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G. Fragnière et al.
In order to account for the full particle size distribution, the change of the particle
size due to grinding is calculated via population balance equations. Thus, the mass
balance for size class i in cell r is given by
dm i,r
dt
= ˙
m
i,r−1
i,r
+ ˙
m
i,r+1
i,r
− ˙
m
i,r
i,r+1 − ˙
m
i,r
i,r−1 − S i,r m i,r +
i max
j=i
S j,r m j,r b ij
(1)
with the mass flow over cell boundaries ˙
m, the specific breakage rate S of particles
with size x i in size class i, and the breakage distribution function b, where b ij describes
the mass fraction of material that breaks from size class j into size class i. The breakage
rate is considered to be dependent on the local stress conditions in each cell, while
the breakage distribution function is here assumed to be constant irrespective of the
stress conditions.
Furthermore, this study presents a new approach to determine the breakage function experimentally and relate those data to energy states. Since the dominating stress
mechanism was found to be compression between two surfaces, a two-roll mill was
adjusted to measure breakage characteristics in dependency of different energy levels
down to 5 μm.
2 Stressing Conditions in Stirred Media Mills
In the past century, many research studies have investigated the stressing conditions
in stirred media mills. Researchers developed a broader and better understanding of
breakage mechanisms and breakage energy used in stirred media mills [3–6]. Since
the process optimization is a time-consuming process due to several experiments that
have to be executed for each material, new approaches focus on models describing the
material dependent effects, thus reducing the number of experiments. Therefore, the
following chapter deals with stress mechanisms and conditions in stirred media mills.
First, through Discrete Element Method, stress energies and contact frequencies
could be calculated. Second, the micro scale simulations of two single grinding beads
give detailed information about particle capture probability. These two aspects can
be taken into account for improving the stress model of stirred media mills.
2.1 Stress Energy and Contact Frequency
Coupled CFD-DEM simulations were carried out to investigate the fluid and grinding
media motion and the grinding media collisions. The set-up is shown by Beinert et al.
[7]. The stress energy distributions in a representative mill section were determined
for various operating conditions (grinding bead size, density and stirrer speeds) and
two rotor types. Moreover, they are also calculated for a planetary ball mill. The
G. Fragnière et al.
In order to account for the full particle size distribution, the change of the particle
size due to grinding is calculated via population balance equations. Thus, the mass
balance for size class i in cell r is given by
dm i,r
dt
= ˙
m
i,r−1
i,r
+ ˙
m
i,r+1
i,r
− ˙
m
i,r
i,r+1 − ˙
m
i,r
i,r−1 − S i,r m i,r +
i max
j=i
S j,r m j,r b ij
(1)
with the mass flow over cell boundaries ˙
m, the specific breakage rate S of particles
with size x i in size class i, and the breakage distribution function b, where b ij describes
the mass fraction of material that breaks from size class j into size class i. The breakage
rate is considered to be dependent on the local stress conditions in each cell, while
the breakage distribution function is here assumed to be constant irrespective of the
stress conditions.
Furthermore, this study presents a new approach to determine the breakage function experimentally and relate those data to energy states. Since the dominating stress
mechanism was found to be compression between two surfaces, a two-roll mill was
adjusted to measure breakage characteristics in dependency of different energy levels
down to 5 μm.
2 Stressing Conditions in Stirred Media Mills
In the past century, many research studies have investigated the stressing conditions
in stirred media mills. Researchers developed a broader and better understanding of
breakage mechanisms and breakage energy used in stirred media mills [3–6]. Since
the process optimization is a time-consuming process due to several experiments that
have to be executed for each material, new approaches focus on models describing the
material dependent effects, thus reducing the number of experiments. Therefore, the
following chapter deals with stress mechanisms and conditions in stirred media mills.
First, through Discrete Element Method, stress energies and contact frequencies
could be calculated. Second, the micro scale simulations of two single grinding beads
give detailed information about particle capture probability. These two aspects can
be taken into account for improving the stress model of stirred media mills.
2.1 Stress Energy and Contact Frequency
Coupled CFD-DEM simulations were carried out to investigate the fluid and grinding
media motion and the grinding media collisions. The set-up is shown by Beinert et al.
[7]. The stress energy distributions in a representative mill section were determined
for various operating conditions (grinding bead size, density and stirrer speeds) and
two rotor types. Moreover, they are also calculated for a planetary ball mill. The