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G. Fragnière et al.
the particle size for the given solids concentration is still above or in the range of a
critical value (Knieke et al.) under which the viscosity starts to significantly rise and,
that the effect of the reduction in particle size is compensated by the increase of the
temperature inside the grinding chamber (Fig. 19a). Comparing these results with
the particle size (x 50 ) change in Fig. 19b, only slightly difference in the measurement
values could be found. Even though the increase in viscosity probably improves the
grinding bead distribution along the length of the LM4, the dissipation of kinetic
energy through increased damping of bead collisions decreases grinding efficiency.
Therefore, no effect of viscosity on grinding result could be ascertained here. However, at the beginning of the grinding process, i.e. at low residence times, an increase
in viscosity improves the grinding efficiency in the LM4 (Fig. 19b).
In general, the viscosity is an important aspect for grinding at low grinding times.
With increasing number of cycles, the effect of viscosity is decreasing. One aspect
might be that the product residence time is increasing with higher viscosities, which
is important in the beginning of the process. Another aspect might be that particles
greater than 20 μm can be captured more efficiently at higher viscosities, since the
drag force acting on the grinding beads and particles distributes them equally in
all cells in the mill, so that the effective velocities of grinding beads in the cells is
increased.
In conclusion, viscosity is only changing the grinding process, if the viscosity is
high enough to reduce the kinetic energy of the beads and the bead distribution along
the length of the mill. If the viscosity is only influenced by the particle diameter, the
change in viscosity is marginal as long as the particles sizes are clearly above 1 μm.
The influence of increased solids concentrations is reduced through longer grinding
times, since the energy is distributed among more particles. A longer grinding time
results in a narrower particle size distribution when circulation mode is used at
constant mill throughputs. In case of one passage mode longer grinding times and,
consequently, lower mill throughputs result in wider residence time distributions and,
thus, wider particle size distributions.
5 Product Transport
For stirred media mills it was already shown that the residence time distribution
can be simulated by a series of ideal stirring vessels with recirculating flow [31,
32]. The volumes of the ideal stirring vessels are positioned around the stirring
discs, as shown schematically in Fig. 20. Thereby, the geometry of the stirred mill
is considered. Keeping the series of well mixed cells in mind, in the simulation
the product particle concentration should change stepwise in axial direction after a
change in the product inlet. This also corresponds to the experimentally observed
behavior of the fluid transport [32]. Back mixing is described by the return flow
coefficient R, which indicates the ratio of mixing flow to volume flow: R = ˙
R/ ˙
V
G. Fragnière et al.
the particle size for the given solids concentration is still above or in the range of a
critical value (Knieke et al.) under which the viscosity starts to significantly rise and,
that the effect of the reduction in particle size is compensated by the increase of the
temperature inside the grinding chamber (Fig. 19a). Comparing these results with
the particle size (x 50 ) change in Fig. 19b, only slightly difference in the measurement
values could be found. Even though the increase in viscosity probably improves the
grinding bead distribution along the length of the LM4, the dissipation of kinetic
energy through increased damping of bead collisions decreases grinding efficiency.
Therefore, no effect of viscosity on grinding result could be ascertained here. However, at the beginning of the grinding process, i.e. at low residence times, an increase
in viscosity improves the grinding efficiency in the LM4 (Fig. 19b).
In general, the viscosity is an important aspect for grinding at low grinding times.
With increasing number of cycles, the effect of viscosity is decreasing. One aspect
might be that the product residence time is increasing with higher viscosities, which
is important in the beginning of the process. Another aspect might be that particles
greater than 20 μm can be captured more efficiently at higher viscosities, since the
drag force acting on the grinding beads and particles distributes them equally in
all cells in the mill, so that the effective velocities of grinding beads in the cells is
increased.
In conclusion, viscosity is only changing the grinding process, if the viscosity is
high enough to reduce the kinetic energy of the beads and the bead distribution along
the length of the mill. If the viscosity is only influenced by the particle diameter, the
change in viscosity is marginal as long as the particles sizes are clearly above 1 μm.
The influence of increased solids concentrations is reduced through longer grinding
times, since the energy is distributed among more particles. A longer grinding time
results in a narrower particle size distribution when circulation mode is used at
constant mill throughputs. In case of one passage mode longer grinding times and,
consequently, lower mill throughputs result in wider residence time distributions and,
thus, wider particle size distributions.
5 Product Transport
For stirred media mills it was already shown that the residence time distribution
can be simulated by a series of ideal stirring vessels with recirculating flow [31,
32]. The volumes of the ideal stirring vessels are positioned around the stirring
discs, as shown schematically in Fig. 20. Thereby, the geometry of the stirred mill
is considered. Keeping the series of well mixed cells in mind, in the simulation
the product particle concentration should change stepwise in axial direction after a
change in the product inlet. This also corresponds to the experimentally observed
behavior of the fluid transport [32]. Back mixing is described by the return flow
coefficient R, which indicates the ratio of mixing flow to volume flow: R = ˙
R/ ˙
V