Granular Flow — Bagnold Scaling

Particle collisions · σ ∝ (dv/dy)² · viscous vs inertial regime

Parameters

Measurements

Flow rate Q
Mean velocity
Kinetic energy
Collisions/s
Bagnold regime

About

Bagnold (1954) discovered that granular flows have stress scaling differently from fluids. In the inertial regime (high shear rate γ̇), stress σ ∝ ρd²γ̇² — the "Bagnold scaling". In the viscous regime (low γ̇), σ ∝ ηγ̇. The transition occurs at Bagnold number Ba = ρd²γ̇/η. Particle collisions, not viscosity, dominate dense fast flows.