It is interesting to note that the specific energy selection
function (Eq. (12)) in the upgraded model has a similar form to
the specific power scale-up function (Eq. (3)) used in the Herbst–
Fuerstenau model. The essential feature of the Herbst–Fuerstenau
model is that ki
E in Eq. (3) is a function of the material only and
does not vary with milling conditions nor with mill size. This
assumption is equivalent to the postulate that the amount of
breakage that occurs inside the mill is proportional to the amount
of energy that has been absorbed by the material. However, despite
the similar selection function form, the major difference between
the Herbst–Fuerstenau model and the upgraded ball mill model
is in the utilisation of the selection function. Herbst and Fuerstenau
use it to empirically scale up the specific rate of breakage, then to
calculate product size distribution by the rate-size balance model.
In the upgraded ball mill model, the specific energy selection function
is directly used to calculate the particle breakage index t10
according to the energy-size reduction relationship (Eq. (11)). Nevertheless,
the Herbst–Fuerstenau modelling approach provides
independent evidence to support the validity of the specific
energy-based modelling method adopted in the upgraded ball mill
model.