</math>,

where <math>\phi</math> is the solids fraction and <math>\phi_0</math> is the maximum possible concentration (see random close packing).

In flows with small Bagnold numbers (Ba < 40), viscous fluid stresses dominate grain collision stresses, and the flow is said to be in the "macro-viscous" regime. Grain collision stresses dominate at large Bagnold number (Ba > 450), which is known as the "grain-inertia" regime. A transitional regime falls between these two values.

See also

• Bingham plastic

External links

• Granular Material Flows at N.A.S.A