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G. Fragnière et al.
loss of fines, complicating the detection of further breakage to smaller fractions. It can
be concluded that there is a limit of detection in size reduction for a defined particle
size. At ratios above 94%, most particles simply fall through the gap, resulting also
in smaller energy values.
Summarizing this results, the breakage behavior of materials and especially the
breakage function can be predicted through the tailor-made breakage tester. Further
aim is to calculate the breakage function dependent on feed particle size and breakage
energy for the given material. Further investigations will deliver more information
about the usage of the two-roller tester and will be published soon. One focus will
be to evaluate to what extent the breakage function can be used to predict breakage
in stirred media mills.
4 Grinding
4.1 Effects of Operating Condition Variations
on the Breakage Rate
The evolution of the particle size distribution in grinding processes can be described
by population balance modelling. In order to model the transition of particles to
smaller particle sizes, the parameters specific breakage rate and breakage (distribution) function are required. These can be determined by experiments. However, the
specific breakage rate determined experimentally for one operating condition is not
easily transferable to other operating conditions as it depends strongly on particle
size, material properties and the stressing conditions in the mill.
The stress conditions in stirred mills can be determined with semi-empirical models (e.g. [13–16]). The shear-based power model represents the stirred mill as a viscometer and shows the effect of stirrer speed, geometry and viscosity on the power
consumption of the mill [15]. The stress energy model shows with the parameters
stress energy and stress frequency, which are calculated from simple proportionalities, the influence of process parameters on the grinding result [14]. Eskin et al.
[13] estimate the mean velocity and frequency of grinding media oscillations using
approximate values of turbulent energy dissipations on a micro scale. Based on this
micro hydrodynamic view of the particle stressing, Afolabi et al. [16] define a process parameter depending milling intensity factor that correlates with the breakage
kinetics of drug nanoparticles. As an alternative to the semi-empirical models, the
stress conditions can be obtained by simulating the grinding media motion in wet
operated stirred media mills via coupling of discrete element method (DEM) with
computational fluid dynamics (CFD) (e.g. [7, 17]) or smoothed particle hydrodynamics (SPH) (e.g. [18]). Gers et al. [19] characterize collision characteristics by
determining collisional Stokes and Reynolds numbers from direct numerical simulations. Distribution of stress energy from DEM simulations in combination with
G. Fragnière et al.
loss of fines, complicating the detection of further breakage to smaller fractions. It can
be concluded that there is a limit of detection in size reduction for a defined particle
size. At ratios above 94%, most particles simply fall through the gap, resulting also
in smaller energy values.
Summarizing this results, the breakage behavior of materials and especially the
breakage function can be predicted through the tailor-made breakage tester. Further
aim is to calculate the breakage function dependent on feed particle size and breakage
energy for the given material. Further investigations will deliver more information
about the usage of the two-roller tester and will be published soon. One focus will
be to evaluate to what extent the breakage function can be used to predict breakage
in stirred media mills.
4 Grinding
4.1 Effects of Operating Condition Variations
on the Breakage Rate
The evolution of the particle size distribution in grinding processes can be described
by population balance modelling. In order to model the transition of particles to
smaller particle sizes, the parameters specific breakage rate and breakage (distribution) function are required. These can be determined by experiments. However, the
specific breakage rate determined experimentally for one operating condition is not
easily transferable to other operating conditions as it depends strongly on particle
size, material properties and the stressing conditions in the mill.
The stress conditions in stirred mills can be determined with semi-empirical models (e.g. [13–16]). The shear-based power model represents the stirred mill as a viscometer and shows the effect of stirrer speed, geometry and viscosity on the power
consumption of the mill [15]. The stress energy model shows with the parameters
stress energy and stress frequency, which are calculated from simple proportionalities, the influence of process parameters on the grinding result [14]. Eskin et al.
[13] estimate the mean velocity and frequency of grinding media oscillations using
approximate values of turbulent energy dissipations on a micro scale. Based on this
micro hydrodynamic view of the particle stressing, Afolabi et al. [16] define a process parameter depending milling intensity factor that correlates with the breakage
kinetics of drug nanoparticles. As an alternative to the semi-empirical models, the
stress conditions can be obtained by simulating the grinding media motion in wet
operated stirred media mills via coupling of discrete element method (DEM) with
computational fluid dynamics (CFD) (e.g. [7, 17]) or smoothed particle hydrodynamics (SPH) (e.g. [18]). Gers et al. [19] characterize collision characteristics by
determining collisional Stokes and Reynolds numbers from direct numerical simulations. Distribution of stress energy from DEM simulations in combination with