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.^[1]

The Bagnold number is defined by

${\mathrm {Ba}}={\frac {\rho d^{2}\lambda ^{{1/2}}\gamma }{\mu }}$,^[2]

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

$\lambda ={\frac {1}{\left(\phi _{0}/\phi \right)^{{{\frac {1}{3}}}}-1}}$,

where $\phi$ is the solids fraction and $\phi _{0}$ 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.

See also

• Bingham plastic

References

1. Bagnold, R. A. (1954). "Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid under Shear". Proc. R. Soc. Lond. A. 225 (1160): 49–63. doi:10.1098/rspa.1954.0186.
2. Hunt, M. L.; Zenit, R.; Campbell, C. S.; Brennen, C.E. (2002). "Revisiting the 1954 suspension experiments of R. A. Bagnold". Journal of Fluid Mechanics. Cambridge University Press. 452: 1–24. doi:10.1017/S0022112001006577.

External links

• Granular Material Flows at N.A.S.A