2788 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
GBs are dried and weighed. Experiments are conducted
with 66 µm GBs and also a mixture of 66 µm and 176 µm
GBs with the weight ratio of 40% to 60%, respectively. The
latter is chosen to investigate the competitive attachment of
particles of different sizes.
Knowing the mass of a fully coated bubble (m), one
can calculate the packing density of GBs at the interface
using:
A R 4
3m
GBs b ###t H =
64,3@
(2)
where Ab is the total surface area of the bubble. The average
weight of a single bubble coated to its maximum was mea-
sured to be 0.964 mgr for 66 µm GBs, and 1.56 mgr for
the mixture of 66 µm and 176 µm GBs. Using Equation 2,
a surface packing density of 0.74 is calculated for 66 µm
GBs. However, to calculate the packing density of the
mixed particle system, the ratio of smaller to larger GBs at
the interface must be known, see Equation 3:
4A
3m
GBs
mix
b j j
j j
##
#
/N
/N
t H =
_R
_R
i2
i3
62,0@
63,0@
(3)
It is known that the collision rate depends on the num-
ber density of particles in the suspension (Nguyen et al.
2016). Since the number of particles on the bubble surface
should depend on the collision rate of the particles, one
could assume that the number density of particles in the
bulk phase should control the relative number of particles
on the bubble surface, i.e.,
surface .6 N
N
N
N
12
bulk
176
66
176
66
µm
µm
µm
µm .=(4)
Assuming that the ratio of the smaller GBs to larger ones
at the interface is approximately 12.6, H equal to 0.76 is
calculated. This is slightly larger than the packing density of
the 66 µm GBs system, which is to be expected due to the
higher polydispersity of the mixed system.
Figures 3 a and b show the size distribution of the
66 µm GBs before they are added to the stirred cell and
after they are collected, respectively. The collected GBs
from 50 experimental runs are first dried for weighing and
then redispersed in the water phase for size analysis. It can
be seen that the size distribution of the GBs before and after
collection is almost identical, with a slight shift to smaller
sizes after collection (see the change of mean diameter).
This indicates the higher attachment rate of the smaller
fractions of GBs. Figures c and d show the results of simi-
lar experiments conducted with a mixture of two different
sizes of GBs, i.e., 66 µm and 176 µm GBs with a weight
ratio of 0.4 to 0.6, respectively. The results show that the
majority of the collected particles belonged to the smaller
fractions. This was expected because the smaller GBs have
nearly 13 times the number density of the larger ones and
should therefore have faster coating rates. Figure 4 shows
two different snapshots of the bimodal system. Evidently,
the majority of the GBs at bubble surface are smaller GBs,
with a few larger GBs. This is again consistent with the
Figure 2. a) Surface packing density (H )vs. GBs hydrophobicity (surfactant concentration) for 176 μm GBs. b) Probability
of number of neighbor particles surrounded each particle for 176 μm GBs hydrophobized with 0.003 CMC and 0.01 CMC
CTAB solution