Bagnold number explained
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
,
[2] where
is the particle
density,
is the grain diameter,
is the
shear rate and
is the dynamic viscosity of the interstitial fluid. The parameter
is known as the linear concentration, and is given by
,
where
is the solids fraction and
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
- 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 . 10.1098/rspa.1954.0186 . 1954RSPSA.225...49B . 98030586 .
- 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 . 10.1017/S0022112001006577 . 2002JFM...452....1H . 10.1.1.564.7792 . 9416685 .
External links
