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

^[2],

where ρ is the particle density, d is the grain diameter, γ is the shear rate and μ is the dynamic viscosity of the interstitial fluid. The parameter λ is known as the linear concentration, and is given by

,

where ϕ is the solids fraction and ϕ₀ 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.

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. http://dx.doi.org/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. http://dx.doi.org/10.1017/S0022112001006577. 

External links

• Granular Material Flows at N.A.S.A