Executive Summary
In our third phase of the project we identify a suitable dimensionless number|
The Entrainment Number (^ !)|from a fundamentally-derived granular ow model
of rotating drum ows that facilitates scale-up of the dominant mixing mechanisms
spanning rolling-to-fully-cascading ow regimes. Starting with the linearised form of
dense, viscoplastic granular rheology of (da Cruz et al., 2005; GDR MiDi, 2004), a
subsequent balance of mass, momentum and energy yields di erential equations to the
free surface e z(x), basal interface z e (x), and depth-averaged velocity u(x) under arbitrary
transient and non-uniform ow conditions. Positron Emission Particle Tracking
(PEPT) measurements con rms the successful recovery of bed geometry (free surface
and basal interface) and full velocity eld. Subsequent non-dimensionalisation of
the governing equations yields a set of dimensionless numbers, including the ratio of
forced-to-free entrainment|The Entrainment Number.
Focussing on shear and advective mixing, we isolate the corresponding energy signatures
that classify mixing into three categories: (i) shear dominated, (ii) advective
dominated, and (iii) intermediate (both shear and advection). Scale-up rules of the
three mixing mechanisms are then achieved via the Entrainment number. The theory
successfully scales up mixing con gurations spanning slowly rotated drums operated
in the rolling mode to fully cascading ows consistent with industrial comminution
systems.