Mixing (and segregation) play a vital role in several industrial processes. In the pharmaceutical
industry, the e.ectiveness of the drug is directly related to the mixture of active
ingredient and excipient. Central to the low efficiency (< 5%) reported in mineral grinding
processes is the inability to control the relative mix of grinding balls and small rocks in
the high shear zones where most of the energy is dissipated. The canonical rotating drum
system encountered in the mineral processing, food and pharmaceutical industry is well
known to exhibit axial and radial mixing; however, their interplay for optimal performance
is not well understood. A further limitation relates to the low Froude regimes explored by
many investigators that ultimately lead to a restricted mechanistic interpretation.
In our first phase of the project (year one) Positron Emission Particle Tracking (PEPT)
was used to measure the 3D trajectory of a binary mixture (3mm and 5mm diameter
plastic beads) within a laboratory rotating drum fitted with lifter bars. The experimental
matrix spanned four fill fractions and seven drum rotation rates across the cascading
and cataracting Froude regime. After converting the measured Lagrangian trajectories
of representative radio-labelled beads (the tracer) into Eulerian fields under the ergodic
assumption, we extract the bed shape, solids fraction and kinematics for steady, fully
developed flow conditions.
The initial analyses of PEPT data clearly show radial segregation by size consistent with
the Brazil Nut E.ect (BNE) at low Froude numbers; however, at higher Froude numbers
cascading and cataracting) the Reverse Brazil Nut E.ect (RBNE) is clearly evident from
the data. These findings have significant implications for industrial systems (like tumbling
mills) that operate in the high Froude regimes.
The limitations in the standard definition of the Péclet number precipitated the need for
an alternate definition. In this regard we propose a granular temperature-dependent Péclet
number that is computed directly from the PEPT data. Interestingly, it’s validity seems to
extend beyond simply quantifying the relative importance of advection and di.usion, and
like the Inertial number, also appears to describe the ratio of the microscopic rearrangement
timescale to the macroscopic shearing timescale more naturally. This idea will be explored
in greater detail in the next phase of the project wherein we formulate mixing scaling
relations based directly upon PEPT-derived stress computations.