Bagnold number

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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

Ba=ρd2λ1/2γ˙μ,[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

λ=1(ϕ0/ϕ)131,

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. A transitional regime falls between these two values.

See also

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. Bibcode1954RSPSA.225...49B. 
  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 452 (1): 1–24. doi:10.1017/S0022112001006577. Bibcode2002JFM...452....1H.