Download Bubble Size Distribution in Laboratory Scale Flotation Cells PDF

TitleBubble Size Distribution in Laboratory Scale Flotation Cells
TagsFoam Drop (Liquid) Economic Bubble Solid Gases
File Size310.0 KB
Total Pages9
Table of Contents
                            Bubble size distribution in laboratory scale flotation cells
	Introduction
	Experimental work
		Bubble size distributions
	Results and discussion
		Effect of frothers on bubble size
		Effect of impeller tip speed
		Effect of rotor ndash stator mechanism on bubble generation
		Effect of air flow rate
		Effect of a non-floatable solid
	Conclusions
	References
                        
Document Text Contents
Page 1

This article is also available online at:
www.elsevier.com/locate/mineng

Minerals Engineering 18 (2005) 1164–1172
Bubble size distribution in laboratory scale flotation cells

R.A. Grau *, K. Heiskanen

Helsinki University of Technology, P.O. Box 6200, 02015 TKK, Finland

Received 7 April 2005; accepted 17 June 2005
Available online 18 August 2005
Abstract

Bubble size was measured in two lab scale cells using the HUT bubble size analyzer. The influence of operating conditions on
bubble size was investigated. The Sauter mean bubble size was found to vary over the range of 1.2–2.9 mm. The experimental bubble
size distributions were satisfactorily represented by the upper-limit distributions.

The frothers were found to have a profound impact on bubble size. It seems that frothers not only prevent bubble coalescence,
but they also, affect the bubble break-up process. The air flow rate was also found to have a strong influence on bubble size. The
Sauter mean bubble diameter increased as the air flow rate increased. The Sauter mean bubble diameter was found to decrease with
increasing impeller speed. The addition of quartz on the other hand was found to increase the size of bubbles, this effect was more
evident at solid concentration exceeding 20% (kg/kg). The size of bubbles generated with the multi-mix and free-flow mechanisms
were different at similar operating conditions, in a non-coalescing environment. The free-flow design generated broader bubble size
distributions than the multi-mix mechanism.
� 2005 Elsevier Ltd. All rights reserved.

Keywords: Flotation bubbles; Flotation frothers; Flotation machines
1. Introduction

Bubble size (db) is an important parameter, which de-
fines along with gas hold-up and gas velocity how effi-
ciently the air is dispersed in a flotation cell. Ahmed
and Jameson (1985) assumed that the removal of parti-
cles can be described by a first-order rate equation. They
found that bubble size has a strong influence on the flo-
tation rate constant (k), recognizing also that the flota-
tion rate constant is a complex function of the particle
properties and the hydrodynamic conditions in the cell.
Yoon (2000) derived from first principles that the first-
order kinetic constant varies as d�3b at quiescent condi-
tions. However, under turbulent conditions, as the case
in mechanical cells, it is known that the flotation rate
constant is less influenced by bubble size (Heiskanen,
0892-6875/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.mineng.2005.06.011

* Corresponding author. Tel.: +358 9 451 3829; fax: +358 9 451
2795.

E-mail address: [email protected] (R.A. Grau).
2000). The flotation rate constant is expected to approx-
imately vary as d�1:5b under turbulent conditions. Re-
cently, Gorain et al. (1998) experimentally obtained
that the overall flotation rate constant k is strongly cor-
related with Sb, the average bubble surface area flux in
the cell, as

k ¼ PSbRf ð1Þ
where, P is a parameter which represents the mineral flo-
atability and Rf is the froth recovery factor and Sb ¼ 6Jgd32
(where Jg is the superficial gas velocity and d32 is the
Sauter mean bubble diameter). This model has been crit-
icized for being too simplistic, mainly because particle
properties were not considered in the model (Heiskanen,
2000).

Although, it is beyond doubt that bubble size is a key
parameter in froth flotation, bubble size has rarely been
studied in lab scale flotation cells, probably due to
the fact that bubble size determination in aerated
stirred vessels and particularly in three-phase systems

mailto:[email protected]

Page 2

35
0

m
m

22
5

m
m



Bubble sampler
system

42
0

m
m



25
0

m
m

(a)

(b)
Liquid level

Liquid level

Fig. 1. Sampling location in the (a) OK-50 and (b) OK-70.

R.A. Grau, K. Heiskanen / Minerals Engineering 18 (2005) 1164–1172 1165
(solid–liquid–gas) is complex. Tucker et al. (1994) exam-
ined the influence of physical and chemical variables on
bubble size in a modified 3 dm3 Leeds flotation cell. Re-
cently, Laskowski et al. (2003) extensively studied the
influence of several commercial frothers on bubble size
in a 1 dm3 open-top leads flotation cell. In this study,
bubble size was measured using the UCT technique.

Only few investigators have reported measurements
of bubble size in industrial cells probably due to the
complexity of the measurement and the lack of standard
methods to determine it. Jameson and Allum (1984)
measured bubble size in operational cells with the use
of a photographic technique. They reported that Sauter
mean bubble diameters varied over the range of 0.5–
1.8 mm. Gorain et al. (1997) reported values measured
with the UCT (University of Cape Town) technique,
in a 2.8 m3 portable cell, in the range of 0.7–1.8 mm.
While Deglon et al. (2000) using the UCT method found
that d32 values varied over the range of 1.2–2.7 mm in
industrial mechanical cells.

In this project, the influence of operating conditions
such as air flow rate, impeller speed and solid concentra-
tion on bubble size was investigated, as well as the influ-
ence of frother dosage. The objective of this work is to
provide a better understanding of the variations in bub-
ble size observed in industrial scale cells. Furthermore,
four mathematical distributions are fitted to the experi-
mental data. The purpose of this work is to determine
whether bubble size distributions can be satisfactorily
represented by a mathematical distribution. The experi-
mental work was carried out in two Outokumpu lab
scale flotation cells. The cells were equipped with two ro-
tor–stator designs.
2. Experimental work

The experiments were carried out in two Outokumpu
cylindrical flotation cells, a 50 dm3 laboratory scale cell
(35 cm in diameter and 55 cm high) made of stainless
steel and a 70 dm3 cell (42 cm in diameter and 52 cm
high) made of plexiglass. In the 50 dm3 cell (nominal),
the level of liquid in the cell was set equal to 35 cm, so
a liquid volume of 30 dm3 was added to cell (Fig. 1).
The cell was filled with aqueous solutions of three com-
mercial frothers (Dow Frothers DF-200, DF-250 and
DF-1012), which were prepared using municipal tap
water. The 50 dm3 cell is equipped with a multi-mix
system and four baffles (from now on referred to as
OK-50). The larger cell (from now on referred to as
OK-70) was equipped with two rotor–stator combina-
tions: the multi-mix and free-flow mechanisms (Fig. 2).
The level of liquid in the OK-70 cell was set equal to
the diameter of the cell (42 cm), so a solution volume
of 60 dm3 was initially added to the cell. The OK-70 cell
was filled with only aqueous solutions of DF-250.
Bubble size distributions were determined using the
HUT technique (Grau and Heiskanen, 2003). Bubble
size was measured at only one location in the cells,
above the plane of the stator as shown in Fig. 1. All
the experiments were carried out at room temperature
(approx. 20 �C). The HUT sampler system (1b) is also
filled with aqueous solution of the frothers of the same
concentration as the solution in the cell. Each measure-
ment was at least duplicated and on average over 4000
bubbles were sized in each run. The bubble sizes were
corrected and they are in this project reported at stan-
dard temperature and pressure conditions (25 �C and
1 atm). The correction for temperature and pressure in
bubble size determination has been described in detail
by Hernandez-Aguilar et al. (2004).

The power input to the OK-70 cell was determined by
measuring the torque experienced by the cell as a reac-
tion to the rotating impeller. The cell is supported
(mounted) on a thrust bearing, torque table. The torque
experienced by the cell is determined with the use of a
strain gauge. The power is calculated as follows:

P ¼
T � p � N I

30
ð2Þ

where T is the torque value in N m (N stands for New-
ton), NI is the rotational speed of the impeller in rpm
and P is the power in N m/s which is equivalent to watt.
The impeller speed (NI) is controlled by a variable speed
drive and is measured using a digital tachometer.

2.1. Bubble size distributions

The Rosin–Rammler, Tuniyama–Tanasawa, log-nor-
mal and upper-limit distributions were fitted to the
experimental data. These four distribution functions
have been described in detail elsewhere (Mugele and
Evans, 1951; Goering and Smith, 1978; Paloposki,
1994). The experimental data were tabulated and classi-
fied in 13 class intervals which were arranged in a geo-
metric progression (with a ratio of

ffiffiffi
2

p
). The adjustable

parameters of each mathematical distribution were esti-
mated by a nonlinear least squares fit of the cumulative
distribution function to the cumulative bubble volume

Page 3

Fig. 2. Rotor/stator mechanisms. From left to right: free-flow mechanism, multi-mix mechanism and OK rotor. Note that both mechanisms use the
OK rotor.

100

1166 R.A. Grau, K. Heiskanen / Minerals Engineering 18 (2005) 1164–1172
distribution. The curve-fitting algorithm was imple-
mented in MATLAB.
C
um

ul
at

iv
e

b
u

bb
le

v
ol

um
e

di
st

ri
bu

ti
on

(
%

)

Bubble size db (µm)

0

20

40

60

80

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Experimental data
Upper-limit
Nukiyama-Tanasawa
Rosin-Rammler
Log-normal

Fig. 4. Nonlinear least square fit of the experimental data collected in
the OK-70 cell fitted with the multi-mix mechanism.
3. Results and discussion

Figs. 3 and 4 show graphically the fit of the selected
distribution functions to the experimental data obtained
from tests conducted in the OK-70 cell. The air flow rate
was set at 116 L(STP)/min (1.4 cm/s) and the power
consumption in the cell was set at 0.5 kW/m3. The cell
was filled with aqueous solutions of DF-250 at a dosage
of 15 ppm. Fig. 3 shows the cumulative bubble volume
distribution obtained when the incoming air was dis-
persed by the free-flow design (OK-FF) and Fig. 4
shows the cumulative bubble volume distribution when
the multi-mix mechanism (OK-MM) was used. Over
20,000 bubbles were sized and classified to compute
the cumulative bubble volume distributions shown in
Figs. 3 and 4.

It is clear from Fig. 3 that the bubble size distribution
generated by the free-flow mechanism is satisfactorily
described by the upper-limit distribution which is a
modification of the log-normal distribution, in fact the
Bubble size db (µm)

C
um

ul
at

iv
e

b
u

bb
le

v
ol

um
e

di
st

ri
bu

ti
on

(
%

)

0

20

40

60

80

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Experimental data
Upper-limit
Nukiyama-Tanasawa
Rosin-Rammler
Log-normal

Fig. 3. Nonlinear least square fit of the experimental data obtained
from the OK-70 cell equipped with a free-flow mechanism.
upper-limit distribution is also referred to as a three-
parameter log-normal distribution. Tavlarides and
Stamatoudis (1981) reported that the log-normal distri-
bution appears to be the most common distribution
used to describe droplet size distributions in liquid–
liquid dispersions. Pacek et al. (1998) suggested that
for systems where drop (in this case bubble) break-up
occurs as drops break in two, the drop size distribution
might be satisfactorily represented by a log-normal dis-
tribution. Karabelas (1978) found that drops broken in
turbulent liquid–liquid dispersions are satisfactorily rep-
resented by the upper-limit distribution.

The bubble volume distribution expressed as the
upper-limit distribution is given as (Mugele and Evans,
1951):

dV
db

¼
dffiffiffi
p

p
db max

dbðdb max � dbÞ
exp �d2 ln

adb
db max � db

� �� �2

ð3Þ
where db is the bubble diameter. Integration of Eq. (3)
gives the cumulative volume distribution which is pre-
sented in Eq. (4) (Goering and Smith, 1978). Note that
Eq. (3) is equivalent to the cumulative standard normal
distribution.

Page 4

R.A. Grau, K. Heiskanen / Minerals Engineering 18 (2005) 1164–1172 1167
V ¼
1ffiffiffi
p

p
Z dz
�1

expð�uÞ2 du ð4Þ

where z is defined as

z ¼ ln
adb

db max � db
ð5Þ

As can be seen from Eqs. (3) and (4), three parameters
are required to specify the upper-limit distribution:
dbmax is the hypothetical maximum bubble diameter in
the distribution, a is a dimensionless parameter and d
is a dimensionless parameter related to the geometric
standard deviation. When these three parameters are
known, the Sauter mean bubble diameter can be deter-
mined from the bubble size distribution equation (Mug-
ele and Evans, 1951):

d32 ¼
db max

1þ a � exp 1
4d2

� � ð6Þ

The upper-limit distribution also provided a good fit of
the experimental data obtained from the tests conducted
in the OK-70 cell equipped with the multi-mix mecha-
nism, as can be seen from Fig. 4. It also clear from Figs.
3 and 4 that the log-normal, Nukiyama–Tanasawa and
specially the Rosin–Rammler distribution provided a
poor fit to the experimental data. The same trend was
also evident when these four mathematical models were
fitted to experimental data obtained at different operat-
ing conditions in the OK-50 cell. Table 1 summarizes the
upper-limit distribution parameters obtained through
curve fitting. Sauter mean diameter values (d32) com-
puted directly by summation of the data and from Eq.
(6) are also listed in Table 1.

The Sauter mean diameter or surface-volume mean
diameter d32 is usually the most relevant average in cases
Table 1
Parameters of the fitted upper-limit distribution

Cell rotor/stator Jg (cm/s) Impeller speed
(rpm)

a

OK-50a multi-mix 0.7 350 1.
450 1.
550 1.
650 1.
750 2.
850 2.
950 2.
1050 2.
1100 3.

OK-50 multi-mix 10% solids 0.7 1050 3.

OK-50 multi-mix 30% solids 0.7 1050 1.

OK-70a multi-mix 1.4 700 2.

OK-70a free-flow 1.4 660 2.

a The tests were conducted with only aqueous solutions of the frothers.
where the interfacial area is a control parameter. Jame-
son and Allum (1984) suggested that the Sauter mean
diameter is the appropriate average bubble diameter to
represent bubble size distributions in flotation machines.
Lately, several authors have adopted the Sauter mean
diameter to describe bubble size distributions (gas dis-
persion conditions) in flotation cells and columns.
Therefore, the good agreement found between the Sau-
ter mean diameters calculated directly from the experi-
mental data and from Eq. (6) (Table 1), reinforces the
argument that the upper-limit distribution can be used
to represent bubble size distributions. In addition, the
quality of the fit of the upper-limit function to the exper-
imental data is shown graphically in Figs. 6, 8, 11, 13, 14
and 16.

3.1. Effect of frothers on bubble size

The experimental work using the OK-50 cell was con-
ducted with three commercial Dow frothers: DF-200,
DF-250 and DF-1012. The impeller speed was set at
1050 rpm (tip speed: 6.9 m/s) and the air flow rate was
set at 77 dm3 (STP)/min (superficial gas velocity
Jg = 1.3 cm/s). The results of the measurements are
shown graphically in the form of bubble size vs. frother
concentration curves in Fig. 5.

As can be seen from Fig. 5, the general trend for all
the investigated frothers was fairly similar, the bubble
size decreased with increasing frother dosage, and at a
particular concentration, the bubble size levelled off.
Cho and Laskowski (2002) suggested that frothers con-
trol bubble size by reducing bubble coalescence in the
cell and that coalescence is entirely prevented at concen-
trations exceeding the critical coalescence concentration
(CCC) in a dynamic system. It is clear from Fig. 5 that
d dbmax
(mm)

d32 (Eq. (6))
(mm)

d32 (data)
(mm)

62 0.96 9.69 3.15 2.92
42 0.85 6.35 2.11 1.97
72 0.75 6.47 1.76 1.66
79 0.74 6.16 1.73 1.56
19 0.76 6.63 1.51 1.49
74 0.73 6.50 1.20 1.31
74 0.73 6.50 1.20 1.26
57 0.69 6.20 1.16 1.21
20 0.73 6.90 1.12 1.20

6 0.84 7.31 1.19 1.26

4 0.69 6.04 1.76 1.74

5 0.78 7.28 1.51 1.54

1 0.65 8.03 1.67 1.74

Page 5

S
au

te
r

m
ea

n
di

am
et

er
(m

m
)

Concentration (ppm)

0

0.5

1

1.5

2

2.5

3

3.5

0 10 15 20 25 30 35
0

0.5

1

1.5

2

2.5

3

3.5

DF-200

DF-1012

DF-250

5

Fig. 5. Effect of frothers concentration on bubble size (OK-50).

1168 R.A. Grau, K. Heiskanen / Minerals Engineering 18 (2005) 1164–1172
the CCC value is different for each type of frother. At
frother dosages exceeding the CCC value, the conditions
in the cell can be defined as non-coalescing.

Fig. 6 shows the bubble volume distributions mea-
sured at frother dosages exceeding the CCC values. It
is clear from Figs. 5 and 6 that at frother concentrations
exceeding the CCC values, different bubble sizes were
observed. Thus, it can be mentioned that the DF-200
Bubble size db (µm)

Bubble size db (µm)

C
um

ul
at

iv
e

bu
bb

le
v

ol
um

e
di

st
ri

b
ut

io
n

(%
)

0

20

40

60

80

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0

0.025

0.05

0.075

0 1000 2000 3000 4000 5000 6000 7000 8000

DF-200

DF-250

DF-1012

Upper-limit distribution

DF-200

DF-250

DF-1012

Upper-limit distribution


V

/∆
d b

(%


m
)

DF-200

DF-250

DF-1012

(a)

(b)

Fig. 6. Bubble size distribution measured at concentrations exceeding
the CCC values for three different frothers: (a) cumulative size
distribution represented by an upper-limit distribution and (b)
frequency plots of bubble volume presented as continuous curves
using the fitted upper-limit functions.
was the most effective frother in terms of bubble size
reduction and the least effective was DF-1012. These re-
sults suggest that frothers do not only hinder coales-
cence but also somehow affect bubble break-up under
turbulent conditions, and this effect appears not to be
directly related to the surface tension of the solution.

3.2. Effect of impeller tip speed

Sauter mean bubble diameter is plotted against
impeller speed at different air rates in Fig. 7. The impel-
ler speed in the OK-50 cell was varied between 1.64 and
7.2 m/s (250–1100 rpm). The air flow rate was set at two
levels during the experiments, in terms of superficial gas
velocity, 0.7 cm/s (STP) and 1.3 cm/s (STP). Fig. 7 also
includes mean bubble sizes obtained from tests carried
out in the OK-70 cell. Fig. 7 allows us to compare the
gas dispersion conditions achieved in each cell. In order
to establish non-coalescing conditions in the experi-
ments, DF-250 was used at a dosage of 15 ppm. This
concentration exceeds the CCC value of this particular
frother, which was found to be 9.1 ppm (or
0.035 mmol/dm3). The CCC value determination has
been explained in detail by Laskowski et al. (2003).

It is clear from Fig. 7 that the Sauter mean bubble
diameter in the OK-50 cell decreased continuously with
increasing impeller tip speed. The same kind of trend has
also been observed in stirred vessels (Parthasarathy
et al., 1991). Takahashi et al. (1992) measured bubble
size in a vessel agitated by a Rushton turbine using a
photographic technique. At very low aeration condi-
tions in the vessel, they observed that the Sauter mean
diameter at locations very close to the impeller, near
the aerated cavities (vortex cavities), varies as N�0:5I ,
where NI is the rotational speed of the impeller. Machon
et al. (1997) gave the following relationship between
Sauter mean diameter (d32) and impeller speed:

d32 / N�bI ð7Þ
S
au

te
r

m
ea

n
di

am
et

er
(

m
m

)


Impeller tip speed (m/s)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1.0 3.0 5.0 6.0 7.0
0

0.5

1

1.5

2

2.5

3

3.5

Jg=1.4 (cm/s) OK-70, OKMM
Jg=1.4 (cm/s) OK-70, OK-FF
Jg =1.3 (cm/s) OK-50, OK-MM
Jg =0.7 (cm/s) OK-50, OK-MM

41,0
32

−∝ INd

55.0
32

−∝ INd

2.0 4.0

Fig. 7. Effect of impeller tip speed upon bubble size. OK-MM refers to
the multi-mix design and OK-FF to the free-flow design.

Page 6

R.A. Grau, K. Heiskanen / Minerals Engineering 18 (2005) 1164–1172 1169
where 0.34 < b < 0.61. In spite of the differences in the
experimental operating conditions, the b values derived
from the experimental data shown in Fig. 7, agree very
well with the values given by Machon et al. (1997). In
the larger cell (OK-70), no clear trend was observed be-
tween the bubble size and impeller speed, probably due
to the narrow range of impeller speeds tested.

In terms of bubble generation, it is clear from Fig. 7
that the OK-70 cell was capable of producing finer bub-
bles sizes even at higher air rates (see Fig. 12). An expla-
nation of the difference observed in bubble size can
probably be found in the cell geometries. The OK-50 cell
is fitted with four equidistant vertical baffles, while the
OK-70 cell does not contain any baffle. The baffles
might dampen the turbulent intensity in the cell.

As can be seen from Figs. 8 and 9, the amount of fine
bubbles increased as the impeller tip speed increased. In-
tense agitation combined with fine bubbles improves the
attachment process. However, intense agitation could be
detrimental to flotation, owing to particle detachment
(Deglon et al., 1999).
C
um

ul
at

iv
e

bu
bb

le
v

o
lu

m
e

di
st

ri
bu

ti
on

(
%

)

Bubble size db (µm)

0

20

40

60

80

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Imp. tip speed:2.3 m/s (350 rpm)

Imp. tip speed:3.6 m/s ( 550 rpm)

Imp. tip speed:4.9 m/s (750 rpm)

Imp. tip speed:7.2 m/s (1100 rpm)

Upper-limit distribution

Fig. 8. Effect of the impeller speed on cumulative bubble volume
distribution. The solid lines correspond to the fitted upper-limit
distribution (OK-50).

0

0.025

0.05

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

1100 rpm


V

/∆
d b

(
%


m

)

Bubble size db (µm)

350 rpm

550 rpm

750 rpm

Fig. 9. Fitted upper-limit distributions at different impeller speeds
(OK-50).
3.3. Effect of rotor–stator mechanism on bubble

generation

Fig. 10 shows the results of the bubble size measure-
ments conducted in the OK-70 cell. Two set of rotor–sta-
tor mechanisms were used for the experimental work in
the 70 dm3 cell, the multi-mix mechanism (OK-MM)
and free-flow mechanism (OK-FF). The rotor–stator de-
signs are shown in Fig. 2. The power input to the cell was
kept constant at 0.5 kW/m3 (power input per unit vol-
ume) by altering the impeller speed at constant air rate.

As can be seen in Fig. 10, the multi-mix design ap-
pears to produce slightly finer bubbles than the second
mechanism. The variations in bubble size are also illus-
trated in Fig. 11. These differences appear to be related
to the specific function of the mechanisms. The multi-
mix mechanism is the general-purpose design, which is
commonly used to treat fine and medium range particle
sizes. The free-flow mechanism is designed primarily for
coarser particle flotation. With this mechanism excessive
turbulence is avoided in order to reduce particle detach-
ment. It is clear from Fig. 11 that the free-flow mecha-
nism produces bubbles of a wider size range. Broad
bubble size distributions might have a positive effect
on the flotation of coarse particles. According to Tao
(2004), the presence of larger bubbles strengthens the
levitation of coarse particles (bubble–particle
aggregate).

3.4. Effect of air flow rate

The effect of superficial gas velocity on bubble size is
shown graphically in Figs. 12–14. As can be seen in
Fig. 12, bubble size increased with increasing air flow
rate. It was found that the bubble-size distribution was
shifted towards larger bubble size as the air rate was in-
creased (Fig. 14). It was also observed that the width of
the distribution increased with increasing air flow rate
over the range of air rates investigated. These measure-
ments were also conducted in what can be considered
0

1

2

3

4

5

6

Multi-Mix

d10 mean diameter

d32 Sauter mean diameter

d90 90 percent bubble size

B
ub

bl
e

si
ze

(
m

m
)

Rotor-Stator design
Free-Flow

Fig. 10. Bubble size measured using two rotor–stator combinations
(OK-70), d90 was calculated graphically from Fig. 11.

Page 7

0

20

40

60

80

100

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

OKMM
OK-FF
Upper limit distribution

C
um

ul
at

iv
e

bu
bb

le
v

ol
um

e
di

st
ri

bu
ti

on
(

%
)

0

0.025

0.05

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Upper limit distribution

OK-MM

OK-FF


V

/∆
d

b
(%


m

)

Bubble size db (µm)

Bubble size db (µm)

OK-MM

OK-FF

(a)

(b)

Fig. 11. Bubble size distributions generated by two different rotor–
stator mechanisms: (a) cumulative size distribution represented by an
upper-limit distribution and (b) comparison of experimental data with
the fitted upper-limit distributions (OK-70).

S
au

te
r

m
ea

n
di

am
et

er
(

m
m

)


Gas velocity Jg (cm/s)

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2

Sauter diameter d32, OK-50, 50 dm3

Average diameter d10, OK-50, 50 dm3

Laskowski et al. (2003), 1 dm3 Open-
Top Leeds Cell

Fig. 12. Effect of air flow rate on bubble size. DF-250, 10 ppm and
impeller speed 800 rpm (Grau and Heiskanen, 2003).

C
um

ul
at

iv
e

bu
bb

le
v

ol
um

e
di

st
ri

bu
ti

on
(

%
)

Bubble size db (µm)

0

20

40

60

80

100

0 1000 2000 3000 4000 5000 6000 7000 8000

Jg= 1.7 cm/s

Jg= 1.1 cm/s

Jg = 0.9 cm/s

Jg = 0.6 cm/s

Upper-limit distribution

Fig. 13. Cumulative bubble volume distribution in a mechanical cell at
different air rates (OK-50).

0

0.025

0.05

0.075

0.1

0.125

0.15

0 1000 2000 3000 4000 5000 6000 7000 8000

Upper-limit distribution

Jg = 1.7 cm/s

Jg = 0.9 cm/s

Jg = 0.6 cm/s


V
/∆

d
b

(%


m
)

Bubble size db (µm)

Jg = 0.6 cm/s

Jg = 0.9 cm/s

Jg = 1.7 cm/s

Fig. 14. Influence of the air flow rate on bubble size distribution,
comparison of experimental data with the fitted distributions (OK-50).

1170 R.A. Grau, K. Heiskanen / Minerals Engineering 18 (2005) 1164–1172
non-coalescing conditions. Fig. 12 also includes experi-
mental data published by Laskowski et al. (2003) at sim-
ilar operating conditions.

The influence of the air flow rate (or gas velocity) on
bubble size is intrinsically related to presence of air cav-
ities behind the blades of the rotor. The presence of air
cavities and their size affect the power consumption in
the cell. Grainer-Allen (1970) observed that as air is
introduced into the flotation cell, the air collects behind
the blades of the rotor forming air cavities. Bruijn et al.
(1974) observed that in aerated vessels with Rushton
turbines, these air cavities enlarge as the gas flow rate in-
creases, causing the power requirement to continuously
diminish. Parthasarathy et al. (1991) found that the
maximum stable bubble size, in non-coalescing condi-
tions, varies as ½P

V
��2=5, where P is the power consump-

tion and V is the impeller swept volume.

3.5. Effect of a non-floatable solid

The material selected for the experimental work was
quartz (d50 = 160 mm). The tests were conducted in
the OK-50 without collector, therefore, the solid can
be classified as a non-floatable solid. The air flow rate
in the cell was set at 38 dm3 (STP)/min (Jg = 0.7 cm/s)
and the impeller speed was set at 1050 rpm. The solid
concentration was varied over the range of 0–30% (kg/
kg) using two frothers, DF-250 and DF-1012, at concen-
trations of 15 ppm and 10 ppm, respectively. The frother

Page 8

R.A. Grau, K. Heiskanen / Minerals Engineering 18 (2005) 1164–1172 1171
concentrations were selected in order to establish non-
coalescing conditions in the cell. The measurements con-
sisted of two runs, on average over 7000 bubbles were
sized in each run.

The effect of the non-floatable solid concentration on
the mean bubble size is shown graphically in Figs. 15
and 16.
Solids percentage (kg/kg)

S
au

te
r

m
ea

n
di

am
et

er
(

m
m

)

1

1.5

2

0 10 15 20 25 30

DF-250

DF-1012

5

Fig. 15. Effect of a non-floatable solid upon bubble size (OK-50).

C
um

ul
at

iv
e

b
u

b
b

le
v

ol
um

e
di

st
ri

b
u

ti
on

(
%

)


V
/∆

d b
(

%


m
)

Bubble size db (µm)

Bubble size db (µm)

0

20

40

60

80

100

0 1000 2000 3000 4000 5000 6000 7000 8000

Upper-limit distribution

10%

30%

0

0.025

0.05

0.075

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Upper-limit distribution

10% solids

30% solids

(a)

(b)

Fig. 16. Bubble size distribution at two solids concentrations: (a)
cumulative size distribution represented by an upper-limit distribution
and (b) comparison of experimental data with the fitted distributions
(OK-50).
It is clear from Fig. 15 that the Sauter mean bubble
diameter increased with the addition of quartz, indepen-
dent of the type of frother used. The influence of the
particles in the pulp was found to be stronger at concen-
trations exceeding 20% (kg/kg). It was also found that
DF-250 produced smaller sizes of bubbles than the
second frother over the range of operating conditions
investigated. Similar findings on the effect of solids
concentration have been reported by Tucker et al.
(1994).

It seems that the presence of solids dampens the tur-
bulent intensity in the cell, which produces an increase in
the amount of bubbles in the larger classes, as is illus-
trated in Fig. 16. The increase in solid concentration
has a strong influence on the apparent density and vis-
cosity of the suspension.
4. Conclusions

1. The experimental data obtained from the tests con-
ducted in two lab scale flotation cells was well repre-
sented by the upper-limit distribution. The Sauter
mean diameter values computed from the experimen-
tal data, showed a good agreement with the values
calculated from the fitted cumulative bubble volume
distributions.

2. It seems that frothers mainly control bubble size in
flotation cell by decreasing coalescence and that coa-
lescence is completely hindered at frother dosages
exceeding the CCC value. Non-coalescing conditions
in a flotation cell can therefore be established using
frothers at dosages exceeding the CCC values. The
CCC value seems to be different for each type of
frother. It was found that with increasing frother con-
centration, bubble size decreased until the CCC value
is reached. At concentrations above CCC, no further
changes in bubble size were observed.

3. The air flow rate was found to have a profound
impact on bubble size. The Sauter mean bubble diam-
eter increased with increasing air rate over the range
of operating conditions investigated.

4. The impeller speed was found to have an important
effect on bubble size, the mean bubble size (d32)
decreased as the impeller speed increased.

5. With the addition of quartz, the mean bubble size was
found to increase. The influence of the solid concen-
tration on bubble was more evident at concentrations
exceeding 20% (kg/kg).
References

Ahmed, N., Jameson, G., 1985. The effect of bubble size on the rate of
flotation of fine particles. International Journal of Mineral
Processing 14 (3), 195–215.

Similer Documents