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Virginia Tech | of the thermodynamic studies conducted by one of us showing that hydrophobic force may
originate from the changes in water structure as a thick film becomes a thin film.70
2.6 Summary
The results of present investigation show that the kinetics of thinning for the wetting films of
water formed on hydrophilic silica surface can be fitted to the Reynolds lubrication
approximation with non-slip boundary conditions. The same approach has also been used to study
the kinetics of film thinning on the surface of gold substrates hydrophobized by KAX. The results
show that the kinetics increases with increasing hydrophobicity. This finding suggests that
hydrophobization of a substrate causes the disjoining pressure in the wetting films to decrease,
which in turn can be attributed to the presence of hydrophobic force in the wetting films. It has
been found that the hydrophobic force constant (K ) of the wetting film, as determined by fitting
132
the kinetics data to the Reynolds approximation, increases with increasing receding contact angle
of the substrate. It has been found also that K decreases with increasing NaCl concentration and
132
after an excessively long contact time between the substrate and KAX. The former can be
attributed to the decrease in the cohesive of energy of water (W ) in the presence of the
c
electrolyte, while the latter to the increase in surface roughness associate with a possible
multilayer formation. Further, the values of K can be predicted from the values of the
132
hydrophobic force constants (K ) for the interaction between solid surfaces of identical
131
hydrophobicity and those (K ) for the soap films using the geometric mean combining rule.
232
25 |
Virginia Tech | Chapter 3
Thinning and Rupture of Wetting Film on Silica Plate in the C TACl
18
Aqueous Solution
Abstract
Thin Film Balance (TFB) technique is employed to measure the thinning kinetics and critical
rupture thickness of dimpled wetting film on a silica plate in C TACl aqueous solution.
18
Assuming the immobile surface at the air/water interface and no hydrodynamic pressure at the
barrier rim of dimpled film, the thinning of wetting film is controlled by the sum of the capillary
pressure and disjoining pressure. The kinetics of wetting film thinning is, therefore, viewed as
Reynolds lubrication theory when only considering the thinning of wetting film at the rim of film.
It is found that thinning kinetics of film on silica plate in C TACl aqueous solution could be
18
predicted only when considering the extra attractive forces named as “hydrophobic forces”, since
van der waals forces and electrostatic forces both are repulsive. The values of hydrophobic forces
constant (K ) varies with different concentration of C TACl and different immersion time. At
132 18
5x10-6 M C TACl aqueous solution, K reaches the maximum for 1 hour which is consistent
18 132
with the contact angle measurement. The effect of electrolyte on kinetics of wetting film thinning
and critical rupture thickness is also examined. The critical rupture thickness (H) and
r
hydrophobic forces constant (K ) decreases with increasing the NaCl concentration, probably
132
because of the compression of electrostatic double layer forces and decrease of hydrophobic
forces. It is, therefore, suggested that hydrophobic forces plays a vital role in destabilizing the
wetting film between air bubbles and hydrophobic particles.
38 |
Virginia Tech | 3.1 Introduction
Froth Flotation has been used for more than 100 years for separating different minerals from
each other since 1905, when the air bubble was first used for flotation.1 The basic principle of
froth flotation is rendering the target minerals hydrophobic and unselected minerals hydrophilic
to achieve the separation of minerals, and therefore, the attachment between the air bubble and
hydrophobic particles is the fundamental process for successful flotation. The attachment between
air bubble and hydrophobic particles involves three sub-processes: 1) air bubble approaches the
particles by hydrodynamics; 2) the thinning of wetting film between air bubble and particles; 3)
rupture of wetting film to form the three-phase froth. Many investigators attempted to model the
flotation process by hydrodynamics parameters without considering any surface forces. In most
flotation condition, however, both the van der Waals forces and electrostatic double layer forces
are repulsive, which give no driving forces for thinning and rupture of wetting film on
hydrophobic particles2. It appears, therefore, the interaction between the bubbles and particles are
the key for modeling the flotation process.
Derjaguin and Duhkin3 were the first to introduce the surface forces to investigate the bubble-
particles interaction, but they only considered van der Waals and electrostatic forces. It was till
1968 that Laskowski and Kitchener4 found that the water films of a certain film thickness on the
methylated silica surface were unstable and the wetting film would rupture spontaneously, while
both double-layer and dispersion forces were repulsive. Blake and Kitchener5 later found that the
rupture thickness of wetting film on methylated silica was 60 to 220 nm, which indicated that the
thin water film on methylated silica was unstable due to the presence of a “long-range” attractive
forces. More recently, Israelachvili and pashley6, 7 firstly measured the long-range attractive
forces (or hydrophobic forces) between two macroscopic surfaces in CTAB solution using
Surface Forces Apparatus (SFA). Other investigators8-10 also measured attractive hydrophobic
forces between two hydrophobic surfaces using Atomic Force Microscope (AFM).
The drainage and rupture of wetting film studied by Thin Film Balance (TFB) technique also
showed evidences of existence of hydrophobic forces in wetting film. Tchalivska et al.,
11investigated the wetting properties of hydrophobic mica in dodecyl ammonium chloride (DAC)
solution, and found that hydrophobic attraction forces played a vital role in thin-film lifetimes as
well as the rates of expansion of the meniscus perimeter. The papers2, 10, 12, 13 published by Yoon
et al. suggested that thinning and rupture of thin water film intervened by hydrophobic surfaces
must include the influence of hydrophobic attractive forces.
The discussion of existence of hydrophobic attraction forces on the wetting film, however, did
not turn out a well-accepted explanation. Schulze et al.,14, 15 suggested that gas bubble at
heterogeneities of solid surfaces was responsible for the rupture of wetting film on methylated
silica without considering any long-range hydrophobic attraction, yet they ignored the slight
difference on slope of kinetics of wetting film thinning. Mahnke et al.16 observed a hole in the
dimpled wetting film on hydrophobic glass surfaces coated with fatty acid Langmuir-Blodgett
layers, and they indicated that nucleation of the air bubble is the reason for the high rupture
thickness. Stckelhuber et al.,17, 18recently proposed that nanobubble on the hydrophobic solid
39 |
Virginia Tech | surface can be the cause of rupture of wetting films without considering any surface forces acting
on the interface.
In the present work, kinetics of wetting film thinning on the silica surface in C TACl solution
18
was studied using Scheludko cell19 by TFB2, 12, 13 techniques. Assuming the immobile surface at
liquid/vapor interface and no hydrodynamic pressure at the barrier rim of dimpled film, film
drainage at the barrier rim was viewed as satisfying the Reynolds lubrication theory20-22. The
result was analyzed using the Reynolds equation to determine the hydrophobic forces constant
K as function of C TACl and electrolyte (NaCl) concentration. The origin of long-range
132 18
hydrophobic forces in the wetting films was discussed.
3.2 Experimental Details
Octadecyltrimethylammonium chloride (C TACl, 97%) was obtained from TCI America
18
without any purification. Sodium chloride (99.999%, Sigma-Aldrich) was used as electrolyte. It is
further roasted in furnace at 500°C for six hours to remove the organic impurity. Milipore water
was obtained by Direct-Q 3 water purification system with the resistivity of 18.2 MΩ/cm. H SO
2 4
(98%ACS, Fisher Scientific) and H O (29-32%, Alfa Aesar) was received without any treatment.
2 2
The C TACl aqueous solution was prepared newly before each experiment to prevent the
18
adsorption of surfactants on the glassware. Polished Fused quartz (Technical Glass Product, Inc)
was boiled in a piranha solution (7:3 volume% H SO /H O ) for 1 hours. The plate is rinsed with
2 4 2 2
pure water ultrasonically for 30min, and then dried in a nitrogen gas stream.
The kinetics of film thinning between air bubble and plate is measured by Thin Film Balance
(TFB) technique developed by Scheludko and Exerowa23. The original design is to measure the
thickness of soap films between two air bubbles as function of time19, while we use this technique
to measure the film thickness of wetting film between air bubble and flat plate as function of time
in the present work. The inner radius of the film holder (R ) is 2.0 mm. The plates are placed on
c
the top of film holder in liquid prior to each experiment, to make sure that there is no observable
air bubble attached on the plate in the film holder. The whole cell is then placed on an inverted
microscopic stage (Olympus IX51). Halogen Lamp (100W, Osram) is used as light sources for
the microscope, and the band-pass filter (NT46-053, Edmund Optics) is placed after the light
sources to get the monochromic green light with center wavelength of 526 nm. The initial
thinning of wetting film above the 1000 nm is by squeezing liquid out by pistons. To capture the
changing thinning process of wetting film in several seconds, the monochromic interference
images are recorded by high speed CCD camera (Fastcam 512PCI, Photron), and from which the
changing profile of wetting film is obtained using the microinterferometric technique by
programming in Matlab.
The surface tension isotherms of C TACl solution at low concentration in absence and
18
presence of NaCl are measured using Wilhelmy-plate method. The platinum that we use in
experiment is assumed perfect hydrophilic. The surface tension of pure water that we use at room
temperature is 72.3 mN/m.
40 |
Virginia Tech | where R is the radius of film holder, σ is the surface tension of liquid, Π is the disjoining
vdW
(cid:3097) (cid:3105) (cid:3105)(cid:3035)
pressure contributed by van der Waals dispersion forces and (cid:4672)(cid:1870) (cid:4673) is the hydrodynamic
(cid:3045)(cid:3105)(cid:3045) (cid:3105)(cid:3045)
pressure term due to the local curvature of film. It is shown that the theoretical model by
Reynolds equation successfully predicts the thinning kinetics of wetting film at the rim of film
without considering any hydrodynamic pressure. The thinning rate at the center of film is slower
than that at the barrier rim of film, mainly due to the hydrodynamic repulsive pressure resisting
the thinning of film at the center.
Fig. 3.3 shows comparison of changing film profile of wetting film on the polished quartz
surface in the pure water (Fig. 3a) and in the 5x10-6 M C TACl solution (Fig. 3b) for 10 minutes
18
after film formation. Since the initial drainage of wetting film is only driven by the capillary
pressure, we set the reference time t=0 s after the “dimple” is formed. In the pure water, the
wetting film is thinning gradually and reaches the equilibrium film thickness (H ≈ 130 nm), at
e
which the disjoining pressure equates to the capillary pressure, as shown in Fig. 3a. However the
wetting film on the quartz surface in the 5x10-6 M C TACl solution for 10 min is thinning much
18
faster than those in the pure water, as shown in Fig. 3b. The thin film only takes 0.48 s to rupture
since the formation of initial “dimpled” film, while the wetting film in the pure water does not
rupture in the infinite time. The thinning of wetting film at the center of film is much slower than
that at the barrier rim of film in the 5x10-6 M C TACl solution, due to the strong attractive
18
surface forces between gas bubble and flat hydrophobic surface inducing liquid drag at the
solid/liquid interface.
Assuming no hydrodynamic pressure acting at the barrier rim of film, the film thinning is
controlled by disjoining pressure and capillary pressure, as discussed above. The comparison of
thinning curve of wetting film at the barrier rim in the pure water and in the 5x10-6 M C TACl
18
solution for 10 min is shown in Fig. 3.4. The solid line represents the theoretical prediction of
film thinning at the rim of film by Reynolds equation, which is exactly agrees with experimental
date of wetting film thinning in the pure water, while it failed to predict the wetting film drainage
in 5x10-6 M C TACl solution if not considering any attractive forces contributing to DLVO
18
theory. Thus it is necessary to propose that there is another attractive disjoining pressure causing
the faster thinning rate of wetting film. Tchalivska et al. 11 and Yoon2 suggested that hydrophobic
forces should be the driving forces for attachment of air bubbles and hydrophobic particles.
It is proposed that hydrophobic forces induce the unpredicted faster thinning kinetics of
wetting film on quartz surface in C TACl aqueous solution. Fig. 3.5 shows the kinetics curve of
18
wetting film at the barrier rim in 5x10-6 M C TACl solution for 30 min. The film radius of
18
dimpled film is 0.11 mm. The dotted line stands for the Reynolds equation prediction without
considering hydrophobic forces, while the solid line stands for the Reynolds equation prediction
corrected by the hydrophobic forces. In 5x10-6 M C TACl solution, the silica surface reaches the
18
point of ξ-potential reversal25, and thus, the electrostatic double layer forces is negligible. The
fitting hydrophobic forces constant K =3.3x10-17 J, which is two thousand times larger than
132
Hamaker constant (A =1.13x10-20 J). The deviation between experimental date and corrected
132
Reynolds prediction at the separation distance below the 200 nm is probably due to the
heterogeneous thinning of wetting film.
42 |
Virginia Tech | Fig. 3.6 shows microinterferometric images of wetting film on the silica surface in 5x10-6 M
C TACl solution before rupture to explain the heterogeneous drainage. The reference time (0 s)
18
is set for comparing the images in different time interval. As shown in Fig 3.6, there exists a
distinct point at the barrier rim of film which indicates that the film thickness at this point is much
thinner compared with surroundings. Thus the thin water film on the silica surface in C TACl
18
aqueous solution collapses at specific point of barrier ring. Different from the relatively uniform
coating of potassium amyl xanthate (PAX) on the gold due to chemical bonding between S atom
of PAX molecule and gold palte as described in previous chapter, the C TA+ ions are more likely
18
form cluster on the quartz isolated. Zhang et al. 26observed that cluster is formed on the quartz
surface in the C TACl aqueous solution by AFM. Therefore, the jump phenomenon on the
18
draining thin film is probably due to the cluster formation on the quartz surface in C TACl
18
aqueous solution.
The effect of the immersion time on the thinning rate of wetting film in 5x10-6 M C TACl
18
solution is studied, as shown in Fig. 3.7. The radius of film is around 0.115 mm, and surface
tension of aqueous solution is 66 mN/m. It is shown that the critical rupture thickness of wetting
film is nearly same for different immersion time, while the thinning rate strongly depends on the
immersion time. At the immersion time of 10 min, the kinetics of film thinning is fastest and
hydrophobic forces constant K = 3.4x10-17 J. As the immersion time increases from 10 min to
132
100 min, the thinning rate becomes slower and corresponding hydrophobic forces constant K
132
decreases to1.2x10-17 J when the immersion time is 100 min. It may be attributed to the formation
of multilayer of surfactants on the silica surface which reduces the hydrophobicity of surface.
Fig. 3.8 shows the thinning kinetics of wetting film on the silica surface in different
concentration of C TACl aqueous solution for 60 minutes. The fitting parameters to determine
18
the hydrophobic forces are shown in Table 3.1. The increase of zeta potential on the air/water
interface is due to the adsorption of C TA+ ions onto the air/water interface. The reversal of zeta-
18
potential on the solid/liquid interface above the 5x10-6 M for C TACl solution results in the
18
attractive electrostatic double layer forces. It is probably due to the flip-flop orientation of C TA+
18
surfactants on the silica surface with the positive ions toward the liquid phase. However, the total
disjoining pressure contributed from both dispersion forces and attractive electrostatic double
layer forces still fails to predict the faster drainage rate of wetting film in C TACl aqueous
18
solution. At the 5x10-6 M C TACl, the hydrophobic forces is strongest with the hydrophobic
18
forces constant K =3.5x10-17 J. At 1x10-5 M C TACl solution, the hydrophobic forces
132 18
decreases probably due to the reversal orientation of C TA+ molecules on the quartz plate, which
18
reduces the hydrophobicity of solid. At the low concentration of C TACl solution, the drainage
18
rate of wetting film is relatively slow with hydrophobic forces constant K =1x10-17 J at 2x10-6
132
M C TACl solution.
18
According to Dupre’s equation, the change in the free energy due to the replacement of the
solid-liquid interface by solid-gas interface is given by:
∆(cid:1833) (cid:3404) (cid:2011) (cid:3398)(cid:4666)(cid:2011) (cid:3397)(cid:2011) (cid:4667) (cid:4670)3.4(cid:4671)
(cid:3020)(cid:3008) (cid:3020)(cid:3013) (cid:3013)(cid:3008)
43 |
Virginia Tech | Combined with Young’s equation, the Dupre’s equation could be rewritten as follows:
Δ(cid:1833) (cid:3404) (cid:2011) (cid:4666)cos(cid:2016)(cid:3398)1(cid:4667) (cid:4670)3.5(cid:4671)
(cid:3013)(cid:3008)
It is obvious that the free energy associated with bubble-particle attachment is dependent on
contact angle on the solid surface. The higher the contact angle is, the more likely the bubble
attaches the particles. Fig. 3.9 shows the correlation between the lifetime (t ) of wetting film after
lt
the film formation and receding contact angle (θ) at various low concentration of C TACl
r 18
solution. In the present work, the liquid is sucking out due to the capillary pressure, and thus, the
drainage rate is more correlated to the receding contact angle instead of advanced contact angle.
As shown in Fig. 3.9, high contact angle relates to the short lifetime of wetting film. At 5x10-6 M
C TACl solution, receding contact angle is 66 o and film lifetime is around 0.4 s. As the C TACl
18 18
concentration increases or decreases, the lifetime of film increases while the receding contact
angle decreases. Thereby, contact angle relates to the attachment of air bubbles and particles and
following floatability of minerals.
In Fig. 3.10, the effect of electrolyte (NaCl) concentration on the kinetics of wetting film
drainage in an air-equilibrium 5x10-6 M C TACl solution is shown. The surface potential (zeta
18
potential here we used to represent the surface potential) of plate in aqueous C TACl solution
18
that used to calculate the hydrophobic constant is obtained by experiment. As the electrolyte
concentration increases, electrostatic double layer forces between air bubble and solid plate are
screened. Also the hydrophobic forces decrease with increases of electrolyte concentration. At
3x10-3 M NaCl solution, the wetting film does not rupture up to 11 s. Hydrophobic forces
constant K decreases from 2x10-17 J without electrolyte to 6x10-19 J at 3x10-3 M NaCl solution.
132
Fig. 11shows the critical film thickness and lifetime of film of wetting film in 5x10-6 M C TACl
18
solution as a function of NaCl concentration. It is shown that the critical film thickness decreases
as the electrolyte concentration increases. It is probably because both electrostatic double layer
forces and hydrophobic forces decrease with increasing the electrolyte concentration. Thus the
only driving forces for wetting film thinning is capillary pressure, which is not enough to
introduce the surface wave to induce the rupture of wetting film.
3.4 Conclusion
Reynolds equation is illustrated to predict the thinning kinetics of wetting film at the barrier
ring of film. By assuming negligible influence from the slippage on the solid/liquid interface, the
kinetics curve of wetting film drainage on hydrophobic forces is fitted by Reynolds equation
corrected by considering the hydrophobic forces.
Film profile on the hydrophilic surface and on the hydrophobic surface is compared.
Wetting film on the hydrophilic surface is thinning gradually and stabilizes at certain film
thickness, while wetting film on the hydrophobic surface ruptures spontaneously with large
dimple shape due to the strong attractive forces. The rupture of wetting film on the silica surface
in C TACl aqueous solution is heterogeneous, probably because of the cluster formation of
18
C TA+ cationic surfactants on silica surface.
18
44 |
Virginia Tech | Chapter 4
Conclusion and Future work
4.1 Conclusion
In the present work, the drainage of wetting film on the flat hydrophobic surface
hydrophobized by ex-site adsorption of potassium amyl xanthate (PAX) on gold surface and in-
site adsorption of Octadecyltrimethylammonium chloride (C TACl) on the silica surface is
18
investigated by Thin Film Balance technique. The major findings of the present work are
discussed as follows:
(1) Reynolds equation is illustrated to successfully predict the thinning kinetics of wetting
film at the barrier ring on the hydrophilic silica surface. By assuming negligible
influence from the slippage on the solid/liquid interface, the kinetics curve of wetting
film drainage on hydrophobic forces is fitted by Reynolds equation corrected by
considering the hydrophobic forces in DLVO theory. Long-range hydrophobic forces
are responsible for fast drainage of wetting film on and hydrophobic surface.
(2) The film profile of wetting film on the hydrophilic surface is substantially different from
that on the hydrophobic surface. Wetting film on the hydrophilic surface is thinning
gradually and stabilized at certain film thickness, while wetting film on the hydrophobic
surface ruptures spontaneously with large dimple shape due to the strong attractive
forces. The changing film profile on PAX-coated gold surface is symmetric due to the
uniform coating of PAX on gold surface. The rupture of wetting film on the silica
surface in C TACl aqueous solution is heterogeneous, probably because of the cluster
18
formation of C TA+ cationic surfactants on silica surface.
18
(3) The results obtained in the present work shows that the thinning kinetics of wetting film
on the hydrophobic surface is strongly dependent on collector concentration and
immersion time. The calculated hydrophobic forces constant K is correlated to
132
contact angle, which also suggests that the hydrophobic forces are corresponding to the
thermodynamic condition for bubble-particle attachment. The presence of electrolyte in
solution diminishes the hydrophobic forces between the air bubble and the hydrophobic
plates.
(4) The combing rule for determining K for bubble-particle interaction is firstly
132
illustrated experimentally using the TFB technique. The hydrophobic forces between air
bubbles K in the pure water is extrapolated to the 5.3x10-17 J, which is a little larger
232
than the results we reported previous. It suggests that the air bubble is most hydrophobic
substance due to the high interfacial tension.
54 |
Virginia Tech | 4.2 Future Work
The main objective of present work is to measure the thinning kinetics of wetting film on the
hydrophobic surfaces, and to verify the combining rule for flotation. The future work is focus on
as follows.
(1) The thinning kinetics of wetting film at the barrier ring in the present work is illustrated
to satisfy the Reynolds lubrication approximation. The future work is to predict the whole
film profile of wetting film on the hydrophobic surface including the effect from the
hydrodynamic forces. Also the effect of slippage on the drainage of wetting film on the
hydrophobic surface will be discussed.
(2) In the present work, K determined from the drainage of wetting film on the gold
132
hydrophobized by ex-site adsorption of PAX is used to compare with K determined
131
using AFM to verify the combining rule. The future work is to investigate the drainage of
wetting film on the sulfide mineral surface, which is more related to the real practical
flotation. The combining rule needs to be further verified in sulfide mineral flotation and
possible theoretical explanation will be discussed.
55 |
Virginia Tech | AN INVESTIGATION OF THE GAS DISPERSION PROPERTIES OF
MECHANICAL FLOTATION CELLS: AN IN-SITU APPROACH
by
Sanja Miskovic
ABSTRACT
Bubble size is considered to be one of the most important parameters affecting the
performance of froth flotation cells. However, monitoring, controlling and predicting
bubble size is a very challenging task. This dissertation presents results obtained from a
comprehensive pilot- and industrial-scale experimental investigation of gas dispersion
performance of two commercially available flotation cells. To facilitate this investigation,
a continuous pilot-scale flotation system was developed and tested. The results of the
hydrodynamic and metallurgical testing conducted on the pilot-scale flotation circuit are
presented. In addition, an assessment of the impact of two commercially available
rotor/stator mechanism designs on bubble generation was performed under non-
coalescing conditions. Based on obtained results, the mechanisms of gas dispersion
throughout the flotation cell and gas cavity formation behind the impeller blades have
been presented and discussed.
A new in-situ optical bubble sampling method was also developed as part of this
investigation. The new system allowed an accurate estimation of local bubble sizes and
determination of overall gas dispersion patterns within the cell. The new method was
compared to the existing ex-situ bubble sampling method commonly used in industry.
Two image analysis techniques were also evaluated, i.e., a template matching
BubbleSEdit technique and the edge detection Northern Eclipse technique. Significant
variations in bubble size as a function of the sampling method, sampling location,
operating condition, machine type and image analysis method were observed. Generally,
bubbles observed with the in-situ sampling method appeared to be larger than bubbles
recorded with the ex-situ method. Furthermore, the mean bubble size determined by the
Northern Eclipse bubble sizing method was smaller than the BubbleSEdit value. The
experimental tests also revealed that sampling location had a strong effect on measured
local mean bubble size and bubble size distribution in both vertical and horizontal
directions. In addition, aeration rate was found to have a profound impact on the gas
dispersion pattern in the cell and on local bubble size. Agitation rate also had a significant
effect on bubble size, although the degree of impact strongly depended on the agitation
level, chemical conditions in the cell and the machine type. |
Virginia Tech | ACKNOWLEDGEMENTS
I wish to thank my advisor, Dr. Gerald Luttrell, for his encouragement and
guidance throughout the course of this work. His continuous support helped me
overcome many difficult moments.
Also, I want to express my greatest admiration and sincere gratitude towards Dr.
Roe-Hoan Yoon. His visions and profound way of thinking have always amazed me and
his clear ideas contributed immensely to this work. Further, I would like to thank to Dr.
Greg Adel for his teaching, support, and patience during my studies at Virginia Tech.
Also, I would like to thank to Dr. Dariusz Lelinski and Bartosz Dabrowski for
serving on my committee and for their sincere friendship and great support. Many thanks
go to Dr. Kray Luxbacher, Dr. Emily Sarver, Dr. Serhat Keles, and Dr. Kerem Eraydin
for their friendship.
I want to acknowledge the FLSmidth Minerals for funding my research and for
providing me with the wonderful equipment and instrumentation.
This research would not have been possible without the great help of my dear
friends Mr. James Waddell and Mr. Robert Bratton. I would like to thank them for their
help, encouragement and support on numerous occasions. Also, I wish to express my
appreciation to Ali Zulfiqar and Brad Kelley for their assistance throughout the course of
this work.
Finally, I am grateful to my brother and father for their continuous support and
care for all these years. Above all, I wholeheartedly thank my husband Ilija for his
unconditional love and patience and my daughter Marija for being such a good girl.
iv |
Virginia Tech | CHAPTER 1:
INTRODUCTION
The importance of bubble size on flotation efficiency has been long recognized.
Using high-speed cinematography in his experiments (Bennett, 1958) concluded that, for
a constant air supply rate, flotation rate increases by reducing the bubble size and
increasing the number of bubbles. Recent intensification in research efforts to better
understand gas dispersion and hydrodynamics in flotation cells has come about because
of the growing need to design larger and more efficient flotation cells to treat the lower
grade and more finely disseminated ores that are currently being mined (Sawyerr et al.,
1998). Therefore, among hydrodynamic parameters, gas dispersion is considered to be
the key. In this context, gas dispersion is defined as the dispersion of air into bubbles. It is
well documented that the gas dispersion properties in the flotation process have a direct
effect on the process performance (Schwarz and Alexander, 2006).
Accurate data about gas dispersion are required for understanding of the physical
processes that govern the flotation. Among all gas dispersion parameters, the bubble size
and the bubble size distribution are the most important. Bubble size governs the surface
area over which solid particles and bubbles interact, which contributes significantly to
system hydrodynamics and overall flotation performance. Local bubble size and bubble
size distribution in the flotation cell strongly depends on various operational, technical,
and chemical factors whose effects on bubble size should be taken into account while
designing or modeling a flotation process.
1 |
Virginia Tech | Turbulent flotation models developed to date cannot predict bubble size in the
flotation system from commonly measured flotation parameters such as pulp surface
tension, aeration rate, energy input, particle size, and particle surface characteristics. Due
to this limitation, the bubble size and bubble size distribution must be obtained
experimentally and subsequently used as an input for current flotation models. On the
other hand, bubble sizing in the pulp phase is difficult because of the high concentration
of bubbles and solid particles in standard flotation cells (Nelson and Lelinski, 2000). The
sizing technique must be robust and rugged to withstand the environmental conditions
wherever it might be installed. This is especially important if equipment has to be
deployed in industrial environments, where erosive/corrosive conditions are present and
flotation cells may be dusty and vibrating and difficult to access.
There are many bubble sizing systems currently available, most of which are
design to measure bubble size in two-phase laboratory conditions. Only few bubble
sizing methods have been successfully employed in real industrial settings. Although they
are typically very easy to operate (bubble sample is drawn from the top, quiescent zone of
the cell to the external viewing box where bubbles are viewed) the results obtained are
not particularly reliable. Only few studies on spatial distribution of bubble sizes in the
stirred vessels have been published so far. On the other hand, a large amount of data is
necessary for the successful assessment, support, and validation of the current and future
models. Therefore, there is a great necessity for a rugged, reliable, and efficient bubble
sampling system that can be used for bubble sizing in different regions of flotation cell.
The gas-liquid hydrodynamics in the system will also strongly depend on the type of
bubble generator used, so the choice of a proper impeller/stator assembly to satisfy the
2 |
Virginia Tech | necessity of optimal gas dispersion is the key for the success and economy of the process.
However, the mechanism of bubble generation in flotation systems has not yet been
explored in depth and the differences between the bubble generation mechanisms of
different flotation cells have not yet been well addressed in the literature.
1.1. OBJECTIVES
The main objective of this dissertation is to generate a better understanding of gas
dispersion properties of different mechanical flotation cells. Also, the mechanisms
affecting and controlling bubble size, and thereby the phenomena of bubble generation in
different mechanical flotation cells, have been investigated. Specifically, this study
primarily deals with the effect of hydrodynamic variables on bubble size in pilot-scale
flotation cells, although some measurements were also performed on full-scale industrial
machines. The results of this study provides ample data necessary to support and validate
current flotation models, which are relevant to the design, scale-up, optimization and
control of mechanically agitated flotation cells.
The main goals of this research are:
to design and construct a new in-situ bubble sizing method for accurate
measuring of gas dispersion properties in pilot-scale flotation cells;
to compare the performance of the new in-situ method with another
commercially available bubble sizing method;
to determine operating limits of the new system in both two- and three-
phase flotation environments;
3 |
Virginia Tech | to design and construct a new, automated, modular, pilot-scale flotation
circuit, which can accommodate different impeller/stator mechanisms and
allow continuous testing of multiple process parameters while the system
is operated as a batch reactor or continuously;
to use developed systems to study gas dispersion properties of different
mechanical flotation cells over various operating conditions;
to investigate the effect of sampling location, aeration rate, agitation rate
and image analysis technique on estimated bubbles size;
to study gas dispersion efficiency of different mechanical flotation cells
(forced-aerated vs. self-aerated flotation systems);
to evaluate and characterize bubble generation mechanisms of different
rotor/stator mechanisms;
to perform hydrodynamic and metallurgical performance investigation of
the pilot-scale flotation cell; and
to provide data for validation and support of current flotation models.
1.2. OUTLINE
This dissertation is composed of three papers, which have been published or
submitted to a peer-reviewed journal or are ready for submittal (Chapters 3 to 5).
A literature review pertaining to fundamental concepts of the flotation process are
given in the Chapter 2. Also included in the Chapter 2 is the overview of the current
research on bubble formation, gas dispersion and bubble size measurement techniques.
4 |
Virginia Tech | Chapter 3, A New Modular Pilot-Scale Setup for Hydrodynamic and
Metallurgical Flotation Performance Evaluation has been presented during the Flotation
’11 Conference, Cape Town, South Africa, and is to be submitted for a review for the
special issue of the Minerals Engineering by December 2011. Dr. Gerald Luttrell and Mr.
Robert Bratton served as co-authors in this work, and are acknowledged as such at the
beginning of the chapter. This chapter also presents details of the pilot-scale flotation
circuit design and describes results obtained during hydrodynamic and metallurgical
investigation of the pilot-scale flotation cell.
Chapter 4, Comparison of Two Bubble Sizing Methods for Performance
Evaluation of Mechanical Flotation Cells has been presented during the Roe-Hoan Yoon
International Symposium on Advanced Separation Processes and Resource Engineering,
SME Annual Meeting, 2011, Denver, Colorado, and is published as a part of the
conference proceedings. Dr. Gerald Luttrell also served as co-author in this work. This
chapter presents details of the new in-situ bubble sizing system design and presents the
results of detailed investigation of effects of bubble sampling method, sampling location,
operating conditions, and image analysis technique on estimated bubble size.
Chapter 5, Comparison of gas dispersion mechanisms for forced-air and self-
aerated mechanical flotation cells has also been presented during the Flotation ’11
Conference, Cape Town, South Africa, and is to be submitted for a review for the special
issue of the Minerals Engineering by the December 2011. Dr. Gerald Luttrell, Dr. Saad
Ragab, and Mr. Hassan Elhady Fayed served as co-authors in this work. Gas dispersion
patterns within two different mechanical flotation cells are presented in this chapter.
5 |
Virginia Tech | CHAPTER 2:
LITERATURE REVIEW
2.1. HISTORY OF FLOTATION
Flotation is the most widely used separation process in the mineral processing
industry today. The importance of flotation technology in the global economy is
significant. A rough estimate of the quantity of crushed ore treated by flotation is about
nine billion tons per year, and the portion of base metals processed using this method is
approximately 95% (Brewis, 1996).
The idea of flotation dates back to 1860 when William Haynes claimed that fine
sulfide ore could be agglomerated by oil and separated from the gangue material by
washing (Fuerstenau et al., 2007). Even though Haynes’s idea had no known commercial
application at the time, his process, originally named bulk-oil flotation, is considered to
be the first patent in the field of flotation. The first commercial flotation process was
designed and successfully tested by Adolf Bessell in his factory in Dresden, Germany, in
the late 1860s (Lynch, 2010).
Today flotation is used for separation of almost all sulfide and many non-sulfide
metallic minerals, industrial minerals, and energy minerals such as coal and bitumen.
Though mainly used in the mineral processing industry, the flotation process has also
been used in other industrial fields such as wastewater treatment and paper recycling, for
the removal of organic contaminants from effluents in the diary and beer industry, and for
remediation of contaminated soil (Brewis, 1991).
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Virginia Tech | 2.2. MACROSCOPIC DESCRIPTION OF FLOTATION PROCESS
Froth flotation is a complex physico-chemical process that utilizes natural and
induced hydrophobicity to separate and collect valuable mineral particles from slurry
(Malati, 1984). In flotation, hydrophobic minerals suspended in the aqueous phase are
collected by air bubbles from a solid-liquid suspension, as illustrated in the Figure 2.1.
Due to bubble buoyancy, bubble-particle aggregates are transported from the pulp to the
top of the flotation cell where they accumulate as froth. Accumulated froth is removed
and valuable mineral concentrate is recovered. The unattached hydrophilic particles
remain in the pulp, and are either discarded or reprocessed separately. Flotation is,
therefore, a heterogeneous, multiphase, and multi-component separation process.
Hydrophobic
Air Bubbles
Particles
Hydrophilic
Air Bubbles Particles
Figure 2.1. Selective attachments of hydrophobic particles to air bubbles.
Efficiency of the flotation process is directly related to the number of collisions
between particles and bubbles, which are strongly dependent on the ratio of particle
diameter to bubble diameter. In a flotation system where bubbles are much larger than
particles, a flow streamlines around the bubble sweep particles near the bubble surface
and prevents attachment of valuable mineral particles to the bubble. Hence, in order to
8 |
Virginia Tech | provide optimal conditions for the flotation, it is necessary to generate bubbles with sizes
similar to the size distribution of particles in the pulp.
Prior to the flotation stage, all crushed and ground material is conditioned with
various reagents, including collectors, frothers, regulators (activators, pH regulators, and
depressants), and other surface modifying agents. The role of collectors is to form a
hydrophobic surface film on a given mineral and to increase its hydrophobic affinity, thus
allowing better conditions for recovery of the processed material by attaching valuable
particles to air bubbles. Frothers are surface-active chemicals used to reduce water
surface tension, enabling generation of smaller bubbles and formation of a stable froth
phase. The main purpose of regulators is to alter the action of the collector and enable
adsorption of the collector on targeted particles (Bulatovic, 2007).
The three distinct zones within a flotation cell are the turbulent zone, quiescent
zone, and the froth zone, as shown in Figure 2.2. The rotating action of the impeller in the
turbulent zone (Zone I) provides the energy necessary to keep particles in suspension,
enables the generation of small bubbles, and maintains the hydrodynamic conditions
needed for efficient bubble-particle interaction. The second zone (Zone II) is the
quiescent zone. This region is less energy intensive than the turbulent zone, and provides
conditions for detaching entrained or entrapped gangue particles from created aggregates.
This zone also helps maintain a quiescent pulp-froth interface, which stabilizes the froth
phase. The froth phase (Zone III) is the upper cleaning zone of the process.
There are three major processes that can be identified within the froth zone of the
flotation cell. Generated dense bubble-particle aggregates are carried vertically from the
pulp-froth to the air-froth interface and horizontally toward the lip of the flotation cell,
9 |
Virginia Tech | simultaneously. For optimal flotation of large, coarse particles, the specific power input
should be kept at the lowest level necessary to keep particles in suspension. On the other
hand, a much higher power input is required for fine particles (Schubert, 1999).
2.3. FLOTATION EQUIPMENT
There are four main types of flotation cells used in the mineral processing
industry: mechanical flotation cells, pneumatic flotation cells, froth separators, and
flotation columns.
Based on the method of air introduction, flotation equipment can also be divided
into the following flotation groups: mechanical, pneumatic, dissolved air, vacuum, and
electroflotation (Brewis, 1991; Brewis, 1996; Young, 1982). Bubbles are generated and
dispersed by forced introduction of the air through a deeply submerged rotating impeller
(forced-air mechanical cells), by self-aeration of shallow rotating impellers (self-aerated
mechanical cells), by self-aeration through an orifice (Jameson cell) (Evans et al., 1992);
by various spargers (flotation columns), and by parallel introduction of air and slurry
through an in-line mixer (Microcel) (Yoon, 1987).
From the beginning, mechanical flotation cells have been the most widely used
flotation cells in the mineral industry. Mechanical flotation cells consist of a tank,
typically cylindrical shaped, fitted with an impeller drive assembly, and a stator. A main
function of the stator, which is positioned around the impeller, is to transform tangential
flow of the pulp in the cell in the radial direction. The impeller, on the other hand,
provides the energy necessary for successful flotation operation and is therefore
considered to be the heart of the flotation cell. Bubbles are generated and dispersed by
12 |
Virginia Tech | forced introduction of the air through a deeply submerged rotating impeller in forced-air
mechanical cells and by self-aeration of shallow rotating impellers in self-aerated
mechanical cells.
Schematic representation of the two main types of mechanical flotation cells is
shown in Figure 1.4. In the forced-aerated cell (Figure 2.4.a), the agitator mechanism is
typically positioned at the bottom, but sometimes in the center, of the cell (Lelinski,
2005). As shown in Figure 2.4.b, the agitator mechanism in self-aerated cells is located
near the top of the cell. For both cell types, the impeller/stator assembly has to be
designed and installed so as to allow re-circulation of pulp through the agitator zone in
order to keep particles in a suspension and to provide good conditions for bubble-particle
interaction (Yianatos, 2007).
a) b)
Figure 2.4. Two basic types of conventional flotation cells with flow patterns: a) Forced-
aerated cell; b) Self-aerated cell. Red zone – high intensity turbulent zone (after
(Yianatos, 2007)).
Most of the mechanical flotation cells used in the mineral processing industry
today are manufactured and sold by three leading suppliers of mineral processing
13 |
Virginia Tech | equipment: FLSmidth Dorr-Oliver Eimco (Dorr-Oliver, WEMCO, XCell), Outokumpu
(OK FreeFlow, OK Multi-Mix, FloatForce™), and Metso (RCS, DR).
The main goal in the process of designing of any flotation cell is to maximize gas-
liquid interface in the pulp (particle-water-air mixture) and hence to increase the
probability of collisions between air bubbles and hydrophobic particles. Furthermore,
every flotation cell should be designed and built to provide all of the following
performance functions:
to generate adequate turbulent conditions for successful bubble-particle
attachment in the contact zone,
to allow sufficient solids suspension,
to perform efficient gas dispersion,
to allow unhindered particle transfer from the pulp to the froth zone,
to allow proper froth removal, and
to provide optimal retention time for all three phases (gas, liquid, and solid)
necessary for achieving maximal material recovery. (Lelinski, 2005).
The total energy introduced by mechanical agitation is, therefore, spent to
perform three main functions: particle suspension and transport, gas breaking into
bubbles and their dispersing throughout the flotation cell, and generation of micro-
turbulences necessary to facilitate bubble-particle collisions (Figure 2.5).
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Virginia Tech | 2.4. FLOTATION CIRCUITS
Slurry is a water mixture of particles of different composition, size, shape, and
density. Due to the complex nature of the slurry, the most efficient and selective way to
separate valuable minerals from slurry is to arrange individual flotation cells in series, or
banks. In this way, both residence time of particles and the number of bubble –particle
collisions in the system are increased. Typical residence time for particles in a bank of
cells ranges from 5 to 15 min. (Wills, 2006).
To achieve better grades of recovered concentrate from a single stage flotation
circuit, re-floating is required in one (cleaner) or more (recleaner) additional stages. A
series of cells producing a primary concentrate is called the rougher stage. The process of
retreatment of the rougher tailings is called a scavenging stage. In order to reduce
entrainment in the froth and recover only high grade particles, pulp in the cleaner stage is
treated with lower reagent concentrations and generally has lower density. In order to
maximize the recovery of valuable minerals, higher dosages of reagents and longer
residence time are needed during the scavenger stage of the process. Mass flow rate and
material properties through the flotation circuit are major factors determining the number
and size of flotation cells that need to be installed in a processing plant (Gupta and Yan,
2006). Several examples of flotation circuits are presented in Figure 2.6.
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Virginia Tech | 2.5. FLOTATION SCALE-UP AND DIMENSIONLESS NUMBERS
Only recently were the basic microscopic processes of flotation and development
of scale-up procedures necessary for successful design and operation of full-scale
industrial cells from the lab- and pilot-scale data identified (Schubert and Bischofberger,
1998).
Flotation is governed by a number of different process variables that can be
classified into three general groups, as shown in Figure 2.7: chemical, operational, and
cell factors. (Harris, 1976; Smar et al., 1994). In the past, the role of cell variables has
received less attention than chemical factors, even though they are a vital part of the
flotation process.
Dimensionless numbers are often used to quantify the effect of different cell
factors on metallurgical performance such as grade and recovery. Brandeer (Brander,
1993), claims that the appropriate application of dimensional similitude can lead to the
discovery of forgotten or excluded variables during the scale-up process.
The advantage of using dimensionless numbers is reflected in the following
(Ruzicka 2008):
a) dimensionless numbers reduce the number of variables needed to describe the
process, simplifying the correlation of the experimental data;
b) dimensionless numbers allow simplification of the governing equations;
c) dimensionless numbers provide valuable scale estimates of key physical
quantities;
d) dimensionless numbers contribute to the physical understanding of certain
phenomena since they typically have a clear physical interpretation.
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Virginia Tech | defines a critical ratio between the
Air flow (cid:1843) aeration rate and the impeller pumping
(cid:1843) (cid:3404) 0.01 - 0.25
number (cid:3039) (cid:1840)(cid:1830)(cid:2871) rate which should be independent of
cell size
where: N - impeller speed; D – impeller diameter; Q – volumetric air flow rate; P – net power
input; ρ - slurry density; g - gravitational constant; γ - surface tension; µ - slurry viscosity.
f
After many years of research there is no general agreement on how to correlate
dimensionless numbers with overall flotation scale-up process(es), and each equipment
manufacturer emphasizes different aspects of the scale-up procedure and uses those
arbitrarily for flotation cell design and scale-up (Yianatos, 2007).
Despite the great advances of general flotation process knowledge, the
mechanisms, design, and scale-up of industrial flotation cells are still not fully understood
and developed. Due to the complexity and multifaceted nature of the problem,
development of a comprehensive theoretical model is required, which would include both
hydrodynamic and chemical factors and provide a reliable scale-up approach.
2.6. FLOTATION KINETICS AND MODELING
Flotation is a process which occurs in time and its results are strongly determined
by a series of random effects and factors. Unlike any other separation process, increased
duration of the separation process does not necessarily improve the metallurgical
performance. Increase in bubble-particle interaction time typically increases the recovery
of the valuable mineral but leads to product grade deterioration.
A stable attachment between a particle and a bubble is formed when a large
enough kinetic energy of colliding species is present at the moment of their collision. On
the one hand, if the kinetic energy exceeds the potential energy of the bubble-particle
21 |
Virginia Tech | interaction, it can result in particle detachment from the bubble. Both the particle-bubble
collisions and particle kinetic energy are random. The higher probability of bubble-
particle connection, the faster is the flotation process. Additionally, the kinetics of the
flotation process depicts not only the statistical character of the phenomena on the phase
boundaries, but also depends on the continuous inflow of free surface into the flotation
system. The fresh surface that continuously enters the flotation system comes both in the
forms of fresh mineral particles (slurry feed) and continuously generated air bubbles.
As a result of the analogy between the bubble mineralization occurring during the
flotation process and the chemical reaction, flotation kinetics is typically described with
the equation for the kinetics of chemical reaction. Zuniga was the first author to describe
the kinetics of batch flotation by using of the differential equation for the kinetics of
chemical reaction (Zuniga, 1935). After Zuniga, many other authors worked on the
problem of the flotation kinetics (Beloglazov, 1939; Bushell, 1962; Gaudin et al., 1942;
Gorain et al., 1998a; Lazić and Ćalić, 2000; Sutherland, 1948; Szatkowski, 1987; Volin,
1964; Yianatos, 2007).
The general form of n-order differential equations describing the kinetics of the
flotation process is (Derjaguin and Dukhin, 1961; Sutherland, 1948):
(cid:1856)(cid:1840)
(cid:2869) (cid:3404) (cid:3398)(cid:1863)(cid:1840)(cid:3041) (Eq. 2.1)
(cid:1856)(cid:1872) (cid:2869)
where N is a concentration of floatable particles remaining in the flotation chamber up to
1
the moment t; k is the flotation rate constant; and n is a constant characterizing the order
of flotation kinetics. The flotation rate constant, k, is a macroscopic parameter containing
information about the factors affecting the process. Flotation rate depends on such factors
22 |
Virginia Tech | as particle composition, size, surface properties, and reagent adsorption. Equation 2.1
describes the flotation kinetics of particles homogeneous in their surface properties that
possess the same value of the flotation rate constant. Consequently, each floatable
component may be represented by its continuous flotation rate (Polat and Chander, 2000).
Assuming identical chemical environments, the variable characteristics of this set
of distributions during scale-up can be attributed to the differences in aeration and
hydrodynamics between cells of different scale.
It is widely recognized that accuracy of the flotation kinetic model strongly
depends on the initial assumptions for the mixing conditions in the cell (Harris, 1978;
Yianatos, 2007). First order kinetics, originally introduced by Gaudin and Schuhmann
(Gaudin et al., 1942) and elaborated by Garcia-Zuniga (Garcia-Zuniga, 1970), has been
used extensively in the past. It is based on the assumption that the bubble concentration in
the pulp remains constant (Sutherland, 1948).
Therefore, a solution of Equation 2.1 for n=1 and plug-flow reactor design is
given as follows:
(cid:1844) (cid:3404) 1(cid:3398)(cid:1857)(cid:2879)(cid:3038)(cid:3047) (Eq. 2.2)
where R represents the fractional recovery of the floatable species; and t is mean
residence time of particles in the cell. This model provides a simplistic way for fractional
recovery calculation of particles in the froth phase of the flotation system (Moys, 1978).
Koh and Schwarz in their recent work (Koh and Schwarz, 2003; Koh and Schwarz, 2006)
23 |
Virginia Tech | of the successful transfer of bubble-particle aggregates to the froth phase (Do, 2010).
Probabilities from Eq. 8 can be easily estimated by knowing several basic hydrodynamic
and surface chemistry parameters for a given system. Some of these properties include
particle size, density, zeta potential (a function of pH), contact angle (a function of
mineral type and collector dosage), surface tension of the liquid phase (a function of
frother concentration), pulp viscosity, and energy dissipation rate. This newly developed
model was found to successfully simulate flotation results reported in the literature in
both laboratory and industry (Do, 2010).
Computational Fluid Dynamics (CFD) modeling is another way to model the
flotation process, and it is particularly useful for simulation of flotation systems in a state
of local dynamic equilibrium between attachment and detachment processes (Koh and
Schwarz, 2003). CFD modeling allows modeling of transport processes of free and
attached particles in the flotation cell by combining source-sink balance equations with
fundamental multi-phase flow equations.
For a flotation cell of known geometry and operating conditions, development of
scale-up simulation from first principles is feasible when dependency between attachment
and detachment rates and physical parameters are known (Koh and Schwarz, 2008). Koh
and Schwarz found that the limiting factor is often not the collision or attachment rate,
but insufficient bubble surface area for the attachment of all valuable particles present in
the pulp.
26 |
Virginia Tech | 2.7. HYDRODYNAMIC CHARACTERIZATION
As can be concluded from the previous section, any flotation process could be
successfully predicted provided that fundamental chemical properties of the system and
hydrodynamic conditions in the cell are known. Two of the most critical hydrodynamic
properties of any flotation system are power input (or energy dissipation) and bubble size
(or bubble size distribution).
2.7.1. Power consumption
Experimental determination of the spatial distribution of energy dissipation of
three phase flotation systems proved to be a very challenging task (Yang, October 6-9,
2007). Several methods of flow velocity measurement of highly turbulent fluid flows
have been noted in the literature, some of them being the Hot-Wire Anemometry Method,
Electrochemical Method (Rubinstein, 1995), Laser-Doppler Velocimetry Method
(Tiitinen, 2003), Particle Image Velocimetry Method (Brady et al., 2006; Zachos et al.,
1996), and Multi-Hole Probe Method (Telionis, 2009). In general, most of the methods
listed previously cannot accurately quantity fluid fields in the pulp with particle
concentration higher than 10% .Even though energy dissipation varies throughout the
flotation cell, the mean value of energy dissipation has been typically used for the
evaluation of the flotation performance and as an input for the most recently developed
flotation models (Do, 2010).
Newell and Grano conducted an experimental analysis of the influence of energy
dissipation in the cell on the undistributed flotation rate constant for a given size fraction.
For laboratory and pilot scale flotation systems, they have found that the N3D product,
27 |
Virginia Tech | which describes energy dissipation, can be used as a good flotation scale-up criterion. N
value in the product represents a rotational speed of the impeller and D is an impeller
diameter (Newell and Grano, 2006).
A number of researchers performed extensive studies on the effect of
hydrodynamics, specifically power consumption, on the flotation process (Oyama, 1955),
(Arbiter, 1965), (Arbiter et al., 1976), (Harris et al., 1983) and (Harris and Khandrika,
1985b). In their research they were considering the following variables: tank diameter,
impeller diameter, liquid depth, distance of the impeller from the tank bottom, length and
width of impeller blades, width of baffles, and size of solid particles. Flotation systems
were described by dimensionless groups.
Arbiter 1965 found a decrease of aerated power consumption to non-aerated
power consumption ratio with an increase of Air flow number. Based on Oyama and
Endoh, the decrease in the power consumption in air-liquid systems is due to the lower
density of the air-liquid mixture. However, the Power number calculated from the
apparent density of the composite mixture was found to be higher than expected if the air
were evenly dispersed throughout the system (Oyama, 1955).
Arbiter concluded that the air-liquid mixture in the vessel was not homogeneous,
and in particular that the density in the zone around the impeller was lower than overall
average density. One explanation for this phenomenon is a diminishing air concentration
gradient of the air-liquid stream, flowing radially outwards from the impeller, with the
distance from the impeller. Another mechanism could be the air re-entrainment, which is
specific to the impeller-stator agitating mechanisms of standard conventional flotation
28 |
Virginia Tech | cells. For mixers operating without vortexing in the fully turbulent regime, the power
consumption is directly proportional to the liquid density:
(cid:1842) (cid:3404) (cid:1840) (cid:2025) (cid:1840)(cid:2871)(cid:1830)(cid:2873) (Eq. 2.10)
(cid:3043) (cid:3039)
where P is the overall power consumption, ρ is liquid density, N is impeller rotational
l
speed, and D is impeller diameter.
Arbitrer 1968 found that, at fixed impeller speed, increase of impeller
submergence of self-aerated flotation cells leads to increased aeration rate (Arbitrer et al.
1968). Experiments were conducted on a Fagergren laboratory flotation cell. For the
same cell, he also found an increase of aeration rate with an increase of tank diameter to
impeller diameter ratio. This relationship is attributed to a lower proportion of fresh air
being drawn in the impeller zone, since more air is being recirculated in the larger tank.
Also, in the same study, Arbitrer explored the difference in impeller blade design on
power consumption. A wedged shaped impeller had a Power number twice that of an
impeller with round posts.
Harris 1985 explained the increase of a degree of self-aspiration with the increase
in impeller speed by the following proportion (Harris and Khandrika, 1985a):
(cid:1827)(cid:1861)(cid:1870) (cid:1871)(cid:1873)(cid:1855)(cid:1872)(cid:1861)(cid:1867)(cid:1866) (cid:1503) (cid:1840)(cid:2870) (Eq. 2.11)
For self-aerated cells, a decrease in the power consumption was also found with
the addition of the frother. It is known that frother addition reduces surface tension of the
liquid phase and, in that way, enhances generation of smaller bubbles. Smaller bubbles
are more readily entrained in the water and the fraction of recycled air increases.
Therefore, one part of the air dispersed by the impeller is returned to the impeller zone by
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Virginia Tech | the flow circulation that reduces the overall capacity of impeller to entrain fresh air into
this zone. This consequently reduces the density in the impeller zone and lowers power
consumption.
2.7.2. Gas dispersion
Among the hydrodynamic parameters, gas dispersion is considered to be the key.
The intensification in research efforts to better understand gas dispersion and
hydrodynamics in flotation cells has come about because of the growing need to design
larger and more efficient flotation cells to treat the lower grade and more finely
disseminated ores that are currently being mined (Sawyerr et al., 1998).
In this context, gas dispersion is defined as the dispersion of air into bubbles. It is
well documented that the gas dispersion properties (e.g. bubble size distribution) in the
flotation process have a direct influence on flotation performance (Schwarz and
Alexander, 2006). This is understandable since the amount of created gas-liquid
interfacial area affects particle collection kinetics.
Pursuing this notion, Gorain found that the flotation rate constant was not readily
related to bubble size, gas holdup, or gas rate individually, but it was related to bubble
surface area flux (Gorain et al., 1996). Bubble surface area flux is defined as the surface
area of bubbles per unit time per unit cross-sectional area of a flotation cell.
2.7.3. Main variables for gas dispersion characterization
In the figure below (Figure 1.8), typical parameters defining gas phase flow in the
flotation system are presented and described briefly.
30 |
Virginia Tech | Bubble size distribution is an important factor determining how well air is
dispersed in a liquid phase. The Sauter mean diameter (D or D ) has been commonly
b 32
used to describe the size of bubble population. The typical bubble size in flotation ranges
from 0.5 to 2.5 mm (Gorain et al., 1995b).
Mean bubble size is usually used to describe a flotation system with a large
number of bubbles of different sizes and can, in general form, be expressed as:
For: Name:
pk=10 Mean number diameter
(cid:3291)(cid:3127)(cid:3286)
∑(cid:3037) (cid:3037)(cid:2880) (cid:2880)(cid:3041)
(cid:2869)D
(cid:2920)(cid:2926) pk=20 Root mean square diameter
(Eq. 2.12)
D (cid:3043)(cid:3038) (cid:3404) (cid:3497) ∑(cid:3037)(cid:2880)(cid:3041) D(cid:2921) pk=30 Mean volume diameter
(cid:3037)(cid:2880)(cid:2869) (cid:2920)
pk=32 Sauter diameter
pk=43 Mean mass diameter
where n is the number of bubbles in the size class i, D is a bubble diameter of certain
i i
bubble size class, f is a volumetric fraction of the size class i. Similarly, n is the number
i
of all bubbles analyzed in an image (sample size), D is measured equivalent bubble
j
diameter, f is a volumetric fraction of a measured bubble j.
j
Frothers have a pronounced impact on reducing bubble size up to a certain
concentration, above which further addition of frother appears to have no effect (Finch,
1990). A decrease in coalescence is the accepted explanation of the decrease in bubble
size with increasing frother concentration. After a certain concentration, which has
recently been referred to as the critical coalescence concentration (CCC), a constant
bubble size is obtained, implying that coalescence is now minimal. Different frothers
reach CCC at different concentrations (Sweet, 1997), (Laskowski, 1998). A number of
authors have tried to link the ability to reduce bubble size to surface tension. Lower
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Virginia Tech | surface tension values are usually associated with higher frother concentration, resulting
in smaller bubbles. On the other hand, Aldrich and Feng found that MIBC solutions with
higher surface tension values than Dowfroth 200 solutions, produced smaller bubbles,
which is counter-intuitive (Aldrich and Feng, 2000). From this it can be concluded that
the bubble coalescence rate is not simply related to surface tension.
Gas holdup is the volume fraction of the mixture occupied by gas at any point in a
flotation cell. It is the simplest gas dispersion parameter which combines the influences
of both bubble size and gas rate. Gas holdup is directly influence by most of the flotation
parameters. For the same gas flow rate, bubble population with larger number of smaller
bubbles result in higher gas holdup, and vice versa. In 1993, Zhou found that frother type
might also have an effect on bubble size and bubble size distribution (Zhou et al., 1993a).
Similar conclusion was given by In 1996, Sam who measured the terminal velocity of a
single bubble in different frother systems. Sam found that the terminal velocity was
dependent on frother type (Sam et al., 1996).
Bubble surface area flux (S ) is emerging as one of the most useful variables to
b
quantify gas dispersion (Gomez, 2002). It is defined as the amount of bubble surface area
delivered per unit time and cell cross-sectional area, and is given by
6(cid:1836)
(cid:3034)
(cid:1845) (cid:3404) (Eq. 2.13)
(cid:3029) (cid:1830)
(cid:3029)
where J is the superficial gas velocity and D is the Sauter mean bubble diameter of the
g b
distribution. Gorain in 1997 and Hemandez in 2003 found that the flotation rate constant
is directly proportional to S . Increasing J , and/or decreasing D can increase S (Gorain
b g b b
et al., 1997; Hernandez et al., 2003). In practice, an increase in J increases bubble size
g
33 |
Virginia Tech | giving a trade-off. This is one reason why there is an optimum J in flotation (Dobby and
g
Finch, 1991).
2.8. BUBBLE FORMATION IN THE FLOTATION SYSTEM
In general, bubble size (or bubble size distribution) in the flotation system is
determined by the following three hydrodynamic processes:
bubble formation in gas generator,
bubble breakup, and
bubble coalescence.
The latter two processes are directly governed by the local turbulence. To develop
a better understanding of the role of gas bubbles in the flotation system, knowledge of the
above-mentioned phenomena is required.
During the process of bubble formation, a fraction of the total energy supplied to
the system is directly transformed into the free surface energy of newly created bubbles.
A majority of bubbles created in flotation systems are generated in the zone between the
impeller and stator blades, which is maximum energy dissipation zone of the cell. Here,
air cavities that are initially formed at the low pressure region of the impeller blades are
detached from the impellers blades edges and are carried into the high energy dissipation
zone where the bubble breakup occurs. Bubble breakup is caused by the dynamic
pressure and shear stresses on the bubble surface induced by shear flow and turbulence
(Hinze, 1955).
34 |
Virginia Tech | Bubbles created in the high energy dissipation zone are carried along by the radial
flow coming from the impeller and are scattered throughout the pulp contained in the
body of the flotation cell (van't Riet and Smith, 1973). Thereafter, bubbles climb through
the vessel due to their buoyancy but are also randomly pushed around by the existing
turbulence in the cell.
In the flotation cell turbulence is the primary mechanism responsible for breakup
of the bubbles that are initially created in the high energy dissipation zone (Kolmogorov,
1949). Only eddies that are of the similar length scale as the bubble size can break the
bubbles. On the other hand, the large eddies can only transport the bubbles, while very
small ones do not affect the bubbles (Olmos et al., 2001). In order to determine the actual
size limit of eddies responsible for bubble breakage, Prince and Blanch (Prince and
Blanch, 1990) conducted experiments to show that only eddies bigger than 0.2d are able
to break bubbles of diameter d, while eddies bigger than d can only move them.
Therefore, based on Wu (Wu et al., 1998), bubble breakup rate depends on the frequency
of collisions between bubbles and eddies of a similar size. Moreover, bubbles will break
up into smaller bubbles only when the maximum hydrodynamic forces in the liquid (that
tend to break up the bubbles) are larger than the surface tension force (that tends to
stabilize the bubbles) (Angeli and Hewitt, 2000; Hinze, 1955; Kerdouss et al., 2006). This
force balance is typically quantified by the liquid Weber number:
(cid:2025)(cid:1873)(cid:2870)(cid:1838)
(cid:1849)(cid:1857) (cid:3404) (cid:3047) (Eq. 2.14)
(cid:2011)
35 |
Virginia Tech | coalescence is the phenomenon that significantly reduces the dispersion efficiency of the
flotation system (Cho and Laskowski, 2002). Coalescence strongly depends on chemical
parameters of the system, such as the liquid surface tension, volumetric fractions of the
dispersed phase, and characteristics of the turbulent flow field (Chesters, 1991).
In the flotation systems, coalescence strongly depends on chemical parameters
characteristic for the system, such as the liquid surface tension, volumetric fractions of
the dispersed phase, and characteristics of the turbulent flow field (Chesters, 1991). For
example, for liquids with low surface tension, the sizes of bubbles formed with one
bubble generator type are always smaller than bubbles created in clear water. Due to their
smaller sizes, the rise velocities are slower, which results in larger residence time, what is
typically beneficent for the overall process performance.
After they have been generated, bubbles in the flotation system will be moved
into different zones of the cell depending on the balance between the bubble buoyancy
force and surrounding drag forces. Eventually, all bubbles leave the pulp by forcing
themselves out through the pulp-froth interface and then, by complex processes that
occur in the froth phase, a majority of the gas finally leaves the cell directly through the
froth surface or is, in less extent, carried from the system by the recovered froth.
Hence, local bubble size and bubble size distribution in the flotation cell strongly
depends on various operational, technical, and chemical factors whose effects on bubble
size should be taken into account while designing or modeling a flotation process. Some
of the factors that have the utmost effect on bubble size in the flotation systems are:
the total gas intake,
38 |
Virginia Tech | the total supplied energy,
the physical and chemical properties of the liquid and solid phases,
the impeller/stator design,
the impeller relative location to the bottom of the cell, and
the size and geometry of the cell.
Therefore, during the flotation process, the gas-liquid hydrodynamics in the
system will strongly depend on the type of bubble generator used, so the choice of a
proper impeller/stator assembly to satisfy the necessity of optimal gas dispersion is the
key for the success and economy of the process. However, the mechanism of bubble
generation in the flotation systems has not yet been explored in depth and differences
between the bubble generation mechanisms of different flotation cells have not yet been
addressed in the literature.
The size of bubbles obtained from the experiments, produced by any flotation
device (impeller, sparger etc.), will be significantly different at different locations of the
cell or column. Only when the bubbles are measured at different radial distances from the
generation zone and device wall can a representative, average bubble size be obtained.
Therefore, in order to obtain a representative bubble size, attention should be paid to the
fact that the size of bubbles produced may be different in the radial and vertical direction.
Larger bubbles are expected near the generator and center of the cell, while smaller
bubbles can be found near the highest energy dissipation zone and close to the bottom of
the cell (Zhou et al., 1993b).
39 |
Virginia Tech | Only few studies on spatial distribution of bubble sizes in the stirred vessels,
including flotation cells, have been published so far ((Alves, 2002; Alves et al., 2002;
Barigou, 1987; Barigou and Greaves, 1991; Barigou and Greaves, 1992; Gorain et al.,
1995a; Kamiwano et al., 1998; Laakkonen et al., 2007; Laakkonen et al., 2005b; Lu et al.,
1993)). On the other hand, a large amount of data is necessary for the successful
assessment, support, and validation of the current and future models.
A lot of experimental and empirical methods for determining bubbles sizes have
been used so far and include: photographic techniques, electroresistivity measurements
(Yasumishi, 1986), dynamic bubble disengagement technique (Standish et al., 1991)and
calculations using empirical or semi-empirical approach. The photographic technique is
the most common method used so far.
2.9. BUBBLE SIZING METHODS
Techniques capable of measuring bubble size in multiphase flows are usually
classified depending upon their operating principles.
2.9.1. Electroresistivity techniques
A commonly used method for bubble size measurement is the two-electrode
conductivity probe (Yasumishi, 1986). This probe consists of two needle sensors that are
mounted within a small vertical distance. Each of the sensors has a binary output signal
that depends on which phase is in contact with the tip. As a bubble passes, the time delay
between signals from the two sensors measures the time for the bubble to proceed from
one probe tip to the other.
40 |
Virginia Tech | There is a possibility of variations in bubble frequencies recorded with this
method. If such variations are statistically significant, this is indication of cross-talk and
capacitive effects. This implies that the sensors are too closely spaced. Based on research
done in the area of bubble sizing, the optimum spacing between two sensors is a function
of the bubble frequency, the range of bubble chord lengths intercepted by the sensors, and
the sensor size and geometry.
There are potential problems in applying this method to multiphase flow. Bubbles
that are rising in a direction not aligned with the two probes lead to major errors, since it
is possible that there is no delay in the signal from the two sensors. This seriously limits
use of the probe in turbulent flow fields. To overcome this difficulty, some authors have
developed multi-point probes (Raper et al., 1982). However, these probes can be utilized
only in flows where the bubble size is at least 6 mm . In order to eliminate the effects of
cross-talk between two closely positioned sensors an alternative method of acquiring the
mean time delay between the signals from the two tips is to obtain it from the cross-
correlation function between the signals (Zun, 1982). In summary, the two-point probe is
an acceptable instrument for measuring bubble characteristics only if the bubbles are
spherical and not too small.
2.9.2. Ultrasound technique
Ultrasound reflection technique offers a way to determine bubble size distribution
in multiphase flows. It is known that bubbles have a resonance frequency that is inversely
proportional to the radius of the bubble. This fact has been exploited for detection and
estimation of bubble sizes by many authors (Hilgert and Hofmann, 1986; Luebbert et al.,
41 |
Virginia Tech | 1987; Broering et al., 1991). Bubbles are excellent sound scatters and have a
characteristic resonant frequency dependent on their sizes (Cathignol et al., 1988).
2.9.3. Optical techniques
2.9.3.1. Optical fibers
Optical fibers exploit differences in the index of refraction of air/liquid phases and
rely on the application of Snell's law at the probe-fluid interface. Depending on which
phase is present at the probe tip, the light from the tip is reflected or refracted. The most
common optical probe consists of two optical fibers fused and ground to a 45° angle with
respect to the probe axis. The other ends of the fibers are free with one of them serving as
an emitter and the other as a receiver. Light detection can be achieved with a
phototransistor. The principle of detecting bubble size and velocity is identical to that of
the two-point conductivity probe described above. Measurement of bubble size using
optical probes is reported by Lee (Lee, 1984), and Saberi (Saberi et al., 1995). In general,
an optical probe can be used only in transparent systems and at low gas holdup (volume
fraction of gas). The success of the probe in discriminating between the phases depends
on good contact between the probe tip and the bubble. Thus, if the bubble size was too
small the probe would be unable to detect variations. The use of optical probes in a three-
phase system is also considered problematic.
2.9.3.2. The isokinetic collection probe
Another optical technique to measure bubble size is the isokinetic sampling probe.
The term isokinetic refers to the condition in which bubbles are collected at uniform
velocity regardless of their size. In this optical technique, bubbles are sampled and
42 |
Virginia Tech | collected into a capillary tube. The end of the capillary is funnel shaped which provides a
uniform acceleration of sampled bubbles through the capillary. In the capillary, bubbles
are converted into cylinders filling the capillary cross-section. A narrow collimated beam
of light is directed through the capillary glass wall. The variation in intensities of the
measured signal due to sequential shifts of gas and liquid slugs are recorded. The time
elapsed between the detection of the two ends of a bubble is inferred from the signal.
This, along with the known cross-sectional area of the capillary, can be used to estimate
the bubble volume. Assuming that the bubble is a sphere, an equivalent spherical bubble
diameter can be computed. Employment of this technique is reported for two-phase (gas-
liquid and liquid-liquid) dispersions, in three-phase (gas-water-paper) pilot-scale flotation
deinking cells, and in flotation columns with gas-water-coal systems.
Capillary size chosen for the method is a function of the smallest bubble needed
to be detected. Bubbles smaller than the capillary diameter cannot be transformed into
slugs and, consequently, they produce signal pulses of a small amplitude and width that
cannot be reliably measured. On the other hand, reducing the capillary size further may
cause bubble breakup at the point of bubble entry. Also, risk of the probe blockage
increases as the capillary size decreases. Slug velocity is strongly dependent on purity of
the capillary, decreasing as the build-up increases. In the case of slurries containing larger
particles or slurries with high solids concentration, this limitation can become important.
A variant to the isokinetic sampling probe is introduced by Randall (Randall,
1989), which is shown in Figure 2.9. This method is often referred to as the University of
Cape Town (UCT) bubble size analyzer.
43 |
Virginia Tech | breakage mechanisms, at the sampling end of the capillary tube, are presented in the
Figure 2.10.
Bubble at the moment it touches the capillary, t , and its fate after the time period
1
t -t are given in the figure. Bubble breakage can happen both inside of the capillary and
2 1
at the entrance point. Large bubbles have typically, more chances to miss the capillary or
to be broken by the capillary tip.
Only under very controllable conditions, when bubbles present in the sampled
pulp are small and have narrow distribution, this system could be successfully employed.
However, studies directed to establish the optimum conditions are scarce in the literature.
2.9.4. Imaging Techniques
The simplest approach for bubble sizing would seem to be the imaging technique.
Studies in which images are used to size bubbles proliferate in the literature. In the most
common setup, pictures of the dispersion are taken through windows installed in the
vessel wall while real sizes are obtained by placing an object of known size (usually a
ruler) in the focus plane. In the most commonly used methods bubbles are captured by
high-speed CCD cameras due to their great precision (Soler et al., 2003). Automatic
sizing through image analysis routines have not been extensively implemented due to the
common practical and fundamental problems associated with this method.
One of the fundamental problems of this method, which is not frequently
discussed, is the impact of the "inherently variant" distance between the focus plane and
the bubble. The oscillating nature of the bubble motion causes the distance between the
bubble and the focus plane to vary. Other fundamental problems include the influence of
46 |
Virginia Tech | optical conditions such as, for example, the lighting characteristics, which may vary
during the sampling process. Other practical problems are well documented in literature:
overlapping, blurring, bubble clustering, poor contrast, etc. Therefore, this is not a
straightforward approach in an industrial-scale system and it was usually used in
laboratory conditions. A variant of the imaging technique is to direct a sample of the
bubbles into a viewing chamber and there expose them for imaging. Some of the most
commonly used systems are:
2.9.4.1. Helsinki University of Technology (HUT) bubble size analyzer
This Helsinki University of Technology bubble size analyzer presented in the
Figure 2.11 has been designed to work only for two-phase systems and it consists of a
viewing chamber made of clear acrylic and small sampling tube. The bubble sampler is
filled with water containing the same frother concentration as the liquid in the cell to
reduce coalescence problems within the device. The high-magnification ratio used yields
really shallow focal depth of fields. This facilitates the identification of overlapping
structures.
In 2006, Grau and Laskowski used this method for measuring bubble sizes in the
two solutions, with DF-200 and DF-1012 frothers (Grau and Laskowski, 2006b). They
tested three locations in the cell prior to the final measurements, and selected a location
near the pulp-froth interface (quiescent flow conditions) to be the most suitable location
for this measurement method. A sampler tube of the HUT method is not able to identify
bubbles that are not traveling upward, as is the case in the turbulent zone. Their
assumption was that the collected sample from a single sampling location is
47 |
Virginia Tech | CHAPTER 3:
A NEW MODULAR PILOT-SCALE SETUP FOR
HYDRODYNAMIC AND METALLURGICAL
FLOTATION PERFORMANCE EVALUATION
Authors: Miskovic, Sanja; Luttrell, Gerald; Bratton, Robert
Submitted: December, 2011
To: Minerals Engineering
3.1. ABSTRACT
Batch laboratory flotation cells are commonly used to obtain information
regarding the maximum achievable mineral recovery and overall process kinetics for a
range of chemical conditions. Unfortunately, considerable technical expertise and process
experience is required to utilize batch data for the design and scale-up of continuous
flotation systems. For this reason, continuous pilot-scale tests are often conducted to
further validate and refine performance projections that are initially based on batch data.
To facilitate this important type of work, a new continuous pilot-scale flotation circuit has
been designed, constructed, and evaluated. This paper describes the flotation test circuit
design and gives details about the automation and instrumentation systems used in the
new circuit. Hydrodynamic and metallurgical results are also presented from several
testing campaigns conducted with the pilot-scale flotation setup using either narrowly-
sized hydrophobized glass spheres or rougher circuit copper concentrate from an
industrial concentrator as floatable feed materials.
68 |
Virginia Tech | 3.2. INTRODUCTION
The design, scale-up, and optimization of flotation systems is challenging and
requires considerable technical expertise and process experience due to their multifaceted
nature and complexity. As flotation systems are scaled to larger sizes, many of the major
parameters controlling the process do not scale in proportion. For example, bubble sizes
measured in large industrial flotation cells are often much larger than those measured in
small laboratory cells, and the specific power input for industrial cells is up to ten times
less than the power used in laboratory units. Moreover, the design of many industrial
flotation cells differs significantly from one industrial scale to another due to a number of
technical limitations, which additionally hinders direct comparison and simplistic scale-
up.
Batch laboratory flotation cells are commonly used to obtain information about
maximum achievable mineral recovery and grade, as well as overall process kinetics, for
a range of chemical conditions. In many cases, the resultant data obtained from these
semi-batch experiments cannot be directly used to design or scale-up industrial cells and
continuous flotation systems without using empirical, semi-empirical or theoretical
algorithms that account for inherent differences in the operational characteristics of cells
of different scales. Nevertheless, information gained from this type of testing is usually
necessary since it is neither practical nor feasible to directly conduct experiments on large
industrial-scale cells.
The thrust of this work is to provide scientifically sound information that can help
bridge a gap in knowledge and help correlate results gained through both industrial and
69 |
Virginia Tech | closely controlled laboratory conditions. Furthermore, this paper provides details about
the design of a new continuous pilot-scale flotation circuit and its operational
performance over a wide range of operating conditions.
3.3. METHODS
3.3.1. Experimental
For the measurement of major hydrodynamic and metallurgical parameters in
pilot-scale mode, a new continuous processing circuit was designed and built (Figure
3.1). The new flotation circuit was specifically designed to reduce limitations associated
with laboratory testing and to approach the operating conditions of industrial-scale
flotation cells as closely as possible. Further attention was paid to ensure that the system
was easy to operate and control and was producing accurate, reliable and reproducible
results. The circuit consisted of four major mechanical components: Dorr-Oliver®
flotation cell (which was the central component of this pilot-scale setup), air blower,
slurry sump, and slurry pump. Additionally, a new state-of-the-art control and data
acquisition system was developed and implemented into the new circuit.
3.3.1.1. Flotation Cell
In order to allow testing of different cell geometries and to accommodate various
flotation cells in the future, a new modular, stainless-steel, 0.8 m3 flotation tank was
fabricated. The modular tank was composed of five interchangeable segments including
three body rings with different heights and internal and external launders. Each launder
segment was designed with three interchangeable launder rings with heights of 5, 10 and
20 cm, so that effects of different froth depths can be investigated without changing the
70 |
Virginia Tech | effective pulp volume. The cell was also designed to accommodate up to a maximum of
eight vertical baffles. Furthermore, new Dorr-Oliver® wetted parts (impeller, stator, and
impeller shaft) were designed and fabricated to fit the new tank.
3.3.1.2. Flotation Circuit
A new flotation circuit was designed and built to facilitate continuous flotation
tests. For this purpose, a 1 m3 sump was used for slurry circulation where both froth
concentrate and tailings streams were collected, mixed together, and then pumped back to
the flotation cell through a feed line. It was discovered during initial testing that a large
volume of air was introduced into the sump by the concentrate and tailing return lines,
and also by the sump propeller mixer, which formed an undesirable mineralized froth
atop the mixing sump. Several modifications were made to the slurry sump to reduce
froth accumulation and to maximize the material circulation through the circuit. For
example, a physical partition was added to the sump to minimize the free surface
available for froth accumulation. Furthermore, a custom overhead washing system was
installed to facilitate efficient bubble breakup and floatable particle release from the
accumulated froth phase. For this application, five small-capacity spiral-jet spray nozzles
were installed. By utilizing these nozzles, a fraction of the feed stream was able to be
bypassed directly through the nozzles back to the sump. The use of feed slurry for froth
breakup avoided the problem of unwanted dilution of the feed that would occur if fresh
spray water were added. Finally, all stream lines were configured to enable simultaneous
full-stream sampling when necessary.
71 |
Virginia Tech | 3.3.1.3. Process Control and Instrumentation
As shown in Figure 3.1, the test circuit was equipped with various sensors,
including a pressure transmitter, level sensor, conductivity probe, magnetic slurry flow
meter, two gas mass flow meters, and a torque meter. To enable data logging, a state-of-
the-art control and data acquisition system was developed and installed. The final
experimental setup, which also included two bubble sampling systems (ex-situ and in-
situ), allowed continuous data collection of multiple flotation parameters such as local
bubble size, local gas holdup, local and global superficial gas velocity, froth depth, feed
flow rate, and power input.
For the measurement of local bubble sizes, only in-situ bubble sampler developed
at Virginia Tech was used. The bubble sampling system was composed of a monochrome
GEViCAM GP-21400 CCD high-speed camera and LED light, which were mounted
inside two aluminum watertight enclosures that faced each other. The gap width between
the light source and the camera was adjustable from 6 to 50 mm. Back illumination of
bubbles was achieved using an Advanced Illumination SL2420 LED red spot light, which
was pulsed with an Advanced Illumination S4000 strobe controller. A ground glass
diffuser was installed in front of the LED light to facilitate more uniform light
distribution. The in-situ system made it possible to examine local bubble size
distributions at various horizontal and vertical positions within the flotation pulp.
Instrumentation used in this study for the measurement of superficial gas velocity
and local gas holdup have been described elsewhere by Nesset and Gomez (Gomez and
Finch, 2007; Nesset et al., 2006). In addition, a shaft mounted strain gauge was chosen
73 |
Virginia Tech | for the purpose of power measurements due to its intrinsic capability to directly, reliably,
and precisely measure the torque of a rotating shaft. Measurements were performed with
an Advanced Telemetrics International’s strain gauge radio telemetry system. A
supporting split collar assembly was mounted directly on the shaft, which housed the
battery, amplifier, radio frequency transmitter, and all associated electronics. Since there
are no mechanical contacting parts to wear out, the system required very little
maintenance and was easy to install.
The operation of the pilot-scale flotation circuit required the coordination of
multiple functions, which was made possible by an integrated automation system. The
main application of the automated system was to provide exact and reproducible
execution of the following functions: level control, feed flow, agitation, and aeration rate
regulation, and overall data acquisition. The process control system was also designed to
provide for real-time monitoring of all input signals from the various sensors. A graphical
trend display allowed for constant monitoring of all key process parameters. The
visualization, operation, and monitoring of process parameters was managed through the
easy-to-use Rockwell Automation FactoryTalk View Studio ME interface, shown in
Figure 3.2, while RSLogix™ 500 ladder logic software was used for the control and
management of input/output (I/O) tags.
The FactoryTalk Historian software allowed reliable data capture and creation of
accurate on-line records of all process parameters. In this way, a single computer, which
was also acting as a main human machine interface (HMI), managed multiple operations
and allowed the analysis and monitoring of all data from a single location.
74 |
Virginia Tech | for this study varied in the range from 3 to 8 m/s, while aeration rates of up to 2.2 cm/s
were utilized. For testing in continuous conditions, feed flow rates were varied from 90 to
500 l/min, which provided mean residence times of 1 to 8 min. Frother concentrations
ranged from 0-14 ppm for MIBC and from 0-7 ppm for Nalco V-20373M frother.
3.4.2. Hydrodynamic measurements
The two-phase tests were performed to investigate both gas dispersion properties
and overall power consumption of the flotation cell. During these tests, the cell was
operated as a batch reactor. All tests were run in both coalescing and non-coalescing
conditions (Grau and Laskowski, 2006a). Once the agitation and aeration rates were set,
the cell was run at least three minutes before measurements were performed. For each set
of operating conditions, all variables were recorded for approximately 10 minutes and
then averaged. To describe the overall variability of each measured variable over a given
time period, the standard deviation of each time series was determined and reported with
error bars. For derived parameters, such as bubble surface area flux, specific power, and
theoretical liquid residence time, the error was calculated by applying the propagation of
uncertainty rule (Meyer, 1975).
In-situ bubble sampling methods was used for local bubble sampling. During the two-
phase testing, bubbles were acquired from six different positions within the cell to allow
assessment of the spatial variation of bubble size distributions. For three-phase tests,
bubbles were sampled at a single location positioned in the impeller jet region for this
particular study. Bubbles detected at this location are believed to be the most significant
since considerable bubble-particle collisions occur in this high energy dissipation region.
77 |
Virginia Tech | The field of view and image capture rate for the in-situ bubble sampling method
were 17.5 x 13 mm and 10 frames per second, respectively. Additionally, a gap size
between the light and camera of the in-situ bubble sampler was set to 20 mm during two-
phase tests and 10mm during three-phase tests with glass particles. During copper
flotation tests, the gap width was reduced to 3 mm and bubble sampling was supported by
a peristaltic pump, which enabled isokinetic sampling of the pulp, containing more than
25% w/w of solids.
Approximately two hundred bubble images were taken for each operating
condition. Images were randomly chosen from each data set and analyzed with
BubbleSEdit image analysis technique (Zabulis et al., 2007). The bootstrap standard
deviation (Efron and Tibshirani, 1993) for each analyzed bubble sample was calculated.
Six image examples acquired with the in-situ bubble sampler in both two- and
three-phase systems are shown in Figure 3.4. Details of operating conditions and
sampling location are given for each presented image. As mentioned before, a detailed
description of experimental procedures for the measurement of superficial gas velocity
and local gas holdup are given by Nesset and Gomez (Gomez and Finch, 2007; Nesset et
al., 2006). Both local gas holdup and local superficial gas velocities were measured in the
quiescent zone of the cell, approximately 35 cm below the froth-pulp interface and at the
mid-distance between the impeller shaft and the tank wall.
Also, since information about the power input during flotation can give insight
into the gas dispersion characteristics of the flotation cell, the torque was measured under
both unaerated and aerated conditions. Each measurement was repeated three times and
78 |
Virginia Tech | the average power consumption and standard deviation were determined for each set of
test conditions.
Figure 3.4 Examples of images recorded with a new in-situ bubble sampler: a) 5 m/s
agitation rate, 1.37 cm/s aeration rate, 14 ppm MIBC, water/air mixture, 10 mm gap
width, without sample pumping; b) 5 m/s agitation rate, 1.31 cm/s aeration rate, 14 ppm
MIBC, water/air mixture, 3 mm gap width, with sample pumping; c) 5 m/s agitation rate,
1.30 cm/s aeration rate, 4 ppm V-20373M, water/air/35 µm glass spheres mixture, 10 mm
gap width, without sample pumping; d) 5 m/s agitation rate, 1.30 cm/s aeration rate, 4
ppm V-20373M, water/air/203 µm glass spheres mixture, 10 mm gap width, without
sample pumping; e) 8 m/s agitation rate, 1.88 cm/s aeration rate, 8ppm MIBC,
water/air/Cu rougher concentrate mixture, 3 mm gap width, with sample pumping; f) 5
m/s agitation rate, 1.25 cm/s aeration rate, 8ppm MIBC, water/air/Cu rougher concentrate
mixture, 3 mm gap width, with sample pumping.
At the end, suspending capabilities of the Dorr-Oliver flotation cell were
investigated under unaerated conditions with slurry containing 5% w/w of 203 μm
SPHERIGLASS® glass spheres. Slurry samples were taken for three different agitation
rates from eleven different locations in the cell. The vertical sampling plane was
positioned 38 cm radial distance from the center of the cell. The slurry sample was
collected with peristaltic pump in the rate of 10 l/min.
79 |
Virginia Tech | 3.4.3. Metallurgical measurements
As described in previous section, continuous flotation tests were performed using
four different size classes of glass spheres. Glass spheres were chosen due to their narrow
particle size range, consistent chemical and physical characteristics, and reasonable price.
By utilizing this material for the metallurgical performance characterization, more
controllable experimental conditions were achieved. During initial batch flotation tests,
the maximum theoretical recovery for all selected particles was determined for a range of
collector and frother dosages. Based on preliminary laboratory testing, standardized
collector and frother dosages for the pilot-scale tests were established. It was found that 4
ppm V-20373M frother and 30±2 g/t of DDA in a 5% ethanol solution were optimal
dosages for glass particle conditioning. In order to minimize froth effects and bubble
loading limits, the froth depth was maintained at 2.5 cm and the weight percentage of
solids in the pulp was kept constant at a relatively low value of 0.5% w/w.
The basic test procedure used in all glass flotation tests was as follows. The
collector was added to the water/particles mixture and circulated through the flotation
circuit. After about ten minutes of conditioning time, the frother was added directly to the
feed sump. The feed flow rate was then adjusted to provide the desired residence time of
slurry within the cell. Once the aeration and agitation rates were adjusted, a minimum of
three residence times were allowed for the system to reach the steady-state, after which
all parameters were measured. Also, the timed cuts of all three streams were collected
simultaneously at the sampling points indicated in Figure 1. Samples of tailing,
concentrate, and feed were weighed, filtered, and dried, and then dry weighted. Mass
balancing was performed to determine the mass and water recoveries.
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Virginia Tech | The second group of continuous pilot-scale flotation tests was conducted using a
rougher concentrate sample from an industrial concentrator. The original slurry sample
was decanted and the remaining wet material, with approximately 5% w/w of water, was
used in tests. In this procedure, MICROSIL® CGS ground silica was used as an artificial
gangue material. To reproduce conditions comparable to industrial, both the rougher
concentrate and ground silica were added in proportions to achieve approximately 25%
w/w of total suspended solids, of which approximately 4% w/w was floatable material.
The generated slurry was treated with 25±1 g/t of FloMin C 3505 collector and
additionally 8±0.5 ppm of MIBC frother was added to the system. Furthermore, in order
to evaluate the effect of froth on flotation performance, three froth depths were tested
(i.e., 2.5, 5 and 7.5 cm).
The basic test procedure used in all copper flotation tests was as follows:
Ground silica and rougher copper concentrate were added in the slurry sump and
circulated through the system.
FloMin C 3505 collector was then added and the system was run for
approximately 15 minutes before frother addition.
The froth depth was set to the desired height and the blower was activated to
introduce air.
After the target aeration and agitation rates were set, the system was run for at
least three residence times.
Tailings, concentrate, and feed samples were collected.
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Virginia Tech | The samples were weighted, filtered, and dried, and the dry sample was weighted
and sent for assay analysis.
3.5. RESULTS AND DISCUSSION
3.5.1. Hydrodynamic investigation in two-phase
To better understand the physical processes that govern flotation, accurate
measurements of all main process parameters under controllable conditions are required.
Generally, there are three hydrodynamic parameters used to characterize gas dispersion
properties within a flotation cell: superficial gas velocity (J ), Sauter mean bubble
g
diameter (D ), and gas holdup (ε ). In the case of aerated stirred reactors, the Froude
32 g
number, Aeration number, and the ratio of unaerated to aerated power consumption can
be used to describe gas dispersion and mixing efficiency (Harris, 1974; Harris, 1976;
Harris and Mensah-Biney, 1977).
Among the gas dispersion parameters, bubble size is perhaps the most important
since it defines the free surface area over which solid particles and bubbles interact,
which directly controls the system hydrodynamics and overall flotation performance. In
order to have a better insight into the overall gas dispersion efficiency, bubbles should be
screened at multiple locations within the cell. The spatial variation of bubble sizes in a
two-phase system (water-gas mixture) was determined using the in-situ bubble sampling
method. In the current study, bubble images were collected at six different locations
within the flotation pulp. Figure 3.5 shows bubble size distributions and mean bubble
sizes obtained under non-coalescing conditions (14 ppm MIBC). During this batch test,
the impeller tip speed and aeration rate were set at 5 m/s and 1.37 cm/s, respectively. For
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Virginia Tech | each location, one representative image was chosen and shown in Figure 3.5. Number
mean (D ) and Sauter mean (D ) bubble diameters with corresponding bootstrap
10 32
standard deviations and number frequency distributions are reported for each location.
The fraction of the total gas volume contained in a certain bubble size class is also given.
As shown in the figure, bubble populations varied significantly at different
vertical and radial distances from the impeller/stator assembly. At this particular
operating condition, a proportionally larger fraction of larger bubbles within a screened
population was recorded in the region above the impeller/stator gap. On the other hand,
bubble populations containing the least number of larger bubbles were detected in the
impeller jet region (zone with the highest energy dissipation) and close to the bottom of
the cell. The number of bubble-particle collisions occurring in the high energy dissipation
zone of the cell is strongly affected by the size of the bubbles in this zone. For that
reason, bubble sizes obtained from the impeller jet region were reported and used for the
Aeration number calculations.
Sauter mean and number mean bubble diameters (with corresponding bootstrap
standard deviations) and local gas holdup values are presented in Figure 3.6 as a function
of different aeration and agitation rates. As can be seen from the plot, the Sauter mean
bubble diameter increased proportionally with the local gas holdup under different
aeration conditions and for constant impeller tip speed. As a result of this relationship,
and the fact that it can be measured directly in real-time, gas holdup can be used as a
direct indication of local gas dispersion properties in the cell.
83 |
Virginia Tech | aeration on power transfer from the impeller to the fluid (Nienow, 1977). Van’t Riet and
Smith (van't Riet and Smith, 1973) explained that the formation of gas cavities behind the
impeller blades and difference in the fluid density under aerated and unaerated conditions
is the reason for the power reduction. Depending on the type of impeller and aeration
rates used, the ratio of the power consumption in aerated (P ) and unaerated (P )
a 0
conditions is usually in the range from 30% to 100%. This ratio determines the actual
power input of the flotation operation and gives insight into the gas dispersion
characteristics of the impeller.
Aeration number (N ) is used to describe the nature of the gas–liquid flow within
Q
the cell and can be calculated using following expression: N = Q /ND3, where Q
Q g g
represents the total volumetric gas flow rate, N is the agitation rate, and D is the impeller
diameter. Figure 7 shows the P /P ratio as a function of the Aeration number at different
a 0
agitation rates (i.e., 3 to 8 m/s impeller tip speed). The drop in aerated power
consumption over the unaerated power consumption with an increase of Aeration number
can be observed for all agitation rates. The P /P ratio of the agitation mechanism used in
a 0
this study ranged from 0.5 to 1.0, depending on the agitation and aeration rates used.
As suggested by Nienow (Nienow, 1977), knowledge of the minimum agitation
rate for complete dispersion of introduced gas, N , is necessary for better understanding
CD
of various flow patterns that occur in the cell. In Figure 3.7, this value is represented by
the agitation rate, where the P /P ratio is minimal for a certain aeration rate. This
a 0
operating condition is characterized by a fully dispersed, bubbly fluid flow pattern,
without impeller flooding (Pangarkar et al., 2002). However, recent research (Hall et al.,
2005) has suggested that gas holdup at this condition cannot support sufficient gross
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Virginia Tech | recirculation of the bubbles throughout the cell, and that the optimal aeration rate for a
certain agitation rate is shifted towards the left of the P /P minimum.
a 0
Figure 3.7 Ratio of the power consumption in aerated (P ) and unaerated (P ) conditions
a 0
as a function of the Aeration number at different impeller tip speeds: ♦ - 8 m/s; ■ – 7 m/s;
▲ – 6 m/s; ● – 5m/s; x – 4 m/s; and + - 3 m/s impeller tip speed.
The jump in the P /P values observed for the 3 and 4 m/s impeller tip speeds
a 0
represents a transition of the overall flow pattern from “loaded” to “flooded” conditions.
A similar trend cannot be observed for higher agitation rates due to constraints associated
with the maximum aeration number that could be achieved in the available setup. One of
the explanations of the power consumption increase during the loaded-flooded transition
is the upward distortion of the gas cavities formed behind the impeller blades, which
result in an increase of the total blade surface area in contact with the liquid. Below the
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Virginia Tech | subjective, three or more measurements were performed randomly during both falling
and increasing aeration rate.
Average critical aeration rates were used for the calculation of the Aeration
number. Figure 3.8 summarizes the results obtained from the series of tests conducted
with the water-gas only and water-gas-frother (7 and 14 ppm MIBC) mixtures. The same
measurements were performed during the three-phase operation (25% w/w of solids in
slurry) and are also reported in this plot. The aeration and agitation rates at the loaded-
flooded transition are expressed in terms of the Aeration number and Froude number
(Fr). The Froude number is given as Fr = N2D/g, where g represents the acceleration due
to gravity. The standard deviation of three measurements, representing the uncertainty in
the visual observations, is also reported through error bars in the plot. The uncertainty
generally increased as the aeration and agitation rates increased due to more turbulent
free surface at the top of the cell, therefore creating an indistinct loaded-flooded
transition.
An effect of agitation rate on particle suspension performance of the flotation cell
was investigated under unaerated conditions. The solids content of slurry samples, taken
from eleven different locations, was determined for three different impeller tip speeds
(4.5, 5.5, and 6.5 m/s). The particles used for this investigation were monodisperse 203
μm glass spheres, and their concentration in the slurry was 5% w/w. Each test was
repeated three times and both average solids concentration and corresponding error bands
are determined (Figure 3.9). As can be seen from the Figure 3.9, three distinct zones, with
significantly different particle concentration profiles, are formed within the cell and this
trend is observed for all three operating conditions. As expected, the zone with the
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Virginia Tech | 3.5.2. Hydrodynamic and metallurgical investigation in three-phase - glass spheres
A series of flotation tests were run independently on all four selected glass sphere
samples to determine the effect of particle size, liquid residence time, aeration rate, and
agitation rate on overall material recovery. Nine different combinations of aeration and
agitation rates were tested for each particle size with one condition being repeated three
times randomly in a testing sequence.
In this way, the reliability of the testing procedure was examined by evaluating
the standard deviation of repeated measurements. Absolute errors of all measured mass
recoveries fell in the narrow range from 0.5% to 1.8%, which confirmed the test
reproducibility.
Figure 3.10 shows the total mass recovery as a function of particle size, obtained
through pilot-scale testing, under the same chemical conditions (4 ppm V-20373M; 30±2
g/t DDA) and 1.5±0.4 min residence time. For reference, the maximum achievable
recoveries for each particle size obtained through preliminary laboratory testing, under
the same chemical conditions as in pilot-scale experiments, are also plotted.
The drop off in recovery for fine particles may be attributed to decreased
efficiency of bubble-particle encounter associated with smaller particle sizes. On the
other hand, the relatively poorer recovery of coarse particles can be explained by an
increased probability of bubble-particle detachment and decreased stability of the bubble-
particle aggregates due to the absence of fine particles.
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Virginia Tech | Figure 3.11 Material recovery as a function of theoretical liquid residence times and
particle size at three different operating conditions. ■ – 35 µm; ▲ – 71 µm; and ♦ – 119
µm; full line – 6 m/s, 1.7 cm/s; dashed line – 5 m/s, 1.3 cm/s; and dotted line – 4 m/s, 0.6
cm/s agitation and aeration rates.
The data summarized in Figure 3.11 also shows a relationship between flotation
recovery and parameters such as aeration and agitation rate. For all particle sizes, higher
aeration and agitation rates resulted in higher material recoveries. It is well documented
that the gas dispersion conditions in the flotation cell have a direct influence on flotation
performance (Schwarz and Alexander, 2006). This is understandable since the amount of
created gas-liquid interfacial area affects particle collection kinetics. Pursuing this notion,
researchers have found that the flotation rate constant was not readily related to bubble
size, gas holdup, or gas rate individually, but was related to bubble surface area flux
(Gorain et al., 1997; Gorain et al., 1998b). Bubble surface area flux (S ), calculated as S
b b
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Virginia Tech | conditions and a single particle size class, the correlation was found to be roughly linear,
which is in agreement with previous publications (Deglon et al., 1999; Finch et al., 2000;
Gorain et al., 1999; Gorain et al., 1998b; Heiskanen, 2000; Vallebuona et al., 2005).
Figure 3.13 illustrates the effect of specific power input (P*), defined as a power-
to-volume ratio, on the flotation performance. Specific power was estimated from the
direct torque readings and the effective liquid volume, while taking into account the
overall gas holdup in the cell. Three sets of operating conditions were chosen from the
test matrix and corresponding results are presented in the plot (4 m/s and 0.82±0.05 cm/s;
5 m/s and 1.34±0.05 cm/s; and 6 m/s and 1.74±0.05 cm/s impeller tip speed and global
superficial gas velocity).
Figure 3.13 Flotation rate constant as a function of specific power input for four different
particle sizes. ■ – 35 µm; ▲ – 71 µm; ♦ – 119 µm; and ● – 203 µm.
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Virginia Tech | Based on the results shown in Figure 3.13, the flotation rate constant increased
with an increase of specific power input for each of the four particle sizes tested.
However, specific power increase mostly affects intermediate and fine particles, which is
reflected through notably stronger k-P* relationship. These results are in good agreement
with the findings of previous studies (Deglon, 2005; Ralston et al., 2007; Ralston et al.,
2010; Schubert, 2008).
Sauter and number mean bubble diameters and local gas holdup, measured in the
impeller discharge stream, are shown as a function of specific power input in Figure 3.14.
The selected operating conditions are the same as those presented in the Figure 3.13.
Figure 3.14 Sauter (D ) and number mean (D ) diameters and gas holdup as a function
32 10
of specific power for three selected operating conditions (4 m/s and 0.82±0.05 cm/s; 5
m/s and 1.34±0.05 cm/s; and 6 m/s and 1.74±0.05 cm/s impeller tip speed and global
superficial gas velocity) and 35 µm particle size. ▲ – D ; ♦ – D ; □ – gas holdup.
32 10
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Virginia Tech | As can be seen from the figure, the increase in the specific power input has
negligible effect on the bubble sizes, which is well reflected through insignificant
changes in both Sauter and number mean diameters. On the other hand, the gas holdup
increases significantly with increase in power input, suggesting that more bubbles with
similar diameters have been generated. It can be concluded that the power input has a
positive effect on the number of bubbles created in the cell, which consequently increases
the probability of bubble-particle attachment, increases overall carrying capacity, and
therefore increases the flotation rate constant (Figure 3.13).
3.5.3. Hydrodynamic investigation in three-phase - copper concentrate
To further explore the capabilities of a new pilot-scale flotation circuit, an
additional series of tests were performed with the copper concentrate and ground silica,
totaling 25% w/w of solids, in order to achieve more realistic industrial-like conditions.
Hydrodynamic measurements of all major gas dispersion parameters and torque
measurements were performed for a series of operating conditions and under identical
chemical conditions.
Figure 3.15 shows the relationship between local gas holdup values and local
superficial gas velocities measured in the quiescent zone of the cell. Error bars in the plot
reflect the standard deviation of a time series for gas holdup and the standard deviation of
multiple readings for superficial gas velocity. The test data shows the gas holdup
increased from 8% to 13% as the superficial gas velocity increased from 0.8 to 2 cm/s.
A gradual broadening of confidence intervals around estimated values can be
observed for both measured parameters as the aeration rate increased. This is largely due
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Virginia Tech | Figure 3.16 Sauter mean bubble diameter as a function of local superficial gas velocity at
four different impeller tip speeds. ♦ – 5 m/s; ■ – 6 m/s; ▲ – 7 m/s; and ● – 8 m/s.
This range of mean bubble sizes, which is wider than bubble size distributions
previously reported in the literature (Fuerstenau, 2007; Laskowski et al., 2003; Sawyerr
et al., 1998), can be attributed to increased precision achieved with the in-situ bubble
sizing method by which up to 98% of all recorded bubbles in an image were detected and
included in the analysis. In addition, the results of the automated image analysis were
revised and manually corrected to ensure that all bubble clusters and non-spherical
bubbles, composed of big bubbles and/or gas slugs, were counted and included in the
bubble sizing analysis. In the current study, this approach significantly increased the
calculated D values compared to previous studies. However, it is believed that the
32
Sauter mean bubble diameters determined in this way present more accurate estimation of
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Virginia Tech | Figure 3.19 Flotation rate constant as a function of bubble surface area flux for the four
superficial gas velocities. ♦ – 0.88±0.02 cm/s; ■ – 1.20±0.02 cm/s; ▲ – 1.54±0.02 cm/s;
and ● – 1.88±0.03 cm/s.
One of the explanations for this observed phenomenon is the detrimental effect of
high agitation rates on flotation kinetics in the pilot-scale cell. In other words, even thou
the selected range of impeller tip speeds (from 5 to 8 m/s) is analogous to the agitation
rates found in industrial conditions, which is believed to be the best approach for the
flotation scale-up, other negative effects observed at higher agitation rates (7 and 8 m/s)
decrease the flotation performance in pilot-scale. For example, it is observed that at 8 m/s
impeller tip speed impeller generates a strong discharge stream, which, due to the short
radial distance from the impeller to the wall, collides intensively to the cell wall. After
the impact, this high intensity stream has sufficient energy to rise directly to the cell top
and causes “geysering” effect at the froth surface. For these reasons, both higher
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Virginia Tech | The error bars in this plot represent the uncertainty of S estimation, which
b
accounts for measurement errors of local superficial gas velocity, total gas flow rate, and
bootstrap standard deviation of D .
32
For most of the operating conditions, the bubble surface area flux values
estimated from global superficial gas velocities appear to overestimate the bubble surface
area flux. Small relative errors from 0.2% to 2% were observed for low aeration rates (0.8
to 1.3 cm/s), while relative errors form 1% up to 14% were found for higher aeration
rates (1.5 to 2 cm/s). One explanation of this finding is that, at higher aeration rates, a
part of the introduced gas contained in large bubbles rises directly from the impeller to
the froth zone. As a result of this heterogeneous gas distribution within the cell, global
superficial gas velocities, calculated by dividing the overall gas flow rate with the cell
cross sectional area, will give slightly larger estimations than superficial gas velocities
obtained by local measurements at a half radial distance from the impeller shaft.
3.6. CONCLUSION
A fully-instrumented 0.8 m3 pilot-scale flotation circuit was developed for the
purpose of providing performance data that can be more readily utilized for the
engineering design, scale-up, and optimization of industrial flotation circuits. This highly
flexible system enabled measurement, monitoring, and control of a number of
hydrodynamic and metallurgical parameters over a wide range of operating conditions
comparable to those found in industrial scales. Preliminary tests indicate that the
continuous circuit can be successfully operated with slurry containing more than 30%
w/w of solids.
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Virginia Tech | Performance of the system was evaluated in both two- and three-phase tests,
utilizing either glass spheres or copper mineral concentrate. Several important
conclusions obtained through hydrodynamic and metallurgical testing in pilot-scale are
listed below:
Bubble populations vary significantly at different vertical and radial distances
from the impeller/stator assembly under the same operating condition, and the
nature of this variation strongly depends on the operating condition.
Measurement of power consumption in flotation cells allows better insight into
the gas dispersion properties of the cell.
Ratio of the aerated to unaerated power plotted as a function of the aeration
number gives important information about the minimum agitation rate necessary
for complete dispersion of the introduced gas.
The first sign of the transition of the overall flow pattern from “loaded” to
“flooded” conditions can be easily observed through the increase of the aerated to
unaerated power ratio as a result of aeration rate increase under constant agitation
rate.
During the operation of mechanical flotation cells, three distinct zones, with
significantly different particle concentration profiles, are formed within the cell.
The increase in agitation rate increases coarse particle of-the-bottom suspension
and increases their concentration in the cell, which ultimately creates more
favorable conditions for bubble-particle encounter in the high-turbulent zone of
the cell.
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Virginia Tech | For all particle sizes, higher aeration and agitation rates resulted in higher material
recoveries and for fine and intermediate particle sizes recovery increased as
residence time increased over all operating conditions.
A correlation between the flotation rate constant and bubble surface area flux is
observed for all glass particles tested, while the nature of this correlation strongly
depends on the size of the particles.
The power input has a positive effect on the number of bubbles created in the cell,
which increases the probability of bubble-particle attachment, increases overall
carrying capacity, and therefore increases the flotation rate constant.
The Sauter mean bubble diameters measured in this study ranged from 0.65 to
2.55 mm, which is wider than bubble size distributions previously reported in the
literature.
Larger mean bubble diameters are obtained due to increased precision achieved
with the in-situ bubble sizing method by which up to 98% of all recorded bubbles
in an image were detected and included in the analysis.
The decrease in mean bubble diameters can be achieved by the decrease in
superficial gas velocity and increase in the specific power input.
Flattening of the D -P* trend can be observed for all aeration rates tested, which
32
suggests that there is a minimum energy input needed to achieve an optimal
bubble size distribution in the cell for a given constant aeration rate.
As a result of this heterogeneous gas distribution within the cell, the bubble
surface area flux values estimated from global superficial gas velocities
overestimate the bubble surface area flux.
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Virginia Tech | Care must be taken during the flotation scale-up process since not all parameters
relevant to flotation scale in proportion.
Different scales of flotation cells, used through the scale-up procedure, have
different range of optimal operating conditions and their own characteristic
limitations.
Data obtained using the pilot-scale system can be used as a baseline for advanced
modeling, control, and optimization of flotation processes. With its functional versatility,
the system can be easily adapted to almost any process condition and, in that way,
provide valuable process-related knowledge necessary for the development of successful
scale-up strategies and more efficient flotation cells.
3.7. ACKNOWLEDGEMENT
The authors would like to acknowledge FLSmidth Minerals and all others who
graciously supported this work.
3.8. REFERENCES
Deglon, D.A., 2005. The effect of agitation on the flotation of platinum ores. Minerals
Engineering, 18(8): 839-844.
Deglon, D.A., Sawyerr, F. and O'Connor, C.T., 1999. A model to relate the flotation rate
constant and the bubble surface area flux in mechanical flotation cells. Minerals
Engineering, 12(6): 599-608.
Efron, B. and Tibshirani, R., 1993. An introduction to the bootstrap. Monographs on
statistics and applied probability 57. Chapman & Hall, New York, xvi, 436 p. pp.
Finch, J.A., Xiao, J., Hardie, C. and Gomez, C.O., 2000. Gas dispersion properties:
Bubble surface area flux and gas holdup. Minerals Engineering, 13(4): 365-372.
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Virginia Tech | CHAPTER 4:
COMPARISON OF TWO BUBBLE SIZING METHODS
FOR PERFORMANCE EVALUATION OF
MECHANICAL FLOTATION CELLS
Authors: Miskovic, Sanja; Luttrell, Gerald
Submitted: March, 2011
To: Roe-Hoan Yoon Symposium, SME 2011, Proceedings
4.1. ABSTRACT
A new in-situ optical bubble sampling method capable of collecting representative
samples through different regions of a flotation cell has been developed. The new system
was compared to the standard McGill ex-situ bubble sampling method. All experiments
were carried out using a fully automated, pilot-scale 0.8 m3 Dorr-Oliver® flotation cell.
Bubble images were taken from multiple locations within the cell. The cell was operated
as a batch reactor under various operating conditions by altering impeller tip speed, gas
flow rate, and frother concentration. Two methods of image analysis were also evaluated,
i.e., a new software package called BubbleSEdit and the standard McGill/ Northern
Eclipse software. BubbleSEdit is a template matching technique that analyzes overlapped
bubbles and bubble clusters, which results in detection of more than 90% of all bubbles in
an image. Bubbles observed with the in-situ sampling method appeared to be larger than
bubbles recorded with the McGill ex-situ method. Furthermore, it was found that the
mean bubble size determined by the McGill/Northern Eclipse bubble sizing method was
smaller than the BubbleSEdit values.
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Virginia Tech | 4.2. INTRODUCTION
The dispersion of gas into bubbles and their rise due to buoyancy are very
important fundamental phenomena that contribute significantly to the hydrodynamics of
the flotation process. Therefore, accurate gas dispersion data are required to better
understand the physical processes governing flotation. The importance of bubble size on
flotation efficiency has first been recognized by Nevett in 1920. He concluded that air
must be completely atomized in the pulp in order to reach optimal separation conditions
(Nevett, 1920). Similarly, using high-speed cinematography in his experiments, Bennett
(1958) concluded that, for a constant air supply rate, flotation rate increases by producing
a larger number of smaller bubbles. This relationship is understandable since the amount
of created gas-liquid interfacial area directly affects particle collection kinetics. In other
words, bubble size governs the surface area over which solid particles and bubbles
interact. Furthermore, this free surface area contributes significantly to system
hydrodynamics and overall flotation performance. Research efforts to better understand
gas dispersion in flotation cells have intensified because of the desire to design larger and
more efficient flotation cells that are necessary to treat the lower grade and more finely
disseminated ores currently being mined (Sawyerr, 1998).
The bubble size distribution (BSD) in flotation systems generally depends on
operational variables such as aeration rate, pulp surface tension, impeller rotation speed,
as well as design variables such as impeller and stator configurations and cell geometry.
Unfortunately, current flotation models developed from first principles cannot predict
bubble size distributions from these basic input variables. On the other hand, by
combining computational fluid dynamics (CFD) and population balance models (PBM),
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Virginia Tech | the calculation of local BSDs becomes feasible. In order to make them reliable tools for
flotation machine design and optimization, predicted BSDs need to be validated
experimentally by performing local bubble size measurements (Ranade, 2002). For that
reason, a reliable and accurate method for local bubble size measurement, in both
turbulent and quiescent regions of the flotation machine, needs to be developed for
laboratory-, pilot- and industrial-scale conditions.
4.2.1. Bubble size measurements
One of the first laboratory measurements of bubble size was performed by Rodger
(1956). At that time, bubble sizing was labor intensive and fully manual process. Over
the last six decades, the bubble sizing methodology has been improved through the
implementation of various new techniques that, typically, brought a greater level of
automation to the process. While automation has increased the speed of the analysis, it
produced undesirable side effects, such as sensitivity to image noise and ignoring of large
bubbles. For this reason, a considerable amount of manual work is still required to assure
correctness of obtained results.
Techniques capable of measuring bubble size in multiphase flows are typically
classified depending on their operating principles. A number of experimental and
empirical methods for determining bubbles sizes have been used so far and include
photographic (Grau, 2002; Tucker, 1994; Yianatos, 1988), laser diffraction (Couto,
2009), interferometric laser imaging (Kawaguchi, 2002), electro-resistivity (Yasumishi,
1986), acoustic (Pandit, 1992), dynamic bubble disengagement (Standish, 1991),
ultrasonic pulse transmission (Stravs, 1986), and many other techniques. Calculations
using empirical or semi-empirical approaches have also been employed (Dobby, 1988).
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Virginia Tech | Of these, the photographic technique is the most commonly used method for bubble
sizing today. The availability of high speed digital cameras and advanced and automatic
image processing techniques has made photographic measurements much easier. Most
commonly, images of bubbles are taken by high-speed CCD cameras through windows
installed in the vessel wall (Soler, 2003). One of the fundamental problems of this
technique is the impact of the inherently variant distance between the focal plane and
bubbles in motion. Another problem with this technique is that a small change in optical
conditions, such as lighting, significantly affects image quality. The minimum detectable
bubble size depends on factors such as camera resolution, CCD cell sensitivity, and
optics type. Also, to eliminate blur caused by bubble motion, image exposure time has to
be kept very short.
Another important aspect of photographic bubble sizing is image analysis. The
image analysis of bubbles captured in multiphase flows, with high concentrations of
bubbles and/or suspended particles, is challenging due to bubble overlap and bubble
clustering (Junker, 2007). Also, bubbles present in the optical path between the camera
and the focal plane, and bubbles behind the field of focus, significantly degrade image
quality. For that reason, image analysis methods available today often fail to clearly
distinguish individual bubbles from bubble swarms, and are limited to transparent, two
phase (gas/liquid) mixtures with low bubble concentrations (<10% by volume).
Moreover, photographic bubble sizing is challenging in industrial-scale systems and is
more often used in simplified laboratory evaluations. The sampling technique must be
rugged to withstand harsh environmental conditions. This is especially important when
the equipment has to be deployed in industrial plants, where erosive/corrosive conditions
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Virginia Tech | are present and flotation cells may be wet, dirty, vibrating and difficult to access.
Additionally, the bubble measuring system should be compact and light in order to
provide the least interference with the natural fluid flow in the cell.
The size of bubbles obtained in flotation experiments also vary significantly at
different locations within a flotation cell. A good measure of overall bubble population
should be obtained by multiple measurements at different points within the cell. Bubble
sizes obtained this way should be weighed based on their relative position to the high
energy dissipation zone (impeller/stator zone) and averaged to get an overall mean bubble
size. Bubble sizes differ in radial and vertical directions throughout the flotation cell, and
larger bubbles are expected near the impeller top and center of the cell, while smaller
bubbles can be found near the highest energy dissipation zone and close to the bottom of
the cell (Zhou, 1993). Therefore, care must be taken to ensure that the method used to
obtain samples of bubbles within the pulp is not biased.
An ex-situ bubble sampling method is the most commonly used photographic
method for evaluation of flotation cells. In this approach, bubbles are directed from the
pulp zone of the flotation cell into an external viewing chamber where they are exposed
for imaging. Some of the most commonly used ex-situ bubble sizing systems in flotation
cells are include the University of Cape Town (UCT) bubble size analyzer (Tucker,
1994), Helsinki University of Technology (HUT) bubble size sampler (Grau, 2002),
McGill bubble size analyzer (MBSA) (Hernandez-Aguilar, 2002), USM bubble size
sampler (Yianatos, 2001), and LTM-BSizer method (Rodrigues, 2003). Unfortunately,
the bubble sizes measured in various flotation systems, which include different scales and
cell types, show a notable spread. The reason for this deviation has not yet been
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Virginia Tech | adequately addressed in detail in the technical literature. It is not clear whether the
problem is caused by chemical variations among the systems, cell configuration (cell
size, type, and geometry), or problems with the experimental sampling and imaging
techniques.
This article describes a new photographic in-situ sampling method for
determining BSDs within a flotation cell. The in-situ method has been tested using a 0.8
m3 Dorr-Oliver® pilot-scale flotation cell operating as a batch two-phase (air-water)
system. The data obtained from the in-situ method have been compared with
measurements obtained using standard MBSA ex-situ method. Both methods have been
used to measure local BSDs at different locations within the flotation cell. This article
highlights the advantages and limitations of each method and discusses major sources of
discrepancies between results obtained with these two methods.
4.3. EXPERIMENTAL
4.3.1. Experimental setup
The bubble sizing work was conducted using a 0.8 m3 Dorr-Oliver® flotation cell
that was designed and installed in the Mining and Minerals Engineering Laboratory at
Virginia Tech. The modular stainless-steel tank was composed of five interchangeable
segments, including three body rings with different heights and two top launders (internal
and external). For the bubble sizing tests, the tank was configured with an internal
launder with the overflow lip positioned 1.12 m from the tank floor. New Dorr-Oliver®
wetted parts (impeller, stator and impeller shaft) were designed and fabricated to fit the
new tank. The tank had a diameter (T) of 1.02 m and impeller diameter (D) of 20.3 cm,
which gave an overall T/D ratio of 5.
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Virginia Tech | 4.4. IMAGE ACQUISITION
A compact GEViCAM GP-21400 1.5 mega pixel Giga-bit Ethernet high-speed
CCD camera (34x34x68 mm) was used to collect bubble images. The required
magnification was achieved using a FUJINON HF9HA-1B 9 mm f/1.4 fixed focal lens.
The monochrome camera was operated with the maximum resolution of 1392x1040
pixels. For measurements with the MBSA method, bubble images were captured as they
passed through the external viewing chamber using a camera frame rate of 23 fps and
1/250 s shutter speed. The depth of field (DOF) was estimated to be 3.8 mm for the
selected optical conditions (observed bubble distance from CCD detector of 7 cm,
selected aperture of f/3.6, and circle of confusion of 10 µm). This DOF was also
measured and confirmed directly by using the Edmund Optics DOF 5-15 depth of field
target.
Details of the MBSA method and corresponding bubble sampling procedures
have been presented previously by Hernandez-Aguilar (Hernandez-Aguilar, 2002). Based
on findings from an initial series of tests with the MBSA method, a couple of new
features were added to this standard system to improve image quality and make it more
suitable for the tests that had to be performed. In order to allow isokinetic bubble
sampling, a peristaltic pump was used to continuously draw a bubble sample to the
MBSA viewing chamber at a rate of 1 and 2 l/min for the quiescent and turbulent zones
of the flotation cell, respectively. To further improve sampling conditions, the suction
tube was aligned with the flow direction by adding either 45° or 90° elbows to the end of
the sampling tube. For example, a 90° elbow was chosen when sampling the primary
horizontal jet from the impeller. The halogen light source provided with the original setup
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Virginia Tech | was replaced with a more uniform 5500 K daylight white panel LED light (3000 lumens)
to provide brighter backlighting. Finally, the standard glass on the viewing chamber was
replaced with frosted glass to provide uniform light diffusion. In this way, image quality
and bubble detection accuracy was improved significantly.
Alongside the standard MBSA ex-situ bubble sampler, a new in-situ photographic
method was utilized. A second GEViCAM GP-21400 CCD camera equipped with a
FUJINON HF9HA-1B 9 mm lens was used with the in-situ system. Back illumination of
bubbles was achieved using a compact, bright field, Advanced Illumination SL2420 LED
spot light, which was pulsed with an Advanced Illumination S4000 strobe controller. A
red LED light (660 nm) was chosen since the long-wavelength light travels longer in
scattering media and was preferable for observation of contaminated liquids and
multiphase flows. Also, the bubble images obtained this way had improved border
definition. A ground glass diffuser was also installed in front of the LED light to provide
uniform light distribution. The system was set up to provide 10-100 µs long LED light
pulses, which defined the total image exposure time. Using this exposure time, bubbles
moving in a fluid flow of up to 15 m/s could be clearly captured. The camera provided
1392x1040 pixel monochrome images at a frame rate of 10 fps. The DOF was estimated
to be 3 mm for the selected optical conditions (distance from focused bubbles to CCD
detector was 6 cm, lens aperture was fixed at f/5, circle of confusion was 10 µm and a 1
mm extension ring was added). An Edmund Optics 5-15 depth of field target was also
used to confirm the expected DOF value.
For the in-situ system, both the high-speed camera and LED spot light were
mounted inside aluminum watertight enclosures that faced each other (bottom left, Figure
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Virginia Tech | 1). The gap width between the light source and the camera was manually adjustable from
6 to 50 mm. As the gap size decreased, more light passed through the moving bubble
swarms. A smaller gap also decreased the number of bubbles viewed per single image,
which provided less overlap and fewer counting errors for dense bubble populations. A
gap size of 20 mm was selected and used through all experiments, which provided about
two times larger depth of the view volume than the largest expected bubble diameter.
This gap width was found to be large enough to allow entrance of larger bubbles into the
measurement field and small enough to produce good bubble images. In this way, the
influence of the sampling method on measured bubble sizes was reduced to a minimum.
Due to its compact and cylindrical design, the in-situ system had a relatively small effect
on fluid flow within the cell. The field of view (FOV) inside the flotation cell obtained
with in-situ method was 17.5 x 13 mm and the system was capable of measuring bubble
sizes in the range from 50 µm to 10 mm. In comparison, the FOV for the ex-situ MBSA
method was 31 x 23 mm, which gave a maximal detectible range of bubble sizes of 90
µm to 20 mm.
4.4.1. Experimental procedure
Measurements of gas holdup and superficial gas rate were conducted for all
experiments performed using the pilot-scale Dorr-Oliver® flotation cell. A detailed
description of the procedures and instrumentation used in these experiments has been
given elsewhere (Gomez, 2007; Gomez, 2002; Hernandez-Aguilar, 2002). Torque
measurements were also performed for all experiments. The cell operating conditions
were modified by changing the impeller speed and gas flow rate. Experiments were
carried out at two impeller tip speeds (4 and 5 m/s) and three gas flow rates (20, 40, and
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Virginia Tech | 60 m3/h) giving overall superficial gas flow rates of 0.69, 1.37, and 2.06 cm/s,
respectively. In order to run tests under non-coalescing conditions, 14 ppm of MIBC
frother was used in all experiments. This concentration (14 ppm) was higher than the
critical coalescence concentration (CCC) for the MIBC frother (Nesset, 2007).
Two bubble sampling methods, the standard MBSA ex-situ method and new in-
situ method, were used simultaneously for local bubble sampling. Since BSDs varied
depending on the sampling location, bubbles were acquired from three different positions
in the cell for both methods (locations 1, 3, and 4) and from three additional locations
using the in-situ method (locations 2, 5, and 6). All sampling locations are presented in
the Figure 2. The locations were selected to allow bubble sampling from the major fluid
streams in the cell and were distributed evenly to allow determination of the spatial
variation of BSDs within the flotation machine.
All sampling positions, except location 6, were arranged vertically at a radial
distance of 15 cm from the stator ring. Location 6 was positioned directly above the
impeller-stator gap, 3 cm above the stator ring. Location 1 was located in the quiescent
zone of the cell, while sampling points 3 and 4 were located in the high energy
dissipation zone. Sampling point 3 was positioned 2.5 cm above the stator ring, sampling
point 4 was 1 cm bellow the stator ring, and sampling point 5 was positioned 6 cm below
the stator ring. Bubbles detected at location 4 were indicative of bubbles carried by the
main high dissipation energy jet leaving the impeller. Based on existing turbulent
flotation models, location 4 was considered most significant since considerable bubble-
particle collisions occur in this region.
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Virginia Tech | 4.4.2. Image processing
After sampling was completed, the captured images were typically pre-processed
and then analyzed using image analysis software. Even though this procedure provided
an efficient alternative to manual counting, miscounting or misclassifications occurred
frequently. The main reason for this problem was the presence of overlapped bubbles and
bubble clusters in the image. Most software packages used for image analysis of
multiphase flows fail to discern individual bubbles from bubble clusters. This problem
became more significant when a wide range of bubble sizes was present in the bubble
sample. In particular, the presence of large bubbles in the image greatly biased the BSD
since they covered a significant portion of the image, overlapped smaller bubbles, created
bubble clusters, had an irregular shape, and touched image edges. For this reason, a more
sophisticated processing technique had to be used to reduce these image processing
errors.
For the analysis of all image sets acquired by MBSA method, a customized
Empix Imaging Northern Eclipse 6.0 software package interfaced with an Excel/Visual
Basic user interface was used. This software offers several advantages including full
automation, fast analysis of a large image sets (2 s/image), and direct export to Excel
spreadsheets where statistical analysis is automatically performed. On the other hand, this
technique also has a number of inherent shortcomings including high sensitivity to the
selected threshold value, lack of visual confirmation of analysis accuracy, incorrect
reporting of noise as bubbles, and the exclusion of overlapped objects (Figure 4.4). In
most cases, only 5 to 40% of all objects in one image were recognized as bubbles using
this commercial package.
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Virginia Tech | images are automatically stored and the user can easily revisit them and make manual
corrections if necessary. Typically, in the final step of BSE analysis, the user is required
to manually add ellipsoidal and irregular bubbles using free-hand drawing tools.
4.4.3. Results reporting
Mean bubble size is the most commonly used parameter to describe a bubble size
distribution. This term can be calculated using:
(cid:2869)
∑(cid:3041) (cid:1866) D(cid:2926) (cid:3043)(cid:2879)(cid:3044)
D (cid:3404) (cid:4678) (cid:3036)(cid:2880)(cid:2869) (cid:3036) (cid:2919)(cid:4679) (Eq. 4.1)
(cid:3043)(cid:3044) ∑(cid:3041) (cid:1866) D(cid:3044)
(cid:3036)(cid:2880)(cid:2869) (cid:3036) (cid:2919)
where D is bubble mean diameter, n is the number of bubbles of diameter d; and p and
pq i i
q are dimensionless indices defining the moment of the mean. The most commonly used
mean diameters include the number or arithmetic mean diameter (D ), surface mean
10
diameter (D ), volume mean diameter (D ), Sauter mean diameter (D ) and mean mass
20 30 32
diameter (D ).
43
In order to obtain number frequency and number cumulative BSDs, as well as
volume frequency and volume cumulative BSDs, measured bubbles are typically
classified into a number of finite size categories. A typical BSD measured in a flotation
cell usually contains a large number of small bubbles and several large non-spherical
bubbles. For that reason, a dense discretization was used for small bubbles, and size
categories were linearly shifted toward larger bubble sizes. To obtain statistically
significant BSDs for wide bubble populations, a greater number of images and a large
number of bubbles must be analyzed. The range of expected bubble sizes reported in
literature varied from 40 µm to 20 mm, with most studies reporting the size range from
40 µm to 2 mm. In most cases, authors working on multiphase flow characterization
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Virginia Tech | claimed to reach statistically significant results by analyzing only from 500 to 1000
bubbles (Junker, 2006). While this might be true for monodispersed, or nearly
monodispersed bubble populations, widely dispersed bubble populations require much
larger samples. In order to reach statistically significant mean bubble diameter, a
population of 1000 bubbles was generally found to be sufficient for D analysis. On the
10
other hand, a sample of 4000 or more bubbles was found to be necessary for D and D
32 43
analyses. In order to reach this population size, a great number of images had to be
analyzed. Generally, the required number of images that had to be analyzed decreased as
the mean bubble size decreased. In light of these requirements, bubble images captured
with modified MBSA method at locations 1, 3, and 4 were analyzed with both the
standard NE and new BSE image analysis techniques. In order to reach a minimum of
4000 bubbles necessary to generate statistically significant results, at least 150 images
were processed with the fully automated NE technique and about 15 random images were
analyzed with the semi-automated BSE technique.
4.5. RESULTS AND DISCUSSION
4.5.1. Effect of image analysis technique on measured bubble size
Figure 4.6 shows the volume and number frequency distributions obtained with
both image analysis techniques for identical image sets. For any experimental condition
and any sampling location, the NE technique failed to count bubbles larger than 2 mm,
which is well illustrated in the volume frequency distribution plots. The number
frequency BSDs revealed insignificantly small numbers of bubbles larger than 2 mm for
most tests. On the other hand, large bubbles represent a significant portion of the total gas
volume and, therefore, need to be detected accurately
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Virginia Tech | under various operating conditions. In order to produce clear presentation of the results
and provide easier comparison between sampling techniques, both BSDs are presented in
a logarithmic bubble diameter scale. Also, presenting the data as cumulative distributions
helped to smooth out variations found in the frequency distributions. The comparison of
BSDs obtained with both methods suggests that the majority of the gas volume is carried
by large bubbles, which makes them extremely important for flotation performance
evaluations. The presence of relatively large bubbles or bubble slugs significantly
increases the Sauter mean diameter, decreases the superficial gas flow rate, and
consequently, decreases the bubble surface area flux, which is known to be a factor
directly related to flotation kinetics.
Intrinsic differences in the optical characteristics of each sampling system did not
greatly influence the size limit of the smallest bubble detected, and this size was nearly
identical for both sampling methods. On the other hand, the size of the largest detected
bubble differed significantly between the methods. Under the same conditions, the in-situ
method managed to capture larger bubbles in the gas-liquid mixture. The data obtained
with the ex-situ method indicate that the majority of bubbles detected are within a narrow
size range (<2 mm), which are contained in the left peak of the bimodal volumetric BSD
curve. It is also interesting to note that all of the cumulative BSDs obtained with the ex-
situ method do not have the standard characteristic S-shape. This irregularity was found
to become more severe as the sampling tip was moved from the top to the bottom of the
cell. This trend may be an indication of the increased likelihood that bubbles interact and
coalesce as they travel along the sampling tube, which would be an inherent problem for
the ex-situ method at greater depths.
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Virginia Tech | Under the same operating condition, bubbles observed at locations 1, 2, 3 and 6
appeared to be larger than bubbles observed at locations 4 and 5, which are positioned
bellow the stator ring. Moreover, regardless of the experimental conditions, bubbles or
slugs of gas that exceeded 6 mm diameter size were observed at most positions except
location 5.
This observation indicates that larger bubbles, with higher rise velocities than
local fluid flow velocities, do not follow the main fluid flow pattern. Only a fraction of
generated bubbles from the impeller/stator zone appear to follow the main streamlines
and return to the high energy dissipation zone multiple times.
This viewpoint is in good agreement with visual observations of flow patterns in
gassed stirred vessels that indicate that very large bubbles often pass directly through the
stirred tank, concentrating near the center of the vessel, while small bubbles recirculate in
the cell (Nienow, 1977).
Occasionally, very large gas slugs are observed at sampling location 6, directly
above the impeller/stator gap, indicating the inability of the impeller to fully disperse all
introduced air. This data also appears to verify that the local fluid flow direction and
velocity, and local bubble velocity, have a direct effect on the local BSD, which is in
agreement with an earlier study made by Schäfer (2000).
To quantitatively assess the influence of sampling location on the measured
bubble size, Sauter mean diameters and volume fractions of bubbles larger than 1.5 mm
are plotted versus sampling locations in Figure 4.10. For a constant impeller tip speed of
5 m/s and various aeration rates, the largest Sauter mean bubble diameters were measured
at location 3. In contrast, the smallest Sauter mean diameters and lowest volume fractions
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Virginia Tech | 4.6. CONCLUSIONS
An existing ex-situ and a new in-situ bubble sampling methods were used
simultaneously to investigate local bubble size distributions in a pilot-scale (0.8 m3)
Dorr-Oliver® flotation cell. In addition, two types of image analysis software, the fully
automated Northern Eclipse package and semi-automated BubbleSEdit package, were
used to analyze captured images and to obtain bubble size distributions for each image
set. All experiments were conducted in two phase system and the flotation cell was run as
a batch reactor.
The experimental data showed that significant variations in bubble sizes occurred
throughout the cell and under different operational conditions. Due to this variability,
care must be taken when performing bubble measurements in mechanical flotation cells.
Bubbles found bellow the froth-pulp interface contribute significantly to the processes
occurring in the froth zone, while bubbles sampled in the impeller discharge stream
contribute to the overall bubble-particle interaction dynamics occurring in the turbulent
zone of the cell.
Measured bubble size distributions and Sauter mean bubble diameters revealed
significant differences between sampling methods and image analysis techniques. In
general, the commonly used ex-situ bubble sampling methods and image analysis
techniques fail to detect larger bubbles. This oversight can result in misleading
conclusions since larger bubbles carry a significant fraction of the total gas volume,
which under some operating conditions can exceed 70% of the total introduced gas
volume that are carried by the bubbles larger than 1.5 mm.
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Virginia Tech | Nevertheless, the general simplicity and ease of use makes the ex-situ method
useful whenever a large number of tests have to be performed in a short timeframe, which
is typical for experiments in industrial settings. However, information gained by the ex-
situ sampling method give local mean diameters of bubbles entering the froth phase.
Therefore, in order to achieve a better insight into the spatial gas distribution profile in
the cell a radial screening of bubble sizes has to be performed.
The new in-situ sampling method and BubbleSEdit image analysis technique are
more demanding, but provide a more accurate estimation of the true bubble size
distribution at all locations within a mechanical flotation cell.
4.7. ACKNOWLEDGEMENTS
The authors would like to thank James Waddell, Robert Bratton and other staff of
Center for Advanced Separation Technologies (CAST) for their generous help throughout
the period of this research study. The financial, equipment, and technical support
provided by FLSmidth Minerals is also gratefully acknowledged.
4.8. REFERENCES
Alves, S.S., Maia, C.I., Vasconcelos, J.M.T., Serralheiro, A.J., 2002. Bubble size in
aerated stirred tanks. Chem Eng J 89, 109-117.
Bennett, A.J.R., Chapman, W. R., Dell, C. C., 1958. Studies in froth flotation of coal,
Third international coal preparation congress, Brussels-Liege, p. Paper E2.
Clift, R., Grace, J.R., Weber, M.E., 1978. Bubbles, drops, and particles. Academic Press,
New York.
Couto, H.J.B., Nunes, D.G., Neumann, R., Franca, S.C.A., 2009. Micro-bubble size
distribution measurements by laser diffraction technique. Miner Eng 22, 330-335.
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Virginia Tech | 5.2. INTRODUCTION
Flotation is the most widely used separation process in the mineral processing
industry today. This process is used for separation of almost all sulfide and many non-
sulfide metallic minerals, industrial minerals and energy minerals such as coal and
bitumen. There are four main types of flotation cells used in the mineral processing
industry: mechanical flotation cells, pneumatic flotation cells, froth separators, and
flotation columns. From the beginning, mechanical flotation cells have been the most
widely used flotation cells in the mineral industry. Mechanical flotation cells consist of a
tank, typically cylindrical shaped, fitted with an impeller drive assembly and a stator. The
main function of the stator, which is positioned around the impeller, is to transform
tangential flow of the pulp in the cell in the radial direction. The impeller, on the other
hand, provides the energy necessary for successful flotation operation and is therefore
considered to be the heart of the flotation cell. Bubbles are generated and dispersed by
forced introduction of the air through a deeply submerged rotating impeller in forced-air
mechanical cells and by self-aeration of shallow rotating impellers in self-aerated
mechanical cells.
The main goal in the process of designing of any flotation cell is to maximize gas-
liquid interface in the pulp (the particle-water-air mixture) and hence to increase the
probability of collisions between air bubbles and hydrophobic particles. Furthermore,
every flotation cell should be designed to achieve the following performance functions:
to generate adequate turbulent conditions for successful bubble-particle
attachment in the contact zone,
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Virginia Tech | Most of this energy is dissipated through micro-interactions of all three phases, which
include:
bubble-particle collisions, attachment, and aggregation (Luttrell and Yoon,
1992a),
liquid-particle viscous friction and lubrication (Eskin et al., 2005), and
particle-particle partially inelastic collisions.
In general, bubble size (or bubble size distribution) in the flotation system is
determined by the following three hydrodynamic processes:
bubble formation in gas generator,
bubble breakup, and
bubble coalescence.
The latter two processes are directly governed by the local turbulence. To develop a
better understanding of the role of gas bubbles in the flotation system, knowledge of the
above-mentioned phenomena is required.
During the process of bubble formation, a fraction of the total energy supplied to
the system is directly transformed into the free surface energy of newly created bubbles.
A majority of bubbles created in flotation systems are generated in the zone between the
impeller and stator blades, which is maximum energy dissipation zone of the cell. In this
zone, air cavities that are initially formed at the low pressure region of the impeller blades
are detached from the impellers blades edges and are carried into the high energy
dissipation zone where the bubble breakup occurs. Bubble breakup is caused by the
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Virginia Tech | dynamic pressure and shear stresses on the bubble surface induced by shear flow and
turbulence (Hinze, 1955).
Bubbles created in the high energy dissipation zone are carried along by the radial
flow coming from the impeller and are scattered throughout the pulp contained in the
body of the flotation cell (van't Riet and Smith, 1973). Thereafter, bubbles climb through
the vessel due to their buoyancy but are also randomly pushed around by the existing
turbulence in the cell.
In the flotation cell, turbulence is the primary mechanism responsible for breakup
of the bubbles that are initially created in the high energy dissipation zone (Kolmogorov,
1949). Only eddies that are of the similar length scale as the bubble size can break the
bubbles. On the other hand, the large eddies can only transport the bubbles, while very
small ones do not affect the bubbles (Olmos et al., 2001). In order to determine the actual
size limit of eddies responsible for bubble breakage, Prince and Blanch (Prince and
Blanch, 1990) conducted experiments to show that only eddies bigger than 0.2d are able
to break bubbles of diameter d, while eddies bigger than d can only move them.
Therefore, based on Wu et al. (Wu et al., 1998), bubble breakup rate depends on the
frequency of collisions between bubbles and eddies of a similar size. Moreover, bubbles
will break up into smaller bubbles only when the maximum hydrodynamic forces in the
liquid (that tend to break up the bubbles) are larger than the surface tension force (that
tends to stabilize the bubbles) (Angeli and Hewitt, 2000; Hinze, 1955; Kerdouss et al.,
2006). This force balance is typically quantified by the liquid Weber number:
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Virginia Tech | collision, the bubble approach velocity has to be sufficient to overcome the pressure rise
due to the liquid being forced out between the bubbles (Lane et al., 2002). Therefore,
coalescence is the phenomenon that significantly reduces the dispersion efficiency of the
flotation system (Cho and Laskowski, 2002). Coalescence strongly depends on chemical
parameters of the system, such as the liquid surface tension, volumetric fractions of the
dispersed phase, and characteristics of the turbulent flow field (Chesters, 1991).
After they have been generated, bubbles in the flotation system are moved into
different zones of the cell depending on the balance between the bubble buoyancy force
and surrounding drag forces. Eventually, all bubbles leave the pulp by forcing themselves
out through the pulp-froth interface and then, by complex processes that occur in the
froth phase, a majority of the gas finally leaves the cell directly through the froth surface
or is, in less extent, carried from the system by the recovered froth.
Therefore, local bubble size and bubble size distribution in the flotation cell
strongly depends on various operational, technical and chemical factors whose effects on
bubble size should be taken into account while designing or modeling a flotation process.
Some of the factors that have the utmost effect on bubble size in the flotation systems are:
the total gas intake,
the total supplied energy,
the physical and chemical properties of the liquid and solid phases,
the impeller/stator design,
the impeller relative location to the bottom of the cell, and
the size and geometry of the cell.
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Virginia Tech | Therefore, during the flotation process, the gas-liquid hydrodynamics in the system
strongly depend on the type of bubble generator used, so the choice of a proper
impeller/stator assembly to satisfy the necessity of optimal gas dispersion is the key for
the success and economy of the process. However, the mechanism of bubble generation
in the flotation systems has not yet been explored in depth and differences between the
bubble generation mechanisms of different flotation cells have not yet been addressed in
the literature.
This work presents results obtained through an initial industrial-scale
experimental investigation on gas dispersion performance of two commercial FLSmidth
mechanical flotation cells: forced-aerated Dorr-Oliver® and self-aerated WEMCO®. The
preliminary results revealed significant differences in bubble size distributions between
the two cells. To better understand this phenomenon, a comprehensive pilot-scale study
under non-coalescing conditions was conducted. Non-coalescing conditions were chosen
to allow separate investigation of bubble break-up mechanisms for each cell type by
eliminating coalescence effects on the final bubble size. Furthermore, the region under
consideration during this investigation was the turbulent zone surrounding the
impeller/stator assembly, where the bubble break-up process occurs and determines the
bubble mean size (Laakkonen et al., 2005a; Parthasarathy and Ahmed, 1994;
Parthasarathy, 1994; Parthasarathy, 1991).
This study aims to determine the effect of different generator designs on the
bubble generation process and on the gas dispersion pattern within the flotation cell.
Further, knowledge of gas dispersion mechanisms provides valuable information on the
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Virginia Tech | bubble size and bubble interfacial area in the flotation system, which are key parameters
governing the flotation process.
5.3. EXPERIMENTAL
5.3.1. Industrial-scale flotation cells
Two industrial-scale mechanical flotation cells, the 300m3 WEMCO® SuperCell
and 330m3 Dorr-Oliver® SuperCell, were tested in order to investigate their gas
dispersion characteristics during a plant survey of a commercial copper concentrator. In
order to collect local bubble samples from the flotation cells a visual/photographic
technique was used. The photographic method was chosen since it is able to detect the
broadest bubble size distribution in comparison with other methods used for bubble
sizing.
For the purpose of this investigation, bubble sizing experiments were performed
on both cells using the McGill ex-situ bubble sampling method (Gomez and Finch, 2002;
Gomez and Finch, 2007). By using this method, bubbles are observed, as they rise from
the sampling tube and enter the viewing chamber, through an inclined glass window of
the viewing chamber illuminated from the back and placed outside of the flotation tank
(Figure 5.2). The suction point of the bubble sizing apparatus was positioned 130 cm
below the launder lip and at the mid-radial distance from the froth crowder to the launder.
The sampling locations for each cell tested are shown in Figure 5.3.
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Virginia Tech | Due to the presence of weak hydrodynamic forces in the pulp surrounding the
bubble sampling tube and relatively long length of the sampling tube, the sampling
apparatus had to be anchored at four points to allow unimpeded operation. Bubble images
were collected for several different operating conditions. Operating conditions were
changed by varying the impeller agitation rate (from 5 to 9 m/s impeller tip speed) and
aeration rate (from 0.7 to 1.88 cm/s global superficial gas velocity) for the Dorr-Oliver
cell and by changing the aeration rate (from 0.8 to 1.5 cm/s superficial gas velocity) and
the froth depth (from 18 to 68 cm) for the WEMCO cell. Bubbles were recorded at the
end of each test period, which was at least fifteen minutes from the moment operating
conditions were changed, to allow the system to reach a steady-state. Approximately 400
bubble images were collected for each operating condition and then subsequently
analyzed with BubbleSEdit image analysis software (Zabulis et al., 2007). BubbleSEdit
utilizes a cross-correlation technique, which ensures detection of all bubbles in an image
and, in that way, allows their inclusion into the final analysis of bubble size distributions.
5.3.2. Pilot-scale flotation cells
In order to extensively investigate a bubble generation process within the flotation
cells, a series of bubble size measurements were performed on two 0.8 m3 pilot-scale,
Dorr-Oliver and WEMCO, flotation cells. The cells were operated as batch reactors, with
water and air only (a two-phase system). The frother selected for this investigation was
methyl isobutyl carbinol (MIBC), which was added in concentrations over its critical
coalescence concentration. This created a non-coalescing environment in the cell
allowing investigation of gas dispersion characteristics of each cell type pertinent to
bubble breakage mechanisms.
154 |
Virginia Tech | Although an ex-situ bubble sampling method represents a well-designed solution
for the bubble sampling in the upper quiescent zone of industrial flotation cells, it cannot
be used successfully for bubble sampling from the lower regions of the cell. Bubbles
present in the turbulent zone generally follow major fluid streamlines and therefore fail to
enter the sampling tube. Since bubble size distribution varies within a flotation cell and is
a direct function of the relative location from the impeller, a new bubble sampling
method, capable of collecting representative samples throughout all regions of the
flotation cell, was developed and used in this pilot-scale study.
A new in-situ bubble sizing apparatus was designed to perform accurate
measurements of bubble sizes through different regions of the flotation cell and to
minimize potential flow interference within the cell. The system can be submerged into
any location of the flotation cell, where it directly captures images of bubbles from the
bubble stream. Moreover, it is capable of measuring bubble sizes in the range of 50 μm to
10 mm as defined by the resolution and magnification of the optical system employed,
which was GP-21400 GEViCAM GigE high-speed CCD camera with 1392×1040 pixels
resolution and a compact red LED backlight. Both elements were mounted inside of
watertight, pressurized enclosure (Figure 5.4).
Gap width between the light source and the camera was set to be 10 mm. This gap
width was found to produce images with the least number of bubble overlaps, which
created better conditions for subsequent image analysis. Image analysis was performed
utilizing BubbleSEdit software. Results of automatic image analysis were manually
corrected for each image analyzed, which ensured that more than 90% of all bubbles in
an image were included in the analysis.
155 |
Virginia Tech | hand, the Dorr-Oliver cell was screened at three different locations in a vertical plane, 15
cm from the stator ring, and from one other location positioned 3 cm above the impeller
stator gap. In both cases, the location 2 was selected to allow bubble sampling from the
discharge stream coming from the impeller. Also, positions 1 and 3 represent,
respectively, fluid streams sampled 8 cm above and 8 cm below sampling point 2.
5.4. RESULTS
Figure 5.6 shows bubble size frequency (bars graph) and bubble size cumulative
(dashed line) distributions, and fractions of the total gas contained in each size class (area
graph) for the 330 m3 Dorr-Oliver flotation cell at different operating conditions. The
illustration also shows corresponding Sauter mean and number mean diameters, as well
as a fraction of the total gas volume contained in bubbles larger than 1.5 mm. The top
row in the illustration shows the effect of increasing aeration rate on the bubble size
distribution, under the same agitation rate. It can be clearly seen that an increase in
aeration rate shifts the bubble size distribution toward larger bubble sizes, which is also
reflected through an increase in mean bubble diameters from 1.5 to 1.97 mm for the
Sauter mean diameter, and from 0.92 to 1.18 mm for the number mean diameter.
The bottom row in the illustration shows the effect of an increase in agitation rate
on bubble size distribution in the cell, under the same aeration rate. In this case, measured
bubble sizes and corresponding distributions do not follow expected trends. The bubble
population shifts toward larger sizes when the impeller speed increases from 5.44 to 7.2
m/s and then they move back toward smaller sizes when the impeller speed changes from
7.2 to 8.95 m/s. The reason for this irregularity may lie in the method of bubble sampling.
158 |
Virginia Tech | Throughout this investigation, bubble sampling was performed in the quiescent zone of
the cell, at half-radial distance from the launder lip to the froth crowder.
TS = 7.2 m/s TS = 7.2 m/s TS = 7.2 m/s
J = 0.75 cm/s J = 1.23 cm/s J = 1.88 cm/s
g g g
TS = 5.44 m/s TS = 7.2 m/s TS = 8.95 m/s
J = 1.43 cm/s J = 1.43 cm/s J = 1.43 cm/s
g g g
Figure 5.6 Bubble size frequency and bubble size cumulative distributions with the
corresponding Sauter and number mean diameters for the Dorr-Oliver SuperCell under
different operating conditions. Also given are the fractions of the total gas volume
contained in a certain size class. Top row represents the effect of the aeration rate
increase; bottom row represent the effect of the agitation rate increase.
Under the assumption that the gas dispersion limit for this cell was exceeded at impeller
tip speed of 5.44 m/s and aeration rate of 1.43 cm/s, the cell was operated under so-called
159 |
Virginia Tech | ‘boiling conditions’. This assumption leads to a conclusion that a fraction of the
introduced gas was not carried by the discharge stream coming from the impeller, but
was by-passing the system through the central zone of the cell. In this case, escaping gas
could not be detected at the chosen sampling location, which could have led to the bias in
final results. Therefore, using a single location for bubble screening in large industrial
systems might significantly affect overall detection efficiency, which leads to
undercoverage error.
Figure 5.7 shows bubble size results obtained for the 300 m3 WEMCO cell. For
the same impeller tip speed, operating conditions were changed by altering the froth
depth, which resulted in change of the aeration rate. Generally, an increase in froth depth
increases the aeration rate. The illustration shows the increase in bubble size with the
increase in aeration rate (froth depth). This increase became more significant as the froth
depth was increased from 43 to 68 cm, which corresponds to 1.18 and 1.42 cm/s
superficial gas velocity, respectively. At the deepest froth depth, the fraction of the total
gas contained in bubbles larger than 1.5 mm reached 78%, and the number mean bubble
diameter became 1.29 mm. This indicates that lowering the pulp level below a certain
(natural) level for the self-aerated cells results in a decrease of the impeller pumping
capacity, which proportionally decreases the impeller gas dispersing capabilities.
160 |
Virginia Tech | TS = 7 m/s TS = 7 m/s TS = 7 m/s
J = 0.94 cm/s J = 1.18 cm/s J = 1.42 cm/s
g g g
Figure 5.7 Bubble size frequency and bubble size cumulative distributions, fractions of
the total gas volume contained in a certain size class, and corresponding Sauter and
number mean diameters for the WEMCO SuperCell for different operating conditions.
It is important to note here that the direct comparison of these two flotation cells
is probably not completely justified. One reason for this is their significantly different
design and principles of operation. Moreover, and more importantly, they were tested on
two different days, which might have caused variations of some operational and chemical
factors that are strongly affecting bubble size, due to expected variations during the plant
operation. Nevertheless, bubble populations sampled from each cell, under similar
operating conditions, were still compared.
Operating conditions selected for this comparison were 7.2 m/s impeller tip speed
and 1.23 cm/s superficial gas velocity for the Dorr-Oliver cell and 7 m/s impeller tip
speed and 1.18 cm/s superficial gas velocity for the WEMCO cell. Under these
conditions, the WEMCO cell generated smaller bubbles, which is well reflected through
both number mean (0.89 mm - WEMCO vs. 0.97 mm - Dorr-Oliver) and Sauter mean
bubble diameter (1.39 mm - WEMCO vs. 1.69 mm - Dorr-Oliver). In addition, a much
narrower bubble size frequency distribution was noted for the WEMCO cell.
161 |
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