Motion of a Particle Bubble Aggregate in a Rectangular Cavity
Motion of a
particle bubble aggregate in a rectangular cavity
is an important particle separation technique using bubbles attach hydrophobic
particles. For
recent years, efforts have been devoted to increase flotation recovery rate of
coarse particles (Jameson, 2010) due to substantial benefits in coarse particle
flotation. According to Bond law of grinding, energy needed to grind mineral
particles of certain size is related to final size of the particle. Grinding,
however, is a highly energy-intensive process. Substantial benefit of coarse
particle recovery is that less energy is required in grinding operations, which
has immense economic benefits. By applying flotation to large particles
separation, less electricity is needed and the amount of greenhouse gas
emission to generate the required electricity is reduced. Moreover, less
grinding operation means less grinding maintenance cost, such as grinding ball
replacement. Nevertheless, it is hard for bubbles to collect coarse mineral
particles with large gravity. Besides, coarse particle bubble aggregates are
usually very unstable and sensitive to fluid hydrodynamics. For this reason,
the high vulnerability of aggregates means that particle bubble detachment is
the major limiting factor in coarse particle flotation. A
force balance approach is usually used to analyse particle bubble detachment
process. Considering equilibrium of all the forces acting on a bubble-particle
aggregate, the maximum floatable particle size can be obtained. Gaudin (1957)
showed the maximum floatable size of minerals in quiescent liquid can be 10
times larger than the maximum particles size of actual flotation process. Such
anomaly exists because in a flotation cell, particle bubble aggregates are
subjected to other disruptive forces due to turbulent fluid motion. In contrast
to the static case (stagnant fluid around the bubble-particle aggregate), turbulent
fluid force is considered to act on the attached particle in actual floatation
cell where a turbulent flow condition persists. To describe such
detaching/disruptive forces, Schulze (1982) hypothesized interactions of
rotating turbulent flow structures (eddies) with the bubble-particle aggregate in
a way that the particle-bubble aggregate was trapped in a rotating eddy and centrifugal
force originated from the rotating flow structures detached particle from
bubble. This theory is based on the assumption that particle bubble aggregate
trapped in the eddy of the same scale will rotate along the eddy to the extent
where centrifugal force exceeds adhesive force. A simpler expression for the
centrifugal force can be obtained assuming isotropic turbulence following
Kolmogorov?s theory:
![](https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/152591/papers/395973/Paper395973_image001.png)
![](https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/152591/papers/395973/Paper395973_image002.png)
acceleration generated by the eddies and can be determined by the root mean
square of the fluctuating velocities
![](https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/152591/papers/395973/Paper395973_image003.png)
rotating length scale
![](https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/152591/papers/395973/Paper395973_image004.png)
![](https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/152591/papers/395973/Paper395973_image005.png)
(1982) assumed that particles moved with the same velocity as the eddy, and the
radius of rotation can be represented by bubble diameter, dB.
Then, centrifugal acceleration
![](https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/152591/papers/395973/Paper395973_image006.png)
![](https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/152591/papers/395973/Paper395973_image007.png)
lots of work have been done to get a clear understanding of coarse particle
flotation, it is still not clear the interactions between hydrodynamics and
particle bubble aggregates. To minimise turbulence influence on particle
detachment whilst ensuring high flotation recovery, it is essential to
understand how turbulence (eddy in more real sense) act on the particle
attached to a bubble. It is still mysterious in the way this detachment process
occurs, but still proactive effort is needed to experimentally presenting particle
detachment process. Given the situation that role of hydrodynamics on particle
detachment is still not fully explored, the objective of this work is focused
on clarifying detachment process, especially on eddy?s influence on particle
bubble aggregate stability. Crowe (1995) studied the
interactions of particles with eddies. Particles and droplets with density
higher than the continuous phase tended to migrate from the centre of eddy to
the ridges of flow structure. On the contrary, bubbles tended to gather in the
centre of flow structures. Different distribution patterns of particles and
bubbles determine the movement of particle bubble aggregates in the turbulent
field. When confronting with eddies, particle bubble aggregate would neither
follow particle nor bubble movement. In the process of interaction, bubbles
tend to flocculate in the centre of the eddy and particles tend to get away
from the centre. Thus, particle bubble aggregate would neither follow bubble?s
or particle?s trajectory in the eddy and the discrepancy leads to particle
bubble detachment.
![](https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/152591/papers/395973/Paper395973_image008.png)
has been done to show particle bubble detachment process where a bubble carries
a plastic particle of 3mm in diameter rising up in a mild turbulent field
generated with a pair of oscillating grids. Fig.1 shows particle detaching
process. Due to bubble?s movement in the trend of zigzag path and disturbance
from surrounding liquid motion, particle sided on the bubble surface as the
particle bubble aggregate rise up. Once detaching effect was higher than
adhesive effect, three phase contact shrinks to form a neck. Detachment
happened afterwards with neck breakage. This was tested with no physical
connection between the particle and the bubble. A large particle was used in
this study which is beneficial to visualize particle bubble detachment process.
Nevertheless, flotation works well in particle separation with particle size
range from 30 micron to 120 micron and our aim is to increase floatable
particle size to 600 micron. However, the existing experimental setup is not
able to provide high turbulence intensity to detach particles in this size
range. To track particle bubble aggregate motion in the eddy, a special
experimental setup was designed as is shown in Fig. 2. It consisted two parts:
a water channel where two rectangular bluff bodies were installed to generate a
cavity in between; a fluidized bed where bubbles are loaded with particles and
allowed to rise up to water channel. Instead of using a traditional flotation
cell, this experiment was designed to view particle bubble performance in the
turbulent, which was otherwise impossible.
![](https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/152591/papers/395973/Paper395973_image009.png)
diagram of experiment. 1. Collector solution. 2. Pump. 3. Capillary of bubble
injection. 4. Fluidized bed. 5. Rectangular bluff body. 6. Water channel. At this stage,
only bubbles were released into the cavity. Average velocity in the water
channel was maintained at 3 m/s. Fast speed camera was used to track bubbles?
movement as is shown in Fig.3. Small bubble diameter is at 1.5 mm and large
bubble diameter is at 2 mm. It is observed that small bubble was in a larger
circular motion at 11 rounds per second. The large bubble moved around a
smaller circle at higher rotational speed. This experiment is elementary to
study particle bubble detachment in the eddy. Particle bubble aggregate is
going to be introduced into the cavity in proving the hypothesis that
centrifugal force leads to particle detachment. Â Â
![](https://www.aiche.org/sites/default/files/aiche-proceedings/conferences/152591/papers/395973/Paper395973_image010.png)
1995. Particle Interactions with Vortices. In: Green, S. (Ed.), Fluid Vortices.
Fluid Mechanics and Its Applications. Springer Netherlands, pp. 829-861. Gaudin, A.M.,
1957. Flotation. McGraw-Hill. Jameson, G.J.,
2010. Advances in fine and coarse particle flotation. Can. Metall. Q., 49(4):
328-330. Schulze, H.J.,
1982. Dimensionless number and approximate calculation of the upper particle
size of floatability in flotation machines. Int. J. Miner. Process., 9(4):
321-328.