XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2787
or without ultrafine particles. A 2 mm diameter bubble is
created at the tip of a capillary using a computer-controlled
micro syringe and placed in the center of the attachment
chamber, approximately 20 mm above the propeller, see
Figure 1a. The water/particle mixture is then agitated by
a propeller and the surface coverage is measured over time.
This is achieved by periodically turning the propeller on
and off, allowing the particles to settle during the off peri-
ods to provide optical access to the bubble surface. Once
the bubble is clearly visible through the camera, the height
of the coating is recorded (Figure 1b). The height of cover-
age is directly related to the surface coverage (A/Ab) quanti-
fied by our model, see Equation 1, as reported in our recent
paper (Eftekhari et al. 2024),
/A ,C A e K
C VP
1 4H
πR
b
p p
1
2
=-=-Kt ^h (1)
where C1 is a constant, Cp is particle number density, V is
the relative approach velocity of the particles towards the
bubble, P is the collection probability, Rp is the particle
radius, and H is the packing density of the particles at the
bubble surface. Equation 1 demonstrates that the surface
coverage (A/Ab) changes exponentially with time, with the
growth rate of K, which has been shown to be a good indi-
cator of particle floatability.
The same experimental setup is used with minor
adjustments to investigate the packing density of GBs on
the bubble surface. This was done by focusing the camera
directly on the particles at the surface of the bubble, rather
than on the edges of the particle cap. From the images
obtained, the packing density of the particles on the surface
of the bubble was calculated using image processing.
RESULTS AND DISCUSSION
Surface Packing and Particles Distribution on
Bubble Surface
Certain parameters, such as particle hydrophobicity, can
affect the dynamics of particle attachment by influencing
both the collection probability (P) and the packing density
of the particles (H ),see K in Equation 1. Therefore, to gain
better insight into the dynamics of particle attachment, the
packing density of the attached GBs is investigated. Two
different sizes of GBs are used for these experiments, 66 µm
and 176 µm, with polydispersity index values of 0.9 and
0.5, respectively. However, to avoid the potential errors
associated with image processing of smaller particles, calcu-
lations are restricted to larger particles, which have a lower
polydispersity and higher sphericity. This results in more
accurate edge detection and therefore more reliable data.
Figure 2a shows the packing density calculated from
image-processing for two different particle hydropho-
bicities. The packing density of the GBs was found to be
unaffected by their hydrophobicity (H ≈ 0.77). Next, the
number of neighboring particles is calculated for each of
the attached particles for two different surfactant concen-
trations (see Figure 2b). As one can see, irrespective of the
particle hydrophobicity, hexagonal packing is the most
prominent configuration.
Since the error in the calculation of the packing den-
sity of the smaller particles by means of image processing
was high, a new approach is used to measure their packing
density. This is done by measuring the mass of the bubble
coated with GBs. A single bubble is coated to the maxi-
mum in the attachment chamber and moved to the collec-
tion chamber a total of 50 times. At the end, the collected
Figure 1. The experimental setup for the dynamic coating experiments (a) and the definition of the surface coverage (b)
or without ultrafine particles. A 2 mm diameter bubble is
created at the tip of a capillary using a computer-controlled
micro syringe and placed in the center of the attachment
chamber, approximately 20 mm above the propeller, see
Figure 1a. The water/particle mixture is then agitated by
a propeller and the surface coverage is measured over time.
This is achieved by periodically turning the propeller on
and off, allowing the particles to settle during the off peri-
ods to provide optical access to the bubble surface. Once
the bubble is clearly visible through the camera, the height
of the coating is recorded (Figure 1b). The height of cover-
age is directly related to the surface coverage (A/Ab) quanti-
fied by our model, see Equation 1, as reported in our recent
paper (Eftekhari et al. 2024),
/A ,C A e K
C VP
1 4H
πR
b
p p
1
2
=-=-Kt ^h (1)
where C1 is a constant, Cp is particle number density, V is
the relative approach velocity of the particles towards the
bubble, P is the collection probability, Rp is the particle
radius, and H is the packing density of the particles at the
bubble surface. Equation 1 demonstrates that the surface
coverage (A/Ab) changes exponentially with time, with the
growth rate of K, which has been shown to be a good indi-
cator of particle floatability.
The same experimental setup is used with minor
adjustments to investigate the packing density of GBs on
the bubble surface. This was done by focusing the camera
directly on the particles at the surface of the bubble, rather
than on the edges of the particle cap. From the images
obtained, the packing density of the particles on the surface
of the bubble was calculated using image processing.
RESULTS AND DISCUSSION
Surface Packing and Particles Distribution on
Bubble Surface
Certain parameters, such as particle hydrophobicity, can
affect the dynamics of particle attachment by influencing
both the collection probability (P) and the packing density
of the particles (H ),see K in Equation 1. Therefore, to gain
better insight into the dynamics of particle attachment, the
packing density of the attached GBs is investigated. Two
different sizes of GBs are used for these experiments, 66 µm
and 176 µm, with polydispersity index values of 0.9 and
0.5, respectively. However, to avoid the potential errors
associated with image processing of smaller particles, calcu-
lations are restricted to larger particles, which have a lower
polydispersity and higher sphericity. This results in more
accurate edge detection and therefore more reliable data.
Figure 2a shows the packing density calculated from
image-processing for two different particle hydropho-
bicities. The packing density of the GBs was found to be
unaffected by their hydrophobicity (H ≈ 0.77). Next, the
number of neighboring particles is calculated for each of
the attached particles for two different surfactant concen-
trations (see Figure 2b). As one can see, irrespective of the
particle hydrophobicity, hexagonal packing is the most
prominent configuration.
Since the error in the calculation of the packing den-
sity of the smaller particles by means of image processing
was high, a new approach is used to measure their packing
density. This is done by measuring the mass of the bubble
coated with GBs. A single bubble is coated to the maxi-
mum in the attachment chamber and moved to the collec-
tion chamber a total of 50 times. At the end, the collected
Figure 1. The experimental setup for the dynamic coating experiments (a) and the definition of the surface coverage (b)