Bagnold number

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

$\mathrm{B}\mathrm{a}=\frac{\rho d^2{\lambda }^{1/2}\dot{\gamma }}{\mu }$,

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

$\lambda =\frac{1}{{({\varphi }_0/\varphi )}^{\frac{1}{3}}-1}$,

where $\varphi$ is the solids fraction and ${\varphi }_0$ 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.

See also

• Bingham plastic

External links

• Granular Material Flows at N.A.S.A