Bagnold number

 ( Granularity Of Materials ) 

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

$\backslash mathrm\{Ba\}=\backslash frac\{\backslash rho\; d^2\; \backslash lambda^\{1/2\}\; \backslash dot\{\backslash gamma\}\}\{\backslash mu\}$,

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

$\backslash lambda=\backslash frac\{1\}\{\backslash left(\backslash phi\_0\; /\; \backslash phi\backslash right)^\{\backslash frac\{1\}\{3\}\}\; -\; 1\}$,

where $\backslash phi$ is the solids fraction and $\backslash phi\_0$ 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.

• Bingham plastic

• Granular Material Flows at N.A.S.A