Bagnold Number
Encyclopedia
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
.
The Bagnold number is defined by
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 (
), 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 (
), which is known as the 'grain-inertia' regime.
Granular material
A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact . The constituents that compose granular material must be large enough such that they are not subject to thermal motion fluctuations...
flow with interstitial Newtonian fluid
Newtonian fluid
A Newtonian fluid is a fluid whose stress versus strain rate curve is linear and passes through the origin. The constant of proportionality is known as the viscosity.-Definition:...
, first identified by Ralph Alger Bagnold
Ralph Alger Bagnold
Brigadier Ralph Alger Bagnold, FRS OBE, was the founder and first commander of the British Army's Long Range Desert Group during World War II. He is also generally considered to have been a pioneer of desert exploration, an acclaim earned for his activities during the 1930s...
.
The Bagnold number is defined by
-
,
where
is the particle densityDensity
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
,
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 packingRandom close pack
Random close packing is an empirical parameter used to characterize the maximum volume fraction of solid objects obtained when they are packed randomly. For example, when a solid container is filled with grain, shaking the container will reduce the volume taken up by the objects, thus allowing...
).
In flows with small Bagnold numbers (
), 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 (), which is known as the 'grain-inertia' regime.