2011-On the gas dispersion measurements in the collection zone of flotation columns

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International Journal of Mineral Processing 99 (2011) 78–83
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International Journal of Mineral Processing
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On the gas dispersion measurements in the collection zone of flotation columns
E. Matiolo, F. Testa, J. Yianatos 1, J. Rubio ⁎
Laboratório de Tecnologia Mineral e Ambiental (LTM), Departamento de Engenharia de Minas-PPGEM, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500/75,
91501-970, Porto Alegre, RS, Brazil
⁎ Corresponding author at: Mining Engineering Dep
do Rio Grande do Sul, Brazil. Tel.: +55 51 33089479; fa
E-mail addresses: juan.yianatos@usm.cl (J. Yianatos)
URL: http://www.ufrgs.br/ltm (J. Rubio).
1 Chemical Engineering Department, Santa María Uni
Chile.
0301-7516/$ – see front matter © 2011 Elsevier B.V. A
doi:10.1016/j.minpro.2011.03.002
a b s t r a c t
a r t i c l e i n f o
Article history:
Received 29 September 2008
Received in revised form 21 February 2011
Accepted 11 March 2011
Available online 29 March 2011
Keywords:
Gas hold-up
Column flotation
Bubble size
Bubble superficial area flux
This work shows the results of gas dispersion parameters in a fully controlled laboratory column flotation cell,
namely gas hold-up (εg), superficial gas velocity (Jg) and bubble size distribution, measured directly by image
analyses using the LTM-BSizer. Gas hold-up and bubble size (and their distribution) were found to be strongly
dependent on Dowfroth 250 concentration and superficial gas velocity. A fairly linear relationship between
experimental εg and bubble superficial area flux (Sb) was established, and results are compared to those
calculated using drift flux analysis. Data obtained are discussed in terms of solution, hydrodynamics and
interfacial phenomena. Possible implications on the role of the frother in the energy dissipation in bubble
generation and on interfacial tensions are explored.
artment, Universidade Federal
x: +55 51 33089477.
, jrubio@ufrgs.br (J. Rubio).
versity, P.O. 110-V, Valparaíso,
ll rights reserved.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
The properties of bubbles (gas) dispersion or hydrodynamic
conditions clearly play an important role in froth flotation and
applied flotation to effluent treatment. Recent developments
(Schwarz and Alexander, 2006; Dahlke et al., 2005; Hernández et al.
2003; Grau and Heiskanen, 2003; Chen et al., 2001; Finch et al., 2000;
Deglon et al., 2000; Gorain et al., 1997, 1998, 1999) have permitted
reliable measurements of some gas dispersion parameters, namely
gas hold-up (εg), bubble size (db), gas rate (Qg) or superficial rate (Jg)
and bubble surface area flux (Sb):
Jg =
Q g
A
ð1Þ
where A is the cell cross-sectional area, and the bubble surface area
flux (Sb) defined by:
Sb =
6⋅Jg
db
ð2Þ
Many attempts to relate these parameters to flotation performance
have beenmade by a number of authors (Hernández et al., 2003; Grau
et al., 2005; Grau and Heiskanen, 2003; Kracht et al., 2005; Deglon
et al., 1999; Gorain et al., 1998). Jameson et al. (1977) derived that the
first-order flotation rate constant (k) is given by:
k =
0:25⋅Ec⋅Jg
db
ð3Þ
where Ec is the collection efficiency, the term ending up in terms of
surface area flux, yielding:
k = 0:25⋅Ec⋅Sb ð4Þ
Some data reported suggests that bubble surface area flux (Sb) and
gas hold-up are related by the following relation (Finch et al., 2000):
Sb = 5:5⋅εg ð5Þ
This relation would have advantages, because the gas hold-up is
easier to measure and would solve the problem of poor bubble size
measurements (Tavera et al., 2001). This appears to be the case for
flotation columns andmechanical cells, both laboratory and plant scale,
over the approximate range Sbb130 s−1 and εgb25%. Yet, Heiskanen
(2000) claims that, in practice, the Sb better matches with the flotation
rates of the fine fractions and suggests thatmore experimental work on
the k–Sb relationship with different mineralogical species, is needed.
With regard to the Sb values, Deglon et al. (2000); Power and
Franzidis (2000) and Gorain et al. (1997) found that for normal (non-
flooding) operating conditions, bubble surface area flux lied typically
within the range of 30–70 s−1.
Recently, some of these hydrodynamic plant data have been
combined, whereby typical mean bubble diameter ranged between
db=1–1.5 mm and Jg=1–2 cm/s. Herein, theoretical and practical
http://dx.doi.org/10.1016/j.minpro.2011.03.002
mailto:juan.yianatos@usm.cl
mailto:jrubio@ufrgs.br
http://www.ufrgs.br/ltm
http://dx.doi.org/10.1016/j.minpro.2011.03.002
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79E. Matiolo et al. / International Journal of Mineral Processing 99 (2011) 78–83
considerations of their border limits have been reported (Yianatos
and Henríquez, 2007).
In summarizing, bubble surface area flux has been related to
flotation performance and claimed to be a key “machine variable”.
However, most of the available data have been taken, calculated or
measured in conventional cell and only a few have been done in
column flotation cells.
The effect of frothers has been revised lately, in terms of air
dispersion into fine bubbles, froth stabilization, interactions at the
water/gas interface and with collector molecules adsorbed into solid
particles, water carrying effect and their main effect on bubble size
and uprising velocity (Finch et al., 2006, Melo and Laskowski, 2006,
Grau et al., 2005, Nguyen et al., 2003).
This article is a contribution to the general discussion on the
possible implications of frothers in bubble generation (energy and
size) -interfacial tensions and system hydrodynamics.
2. Experimental
2.1. Column flotation
A laboratory flotation column, 2.54 cm diameter and 2.20 m total
height, made of Plexiglas was used as the experimental apparatus
(Fig. 1) for gas dispersion measurements in a two-phase system (air/
water). Bubble generator used was a porous stainless cylinder with a
nominal porous size of 5 μm. Fig. 1 shows the set-up for the
hydrodynamic measurements.
2.2. Gas hold-up measurement
For the experiments in a two-phase system (water/air), the
required amount of Dowfroth 250 was added to 30 L of tap water in
Fig. 1. Experimental set-up of the
natural pH (around 6–7). This solution was continuously agitated
using a stirrer and introduced after 10 min in the column, with a
peristaltic pump. The interface level was controlled by a peristaltic
pump located at the column bottom discharge and the air rate
(injected directly into the bubble generator) was measured by a mass
flowmeter and regulated with a pinch valve (Fig. 1). Gas hold-up (εg)
in the two-phase system (air–water) was measured by pressure
difference over a section of length, L of 83 cm in the collection zone
just below the froth. Pressure was sensed by water-filled manometers
and the fractional gas hold-up was determined by:
εg =
ΔH
L
ð6Þ
where ΔH is the difference in the manometer readings.
2.3. Bubble size measurement procedure
Bubble size measurements were made using the LTM-BSizer
(Rodrigues and Rubio, 2003) whereby the image analysis system
included the bubble capture cell, a microscope and a CDD camera
(Fig. 2).
This technique (LTM-BSizer) employs a sampler to draw bubbles,
rising in a column, into a special viewing chamber and exposes them
to a digital camera, after they have decelerated and stopped. Thus
common problems related to the movement of bubbles, namely focus,
illumination, photographic speed and bubbles overlapping are all
overcome. Results obtained are in good correlation with those values
reported with the traditional image analysis method and show that
using this technique, accurate size distributions can be produced,
conveniently and efficiently (Rodrigues and Rubio, 2003, 2007).
laboratory flotation column.
Fig. 2. The LTM-BSizer for the determinations of the bubble size distribution (Rodrigues and Rubio, 2003).
80 E. Matiolo et al. / International Journal of Mineral Processing99 (2011) 78–83
3. Results and discussion
Fig. 3 shows the size distribution of the generated bubbles and
Fig. 4 summarizes the mean bubble diameter (Sauter) at different
Dowfroth concentrations (10 to 40 mg L−1) for a superficial gas
velocity fixed at 0.49 cm s−1. Herein, values obtained from drift-flux
calculations (Yianatos et al., 1988), are enclosed for comparison
reasons.
Results show that when the frother concentration increases, the
bubbles become smaller with the Sauter mean diameters decreasing
from about 1000 μm to about 470 μm. This minimum (reaching a
plateau) for the bubble size (and its size distribution) also depends on
sparger and flow mixer (if venturi, needle valve, and static mixer)
designs. Rodrigues and Rubio, 2003 found, for a similar system and
frother (used in this work), bubbles can be as small as 200 μm with a
venturi, for the same frother concentration range. The higher fluid
velocity (and the higher energy to be dissipated ahead) inside the
venturi, compared to a porous (perforated) cylinder, explains the
difference in bubble size and in the hold-up values.
Explanations for this behavior have been given by a number of
authors and the bubbles size decrease appears to be associated to the
energy required for bubbles generation. This may be related to a
decrease of the liquid–air interfacial tension, when the frother
concentration increases, but there is no agreement on this issue.
A frother may produce a dramatic effect on bubbles size
distribution (and narrowed) but may not substantially decrease the
air/water interfacial tension. In the absence of frother, big (not-
measurable) bubbles are formed while for concentrations higher than
5 mg/L, the average bubbles size decreased substantially. Cho and
Laskowski (2002), studied the effect of frothers on the size of bubbles,
in single and multi-hole spargers and a flotation cell. These authors
found that the size of bubbles strongly depends on frother
concentration only when multi-hole spargers are utilized or when
energy (arising from the liquid turbulence) is transferred, producing
cavity phenomenon, and small bubbles are formed. At low frother
concentrations, lower than a “critical coalescence concentration”
(CCC), the bubble size is much larger, indicating a sort of coalescence
as the main mechanism determining the size. This coalescence
phenomenonmight be prevented at frother concentrations exceeding
this CCC value, which is empirically determined as the froth dosage at
the break point of the slope (Melo and Laskowski, 2006, Laskowski,
2003, Sweet et al., 1997, Grau et al., 2005).
Conversely, Finch et al. (2008) (to appear) believe that there is no
agreed mechanism on how frothers act to reduce bubble size. These
authors claim that there would be a breakup mechanism, phenomena
associated with bubble shape, with its hydrodynamics in pulps
(velocity and surface flows). The resulting force would be associated
with surface tension gradients and it would impulse this breakup
phenomenon.
The fact is, when bubbles are formed in pure water, where little
pressure transfer exists, large bubbles are produced. At operating
pressures lower than 3 atm and in the absence of frothers, there is no
sufficient energy to overcome attrition and nucleation to form small
bubbles. However, a decrease in solution/air interfacial tension provides
low energy nucleation sites and minute bubbles are generated.
Results obtained in previous works (Takahashi et al., 1979, Féris
and Rubio, 1999, Féris et al., 2000) show that the minimum “energy”,
ΔF, to be transferred to the liquid phase to form bubbles by a cavity
phenomenon (arising from the liquid turbulence) is given by the
following equation (Takahashi et al., 1979):
ΔF =
5:3⋅Π⋅γ3
Po−Pað Þ3 ð7Þ
where:
γ air–water surface tension (Nm−1)
Pa flotation cell atmospheric pressure (atm or Pascal units);
Po flow entrance pressure (atm or Pascal units) or pressure in
the sparger
Thus, the energy required to generate bubbles will be smaller with
lower air–liquid interfacial tensionsandwithhigherpressuredifferences
image of Fig.�2
Fig. 3. Bubble size distribution at different Dowfroth 250 concentrations and at constant Jg, 0.49 cm s−1.
81E. Matiolo et al. / International Journal of Mineral Processing 99 (2011) 78–83
across the sparger (inlet e outlet). Thus, when lowering the air–liquid
interfacial tension (Fig. 5) in a few units (7–10mN/m−1 units), the
liquid–solid attrition will be smaller at the sparger outlet (or inside if
water is used as carrier for the air). This results in a faster fluid flow
velocity and in a rapid bubble formation, after nucleation and cavitation.
This would explain the initial very sharp inclination of the curve (Figs. 4
and 5) and the onward plateau appear to be independent on this
decrease in surface tension.
Furthermore, many authors find that there is a poor correlation
between bubble size and surface tension but not many works deal
with errors committed in their experimental work. Fig. 5 for instance,
poses the problem of the data accuracy and reliability, which
highlights this ignored fact. It seems to be clear that surface tension
measurements depend on equipment (method) used, temperature
and on water quality. This situation is clearly shown in Fig. 5, where
curves are different even if the frother sample is the same. Thus,
image of Fig.�3
400
500
600
700
800
900
1000
1100
0 5 10 15 20 25 30 35 40 45
[DF 250], mg.L-1
B
ub
bl
e 
di
am
et
er
, µ
m
LTM-BSizer
Drift flux
Fig. 4. Bubble size (Mean Sauter Db) as a function of DF 250 concentration. Comparison
between bubbles sizes measured using the LTM-BSizer (Jg, constant at 0.49 cm/s and
Jw=0) and calculated by a drift flux method (Yianatos et al. 1988).
0
5
10
15
20
25
30
0.2 0.4 0.6 0.8 1.0 1.2
Superficial gas rate, cm·s-1
G
as
 H
ol
du
p,
 %
[DF250], mg/L 
5
10
20
30
40
Fig. 6. Gas hold-up values as a function of superficial gas rate (Jg), at different DF 250
frother concentration and JW=0.66 cm/s.
10
15
20
25
[DF250], mg/L 
5
10
20
30
40
as
 H
ol
du
p,
 %
82 E. Matiolo et al. / International Journal of Mineral Processing 99 (2011) 78–83
despite using Nima or Kruss tensiometers, which employ the same
interaction of a platinum ring (DuNouy) with the surface being tested,
using very pure and ions free water, the experimental values were
fairly different (assuming that not many differences would be
encountered between 24 and 27 °C). Unfortunately, Grau et al. data
(2005) do not include temperature, neither informed about water
quality (measurements appear to be done using a platinum ring).
0
5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Superficial gas rate, cm·s-1
G
Fig. 7. Gas hold-up values as a function of superficial gas rate (Jg), at different DF 250
frother concentration and JW=0 cm/s.
3.1. Gas dispersion parameters
Figs. 6 and 7 show the experimental gas hold-up values as a
function of superficial gas velocity (Jg) for Dowfroth 250 concentra-
tions 5 to 40 mg L−1, and Jw of 0.66 and 0 cm/s, respectively. These
figures show a typical increase in gas holdup with Jg. Also, for a
constant Jg, the higher frother dosage the higher the gas hold-up. Yet,
increasing the frother dosage, the hold-up values increase probably
due to bubble size decreasing and again, after a certain concentration,
this trend tends to level off (20–40 mg/L Dowfroth 250, in this case).
According to Fig. 4, the bubbles decrease dramatically in size, but only
at very low dosages. According to some authors, the CCC is reached at
higher frother dosages, thus ceasing the increase of gas hold-up
because the bubbles size reduction stops. Also, comparison of Figs. 6
and 7 shows that increasing the superficial liquid rate Jw from 0 to
0.66 cm/s, the gas hold-up increases for the same frother dosage and
superficial gas rate Jg.
Fig. 8 shows the relationship between the bubble surface area flux
(Sb) and the gas hold-up (εg), with JW=0 cm/s, comparing
experimental data (LTM-BSizer) and values calculatedby the drift-
flux relationship (Yianatos et al., 1988). Experimental data shows a
56
60
64
68
72
76
0 10 20 30 40 50 60
Su
rf
ac
e 
te
ns
io
n,
 m
N
.m
-1
Nima (this work, 24 ºC)
Krüss (this work, 27 ºC)
Rodrigues and Rubio, 2003, Krüss 25ºC
Grau et al., 2005
[DF 250], mg.L-1
Fig. 5. Surface tension of aqueous solutions as a function of frother (DF 250)
concentration. Values determined in different periods, conditions and authors.
good correlation and results confirm that for the range of interest, the
relationship between bubble surface area flux and gas hold-up is
reasonably linear (as predicted by drift-flux), with a better fit at low Jg
(closer to a countercurrent flow). This finding reinforces the fact that
the gas hold-up can be considered as a good estimate of bubble
surface area flux to characterize the flotation process (i.e. to correlate
the kinetic rate constant in the collection zone).
Fig. 9 shows the effect of the superficial liquid flowrate Jw on the
Sb–εg relationship, calculated by drift-flux. According to this
prediction an increase in Jw will increase the gas hold-up, keeping
the gas rate and bubble size constant. Otherwise, for a constant gas
hold-up the bubble surface area flux will decrease by increasing Jw, if
the bubble size increases.
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25
Gas Holdup, %
B
ub
bl
e 
su
rf
ac
e 
ar
ea
 f
lu
x 
(S
b)
, s
-1
Jg, cm/s
0.33
0.49
0.66
0.82
0.49 LTM BSizer
Fig. 8. Relationship between the bubble surface area flux (Sb) and the gas hold-up (εg),
with JW=0 cm/s.
image of Fig.�4
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25 30
Gas Holdup, %
B
ub
bl
e 
su
rf
ac
e 
ar
ea
 f
lu
x 
(S
b)
, s
-1
Jw = 0 cm/s
Jw = 0.66 cm/s
Fig. 9. Relationship between the bubble surface area flux (Sb) and the gas hold-up (εg),
with JW=0 and Jw=0.66 cm/s.
83E. Matiolo et al. / International Journal of Mineral Processing 99 (2011) 78–83
4. Conclusions
Gas dispersion parameters were measured in a well characterized
laboratory column flotation cell. Gas hold-up and bubble size (and
their distribution) were found to be strongly dependent on Dowfroth
250 concentration and on superficial gas velocity. A good relationship
between experimental gas hold-up and bubble surface area flux (Sb)
was found for experimental values and with those calculated using
drift flux analysis for Jw=0. Data obtained are discussed in terms of
solution, hydrodynamics and interfacial phenomena. The role of the
frother in the energy dissipation in flow constrictors and in bubble
generation and interfacial tensions was explored.
Acknowledgments
The authors gratefully acknowledge CAPES and CNPq for the
scholarships awarded to E. Matiolo and F. Testa. Special thanks to Prof.
R. T. Rodrigues, Camila Centeno and Alexandre Englert, from UFRGS, for
thehelp in thebubble size and surface tensionmeasurements. J. Yianatos
and J. Rubio wish to thank Conycit-Fondecyt, grant no. 7070233, for
allowing the visit of J. Rubio to Chile and the research on flotation at
U. Santa Maria, Chile.
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	On the gas dispersion measurements in the collection zone of flotation columns
	Introduction
	Experimental
	Column flotation
	Gas hold-up measurement
	Bubble size measurement procedure
	Results and discussion
	Gas dispersion parameters
	Conclusions
	Acknowledgments
	References