In order to examine how the initial non-uniformity in the random mixture (Figures 5.1
and 5.5) affects the segregation tendency, an ordered mixture which has a perfectly
uniform concentration distribution was generated in the shoe before die filling. As
shown in Figure 5.22, the ordered mixture is generated by alternately arranging the
mono-sized light and heavy particles in the horizontal and vertical directions. To be
consistent with the previous cases in which the random mixtures are used, die fillings
been simulated. The results show that the overall powder flow patterns with the
ordered mixtures are similar to those with the random mixtures (Figures 5.2, 5.3 and
5.4). The segregation behaviour with the ordered mixtures will be discussed in the
following sections.
Figure 5.22 Configuration of the ordered mixture of the same size but different density particles. (light and heavy particles are coloured in yellow and magenta, respectively)
5.3.1. The effect of shoe velocity
The horizontal concentration distributions of light particles in the die after die filling
with an ordered mixture (ρh / ρl = 19.5) at different shoe velocities are shown in
Figure 5.23. Similar to those with a random mixture (Figure 5.10), significant
segregation with a lower concentration of light particles on the left hand side is
obtained for die filling with a moving shoe at low shoe velocities (i.e. 35 mm/s and 70
mm/s), and no obvious segregation in the horizontal direction is observed for die
filling with a stationary shoe (i.e. 0 mm/s) and with a moving shoe at high shoe
velocities (i.e. 140 mm/s and 170 mm/s). The corresponding vertical concentration
distributions of light particles with the ordered mixture at different shoe velocities are
particles is obtained at the bottom of the die except for die filling with a stationary
shoe, and the concentration of light particles in the die increases as shoe velocity
increases for die filling with a moving shoe. In the presence of air, a lower
concentration of light particles is also observed for die filling with a stationary shoe.
(a) In a vacuum
(b) In air
Figure 5.23 Horizontal concentration distributions of light particles in the die after die filling with an ordered mixture (ρh / ρl = 19.5) at different shoe velocities.
(a) In a vacuum
(b) In air
Figure 5.24 Vertical concentration distributions of light particles in the die after die filling with an ordered mixture (ρh / ρl = 19.5) at different shoe velocities.
Figure 5.25 shows the horizontal and vertical concentration deviations as a function of
shoe velocity for die filling with the ordered mixture. Similarly as obtained from die
filling with the random mixture (Figure 5.12), the larger concentration deviations are
observed for die filling with a moving shoe at low shoe velocities (i.e. vs = 35 mm/s
deviations are observed for die filling with a stationary shoe (vs =0) and with a
moving shoe at higher shoe velocities (i.e. vs = 140 mm/s and 170 mm/s) in which the
bulk-flow dominates. For die filling with a moving shoe, the concentration deviations
generally decrease as shoe velocity increases, but in the presence of air, the horizontal
concentration deviation increases as shoe velocity increases from 140 mm/s to 170
mm/s due to outflow of light particles from the back of the shoe as observed during
die filling with the random mixture (Figure 5.4h).
Figure 5.25 Horizontal and vertical concentration deviations as a function of shoe
velocity for die filling with an ordered mixture (ρh / ρl = 19.5).
5.3.2. The effect of density ratio
Horizontal concentration distributions of light particles in the die after die filling from
a stationary shoe (vs=0) with ordered mixtures of different density ratios are shown in
Figure 5.26. No segregation occurs in the horizontal direction for die filling in a
vacuum. This proves that the horizontal concentration distribution in the die after die
segregation is induced for die filling in the presence of air. The corresponding vertical
concentration distributions of light particles in the die are shown in Figure 5.27. No
vertical segregation occurs for die filling in a vacuum. For die filling in the presence
of air, segregation occurs with a lower concentration of light particles at the bottom of
the die and as the density ratio increases the concentration of light particles at the
bottom of the die initially decreases and then increases.
(a) In a vacuum
(b) In air
Figure 5.26 Horizontal concentration distributions of light particles in the die after die filling from a stationary shoe (vs=0) with ordered mixtures of different density ratios.
(a) In a vacuum
(b) In air
Figure 5.27 Vertical concentration distributions of light particles in the die after die filling from a stationary shoe (vs=0) with ordered mixtures of different density ratios.
Figure 5.28 shows the horizontal and vertical concentration deviations as a function of
density ratio for die filling with ordered mixtures and a stationary shoe. As observed
in die filling with random mixtures (Figure 5.15), the concentration deviations in air
promote the segregation, especially in the vertical direction. For die filling in air, as
the density ratio increases the vertical concentration deviation initially increases due
to the increasing difference in falling velocities of light (air-sensitive) and heavy (air-
inert) particles and then decreases due to the formation of denser powder flow streams
with increasing particle densities.
Figure 5.28 Horizontal and vertical concentration deviations as a function of density
ratio for die filling with ordered mixtures and a stationary shoe.
Horizontal concentration distributions of light particles in the die after die filling with
ordered mixtures of different density ratios at a shoe velocity of 70 mm/s are shown in
Figure 5.29. In general, segregation occurs in the horizontal direction with a lower
concentration of light particles on the left hand side of the die. As the density ratio
increases, the concentration of light particles on the left hand side decreases. The
corresponding vertical concentration distributions are shown in Figure 5.30.
Segregation also occurs in the vertical direction with a lower concentration of light
particles at the bottom of the die. As the density ratio increases, the concentration of
(a) In a vacuum
(b) In air
Figure 5.29 Horizontal concentration distributions of light particles in the die after die
(a) In a vacuum
(b) In air
Figure 5.30 Vertical concentration distributions of light particles in the die after die
filling with ordered mixtures of different density ratios at a shoe velocity of 70 mm/s.
Figure 5.31 shows the horizontal and vertical concentration deviations as a function of
density ratio for die filling with ordered mixtures at a shoe velocity of 70 mm/s. In
general, the concentration deviation increases as the density ratio increases due to the
velocities to segregate from the heavy ones. The effect of air is limited due to the easy
release of the air from the die cavity in nose-flow dominant die filling process. These
findings are also similar to those for the die filling with the random mixtures (Figure
5.18).
Figure 5.31 Horizontal and vertical concentration deviations as a function of density
ratio for die filling with ordered mixtures at a shoe velocity of 70 mm/s.
5.4. Summary
Density-induced segregation during die filling with binary mixtures of mono-sized
particles in air and in a vacuum was investigated using a coupled DEM/CFD method.
Die filling with random mixtures, which were generated by randomly mixing the light
particles (of low particle density) and the heavy particles (of high particle density),
was considered first. The particles of different densities have different air sensitivities
and the difference in air sensitivity was found to have a significant impact on the
For die filling with a stationary shoe, a low degree of segregation is observed in a
vacuum, which is attributed to the non-uniformity of the initial random mixture in the
shoe. When air is present, the entrapped air resists the downward flow of the air-
sensitive particles (the light particles), so that vertical segregation is induced with a
lower concentration of light particles at the bottom of the die. It is also observed that
the air flow can disturb the flowing stream of particles, by which fluctuations of the
horizontal concentration profile are promoted. As the density ratio (ρh / ρl) increases,
the degree of segregation in air initially increases due to the increasing difference in
falling acceleration from the effect of air drag; and then remains nearly constant or
even decreases due to the formation of the denser powder flow stream that suppresses
the segregation.
For die filling with a moving shoe, nose-flow and bulk-flow are observed to dominate
die filling at low and high shoe velocities, respectively. The degree of segregation
generally decreases as the shoe velocity increases with the transition of die filling
from nose-flow dominated to bulk-flow dominated. For nose-flow dominated die
filling, segregation occurs with a depletion of light particles not only at the bottom of
the die but also at the leading side of the die that the shoe moves towards. When nose-
flow occurs, the air can escape from the die before the die opening is completely
covered by the moving powder mass, so that the influence of air on the powder flow
and segregation behaviours is limited for the nose-flow dominated die filling. For
bulk-flow dominated die filling in a vacuum, no obvious segregation occurs in the
horizontal direction and only vertical segregation occurs with a low concentration of
the die by the fast moving powder mass in the shoe, and the entrapped air can cause
an incomplete filling of the die (for low particle density) or the outflow of a lights-rich
stream of particles from the trailing side of the die (referring to the direction of shoe
motion). Consequently, the presence of air could have an impact on the segregation
behaviour during the bulk-flow dominated die filling. It is also found that the degree
of segregation during die filling with a moving shoe increases as the density ratio (ρh /
ρl) increases, due to the increasing difference in inertia of the particles.
Finally, ordered mixtures, which are perfectly uniform, were employed to eliminate
the initial heterogeneity which exists in the random mixtures. The results from die
fillings with the ordered mixtures were in good agreement with those from die fillings
with the random mixtures. This implies that the slight non-uniformity in the randomly
generated mixtures has a negligible effect on the powder flow patterns and
segregation tendency during die filling. Therefore, the density-induced segregation
discussed in this study is a general consequence of die filling with well-mixed binary