The Bagnold number (Ba) is the ratio of grain collision stresses to viscous fluid stresses in a

granular Granularity (also called graininess), the condition of existing in granules or grains, refers to the extent to which a material or system is composed of distinguishable pieces. It can either refer to the extent to which a larger entity is sub ...

flow with interstitial

Newtonian fluid A Newtonian fluid is a fluid in which the viscous stress tensor, viscous stresses arising from its Fluid dynamics, flow are at every point linearly correlated to the local strain rate — the derivative (mathematics), rate of change of its deforma ...

, first identified by

Ralph Alger Bagnold Brigadier Ralph Alger Bagnold, OBE, FRS, (3 April 1896 – 28 May 1990) was an English 20th-century desert explorer, geologist and soldier. In 1932, he staged the first recorded East-to-West crossing of the Libyan Desert. His work in the fi ...

. The Bagnold number is defined by :

\mathrm=\frac

, where

\rho

is the particle

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...

d

is the grain diameter,

\dot

is the

shear rate In physics, shear rate is the rate at which a progressive shearing deformation is applied to some material. Simple shear The shear rate for a fluid flowing between two parallel plates, one moving at a constant speed and the other one stationary ...

and

\mu

is the

dynamic viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

of the interstitial fluid. The parameter

\lambda

is known as the linear concentration, and is given by :

\lambda=\frac

, 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.

References

External links

Granular Material Flows at N.A.S.A
{{NonDimFluMech Granularity of materials Bubbles (physics) Dimensionless numbers

See also

References

External links