6 Dynamic Process Models for Fine Grinding and Dispersing
209
Fig. 8 Projections and trajectories of grinding bead center points and of particles (Reprinted with
permission from [12])
For approaches with greater angles between the two grinding beads motions,
the product particle velocity reduction caused by the impact itself increases. This
influence increases in the further course as the particles are accelerated and moved
due to the pull induced by the grinding beads [12]. It can be seen that the particles are
accelerated following a contact in the pull of the fluid moving into the gap between
the grinding beads, which are moving away from each other. As a consequence, the
product particles are carried away from their initial position. The paths of the product
particles before and after the grinding media collision are different due to the flow
field around the grinding beads being different as result of the angle of motion during
collision.
The difference for various Reynolds numbers is notable. In general, the decrease in
product particle velocity is lower for higher velocities due to the reduced influence
of friction caused by a more turbulent flow at higher Reynolds numbers. In case
of angled impact, no clear influence on the overall reduction of velocity can be
observed, the influence on the velocity during the contact at different contact angles
is however noticeable. The velocity reduction caused by the impact is greater with
increasing angle between the grinding bead velocity vectors. Thus, in macro scale
simulations the coefficient of restitution should contain the deceleration caused by
the fluid displacement to gain more realistic results [8]. In Table 2 the influence of
grinding bead velocities on product particle motion is displayed. The grinding media
velocity is described by the start velocity in normal direction and a low transversal
velocity. The resulting mean product particle velocity is shown as well as the mean
position change as a function of the product particle diameter d p of eight particles
[12].
209
Fig. 8 Projections and trajectories of grinding bead center points and of particles (Reprinted with
permission from [12])
For approaches with greater angles between the two grinding beads motions,
the product particle velocity reduction caused by the impact itself increases. This
influence increases in the further course as the particles are accelerated and moved
due to the pull induced by the grinding beads [12]. It can be seen that the particles are
accelerated following a contact in the pull of the fluid moving into the gap between
the grinding beads, which are moving away from each other. As a consequence, the
product particles are carried away from their initial position. The paths of the product
particles before and after the grinding media collision are different due to the flow
field around the grinding beads being different as result of the angle of motion during
collision.
The difference for various Reynolds numbers is notable. In general, the decrease in
product particle velocity is lower for higher velocities due to the reduced influence
of friction caused by a more turbulent flow at higher Reynolds numbers. In case
of angled impact, no clear influence on the overall reduction of velocity can be
observed, the influence on the velocity during the contact at different contact angles
is however noticeable. The velocity reduction caused by the impact is greater with
increasing angle between the grinding bead velocity vectors. Thus, in macro scale
simulations the coefficient of restitution should contain the deceleration caused by
the fluid displacement to gain more realistic results [8]. In Table 2 the influence of
grinding bead velocities on product particle motion is displayed. The grinding media
velocity is described by the start velocity in normal direction and a low transversal
velocity. The resulting mean product particle velocity is shown as well as the mean
position change as a function of the product particle diameter d p of eight particles
[12].