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# Bagnold number

The Bagnold number 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, \( \gamma \) 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

\( \lambda=\frac{1}{\left(\phi_0 / \phi\right) - 1}, \)

where \(\phi \) is the solids fraction and \( \phi_0 i \) s the maximum possible concentration (see random close packing).

In flows with small Bagnold numbers \((\mathrm{Ba}<40) \) , 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 \((\mathrm{Ba}>450) \) , which is known as the 'grain-inertia' regime.

References

^ 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.

^ 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

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