Minerals Engineering 98 (2016) 122–126
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Minerals Engineering
journal homepage: www.elsevier.com/locate/mineng
Acoustic measurement of the bubble Sauter mean diameter d32
W. Kracht ⇑, C. Moraga
a
b
Department of Mining Engineering, Universidad de Chile, Chile
Advanced Mining Technology Center, AMTC, Universidad de Chile, Chile
a r t i c l e
i n f o
Article history:
Received 7 February 2016
Revised 16 July 2016
Accepted 1 August 2016
Available online 9 August 2016
Keywords:
Flotation
Bubble Sauter mean diameter
Measurement
Acoustic technique
a b s t r a c t
The importance of gas dispersion variables on the flotation process has led to the development of techniques that allow measuring and monitoring them in flotation. In the case of bubble size, the most used
methods are based on image analysis and, although these methods are well accepted, they have not been
implemented to monitor the flotation process on a regular basis, mainly because they are labor intensive,
require the manipulation of a well trained operator, and are difficult to automate. In the current work, an
acoustic technique for measuring the bubble Sauter mean diameter, d32, is introduced. The technique is
based on the response of bubbles to an acoustic perturbation consisting of a modulated signal with frequencies F1 ± F2, where F1 acts as a carrier set at 1 MHz, and F2 corresponds to the modulating signal that
varies from 1 kHz to 10 kHz. A linear empirical relation was found between the average intensity of the
acoustic response of the bubbles, Imean, and d32, which allows determining the bubble Sauter mean diameter for a wide range of sizes, from 0.75 to 3 mm, covering the range of interest of flotation. The acoustic
method represents an alternative to the image analysis technique as a sensor to monitor the flotation
process, however, it still depends on image analysis as an independent method for calibration.
Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction
It is well known that flotation performance is affected by the
gas dispersion in the flotation cell (Schwarz and Alexander, 2006;
Nesset et al., 2006), which is characterised by the variables
(Gomez and Finch, 2007): superficial gas velocity, Jg, gas holdup,
eg, bubble size distribution, with the bubble Sauter mean diameter,
d32, and derived variables such as the bubble surface area flux,
Sb ¼ 6J g =d32 , or the specific surface area, Ab ¼ 6eg =d32 . The bubble
surface area flux is directly related to the flotation rate constant
(Gorain et al., 1997), and can be either estimated (Gorain et al.,
1999) or calculated, given that both Jg and d32 are known.
Among the available techniques for measuring bubble size
(Randall et al., 1989; Grau and Heiskanen, 2002), the most used
is the McGill Bubble Size Analyser (MBSA) (Hernandez-Aguilar
et al., 2002; Gomez and Finch, 2007), which is a samplingfollowed-by-imaging technique. It consists of a sampling tube that
allows bubbles rising towards a sealed viewing chamber, also
known as bubble viewer, where pictures are taken. The pictures
are then analysed to yield bubble size data. Although the MBSA
has been widely used, and some of its issues have been addressed
⇑ Corresponding author at: Department of Mining Engineering, Universidad de
Chile, Av. Tupper 2069, Santiago, Chile.
E-mail address: [email protected] (W. Kracht).
http://dx.doi.org/10.1016/j.mineng.2016.08.001
0892-6875/Ó 2016 Elsevier Ltd. All rights reserved.
(Zhang et al., 2009; Kracht et al., 2013), it still has some limitations.
In particular, the need for replacing the water inside the bubble
viewer between measurements makes it difficult to implement
the MBSA as a sensor to monitor the process; therefore, so far it
has been used mainly as a diagnostic tool.
Acoustic emissions represent an alternative to monitor gasliquid dispersions. There are two kind of methods that can be
implemented (Boyd and Varley, 2001): passive measurements,
where what is measured is the acoustic signal, sound or ultrasound, generated by the process itself; and active measurements,
which rely on the response of the process to a transmitted acoustic
wave, usually low powered ultrasound.
When a bubble is formed, its surface oscillates (pulsates), which
perturbs the surrounding water, and a sound wave propagates
through water in all directions (Dawson, 2002). The sound generated by bubbles was first studied by Minnaert (1933), who determined the relationship between bubble sizes and their natural
frequency of oscillation. As shown by Leighton and Walton
(1987), bubbles behave like lightly damped simple harmonic oscillators that oscillate at the frequency determined by Minnaert. Bubbles oscillate at their natural frequency when they form or coalesce
(Strasberg, 1956; Manasseh et al., 2001; Manasseh et al., 2008;
Ajbar et al., 2009; Kracht and Finch, 2009; Kracht and Rebolledo,
2013), and also when they are excited by an external source such
as ultrasound (Leighton, 1994). It has been established that, when
W. Kracht, C. Moraga / Minerals Engineering 98 (2016) 122–126
123
exposed to two signals of high (ultrasound) and low frequency, F1
and F2, the bubbles couple both fields and return, as a result, a signal with frequencies F1 ± F2 (Leighton et al., 1996; Buckey et al.,
2005). The dual-frequency approach is used in the current work
to measure bubble Sauter mean diameter, d32, in the range of bubble sizes of flotation systems.
2. Experimental
2.1. Sampling process
The technique consists of sampling bubbles from the flotation
cell, exposing them to an acoustic perturbation, and analysing their
response. A schematic of the sampling procedure is shown in Fig. 1.
Bubbles are sampled from the cell with a 1/2 in sampling tube connected to an acoustic chamber made of transparent acrylic, and
equipped with two transducers (Reson TC3027) to perform the
measurements. The transparent acoustic chamber allows for bubble images to be taken, which are later analysed to yield bubble
size as an independent method of measuring d32. In order to allow
for continuous sampling, and to keep the acoustic chamber full of
water, the chamber is connected to a peristaltic pump that sucks
water and bubbles, returning the sample to the flotation cell. The
measurement can be automated in such a way that no operator
is needed.
The dimensions of the acoustic chamber are: 35 cm height,
24 cm width, and 20 cm depth. The actual acoustic chamber can
be seen in Fig. 2.
Fig. 2. Acoustic chamber showing transducers.
2.2. Acoustic technique
As the bubbles pass through the acoustic chamber, they are
exposed to a modulated signal produced with two function generators, each of them generating a sinusoidal signal, but of different
frequencies: a carrier signal, which corresponds to an ultrasound
frequency, F1, and a modulating signal, of lower frequency, F2
(Fig. 3).
The two signals are mixed to obtain a modulated signal with
frequencies F1 ± F2 that is transmitted to the water and bubbles
inside the acoustic chamber by one of the transducers that acts
as a transmitter. In order to transmit only the frequencies F1 ± F2,
it is necessary to suppress the carrier signal during the modulation.
This is done by using a modulator (Motorola MC1496) with carrier
suppression as the one shown in Fig. 4.
The bubbles respond to the transmitted signal inside the acoustic chamber, and their response is received by the second transducer, which acts as a receiver. Both transducers, transmitter and
receiver, are located perpendicular to each other on the center of
their respective chamber walls. The received signal passes through
a band-pass filter that passes ultrasound frequencies, filtering out
the audible range, before being demodulated by mixing it with
F1, and sent to a (National Instrument) data acquisition unit
Fig. 3. Schematic of acoustic measurement method.
Fig. 4. Modulator with carrier suppression.
(DAQ), and finally to a computer, where it is analysed. The carrier,
F1, is set at 1 MHz, whereas the modulating signal, F2, varies for
each measurement from 1 kHz to 10 kHz with a step of 50 Hz.
3. Results and discussion
3.1. Liquid-air system
Fig. 1. Experimental setup.
A series of tests were performed in a two-phase system (liquidair) to determine the relation between the signal received and the
size of the bubbles being sampled (Fig. 5). The conditions of bubble
generation were defined in order to have values of d32 covering at
least the range between 1 and 1.5 mm, which is a typical range in
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W. Kracht, C. Moraga / Minerals Engineering 98 (2016) 122–126
Imean ¼ m d32 þ n
60
Sound intensity, dB
55
50
45
2
R = 0.94
40
35
30
25
20
0
0.5
1
1.5
2
2.5
Bubble mean diameter d32, mm
Fig. 5. Sound intensity vs d32 in a two-phase system.
where Imean corresponds to the average received signal intensity, in
decibels (dB), m and n are the parameters of the curve, and d32 is the
bubble Sauter mean diameter, in millimetres (mm). The values for
m and n for the 2-phase system are 16.29 dB/mm and 60.0 dB
respectively, with a coefficient of determination R2 equal to 0.94.
Fig. 6 shows two bubble size distributions, determined by
image analysis, corresponding to the extreme values of d32 presented in Fig. 5. One of them is a uni-modal, narrow distribution,
whereas the other is wider and bi-modal, which suggest that the
technique allows determining the bubble Sauter mean diameter
from distributions of different shape.
3.2. Validation of the technique
mechanical flotation cells. The bubbles were generated in a 5 L laboratory mechanical cell (Labtech-ESSA), with a square crosssectional area of 397 cm2. The cell allowed controlling both impeller speed, and gas flow rate. The superficial gas velocity, Jg, was varied between 0.3 and 0.5 cm/s, and the impeller speed between 300
and 600 rpm, which considering the impeller dimensions
(D = 10.7 cm), corresponds to a peripheral velocity between 1.7
and 3.4 m/s respectively. The frother used in all the tests was MIBC,
at a concentration of 30 ppm (well above the critical coalescence
concentration, CCC). At each condition, the response of the bubbles
was recorded and analysed. The bubbles were also photographed
in order to size them by image analysis and determine their bubble
Sauter mean diameter, d32 (two of them are presented in Fig. 6).
The results of the measurements are presented in Fig. 5.
It can be seen that there is a linear relation between the mean
intensity of the received signal, i.e., the response of the bubbles
to the acoustic stimulus, and the values of d32. The relation
between both variables can be written as:
25
d32 = 1.84 mm
Number frequency, %
ð1Þ
In order to validate the technique, a series of 25 tests were run
in a 2-phase system. To obtain a wide range of bubble sizes in the
flotation cell, the agitation was varied between 300 and 600 rpm,
the Jg between 0.3 and 0.7 cm/s, and the frother (MIBC) concentration was varied between 5 and 30 ppm. From the 25 tests, 5 were
run with NaCl instead of MIBC, with a concentration between 0.1
and 0.3 M. The values of d32 for each condition were determined
using both the acoustic technique and image analysis, and are presented in Fig. 7. In the case of the acoustic technique, the bubble
Sauter mean diameter was determined using the linear relation
(Eq. (1)), with the parameters m and n presented above. The data
shown in Fig. 7 correspond to a new set of results, independent
from those presented in Fig. 5, which were used to determine the
coefficients of Eq. (1).
The results validate the acoustic technique. The bubble Sauter
mean diameters determined with the acoustic technique correlate
well with those determined using image analysis, with a coefficient
of determination R2 equal to 0.99. Originally, the condition of
0 ppm of frother had been included, but it was found that the
acoustic technique underestimates the d32 for values higher than
3 mm. The acoustic technique is therefore valid for values of d32
between 0.75 and 3 mm.
20
3.3. Reproducibility
15
In order to test the reproducibility of the technique, a series of
measurements were performed, in triplicate, in a 2-phase system,
at different conditions of bubble generation in the flotation cell:
the frother (MIBC) concentration was varied from 5 to 30 ppm,
whereas the agitation and superficial gas velocity, Jg, were kept
10
5
0
0.5
1
1.5
2
2.5
3
diameter, mm
25
Number frequency, %
d32 = 0.99 mm
20
15
10
5
0
0
0.5
1
1.5
2
2.5
3
diameter, mm
Fig. 6. Bubble size distributions generated at 300 rpm (up), and 600 rpm (down); Jg
0.5 cm/s.
d32 measured using acoustic technique, mm
0
3
2.5
2
1.5
2
R = 0.99
1
0.5
0
0
0.5
1
1.5
2
2.5
d32 measured using image analysis, mm
Fig. 7. Comparison between methods.
3
125
W. Kracht, C. Moraga / Minerals Engineering 98 (2016) 122–126
60
55
Sound intensity, dB
constant at 400 rpm and 0.5 cm/s, respectively, which allowed
generating bubble Sauter mean diameters, d32, ranging from 0.84
to 2.63 mm. The results, and the relative standard deviation
(RSD) are presented in Table 1.
The three runs follow the same trend, which corresponds to a
typical curve of bubble size against frother concentration (Cho
and Laskowski, 2002). The results show a good reproducibility
for a wide range of mean bubble sizes, and, since the shape of
the bubble size distribution changes when increasing the frother
concentration (Finch et al., 2008), it can also be said that with
the technique it is possible to estimate d32 from different distributions, as it was suggested from Fig. 6.
50
2
R = 0.97
45
40
35
30
25
20
0
0.5
1
1.5
2
2.5
Bubble mean diameter d32, mm
Fig. 8. Sound intensity vs d32 in a three-phase system.
3.4. Three-phase system
In order to test the technique in a more realistic condition, a series of measurements were performed in a 3-phase system (waterair-particles), with quartz as the solid phase, at a P80 of 200 um,
and a solid weight content of 30%. The conditions of bubble generation were the same as were previously used in the 2-phase system, i.e., impeller speeds varying between 300 and 600 rpm, Jg
between 0.3 and 0.5 cm/s, and a frother (MIBC) concentration of
30 ppm. As it can be seen in Fig. 8, the relation between the average signal intensity and the bubble Sauter mean diameter, d32, is
linear as in the case of the 2-phase system.
The values for m and n in this case are 16.24 dB/mm and
65.9 dB, with a coefficient of determination R2 equal to 0.97.
The coefficients for both conditions, 2-phase and 3-phase, are
summarised in Table 2. Note that the linear relation is maintained
but the value of n changes. The slope of the curve, on the other
hand, does not change significantly.
As noted in Table 2, the intensity of the signal with a 30% solids
is 5.9 dB higher than in the case of the water-air system. This result
suggests that the particles inside the chamber affect the behaviour
of the acoustic signal. The surface of the particles may be acting as
a signal reflector, which could explain the difference. This implies
that the relation between d32 and the mean intensity of the
received signal, Imean, is influenced by the presence of solids, and,
therefore, the calibration of the acoustic technique would be specific for the particular conditions of the system to be evaluated.
With the technique presented in this work it is possible to
determine the bubble Sauter mean diameter, d32, for a wide range
of sizes, from 0.75 to 3 mm, covering the range of most interest of
flotation. The configuration presented here considers the use of a
pump to take the samples (see Fig. 1), therefore, it is easy to set
up in such a way that it can operate continuously. Since the relationship between signal intensity and d32 is not derived from fundamentals, but from an empirical model, the technique requires
calibration against an accepted method such as the MBSA. Therefore, although the acoustic method represents an alternative to
the MBSA as a sensor to monitor the flotation process, it does not
completely replace the image analysis technique because it still
depends on it for calibration.
Table 1
Reproducibility.
MIBC (ppm)
5
10
15
20
25
30
d32 (mm)
RSD (%)
Run 1
Run 2
Run 3
2.61
1.41
0.98
0.85
0.84
0.87
2.51
1.29
0.88
0.91
0.92
0.94
2.63
1.40
0.90
0.84
0.93
0.94
2.3
5.1
5.4
4.6
5.6
4.4
Table 2
Coefficients for the intensity – d32 curves.
System
m
n
2-phase
3-phase
16.29
16.24
60.0
65.9
4. Conclusions
An acoustic technique for measuring the bubble Sauter mean
diameter, d32, is introduced. The technique consists of exposing
the bubbles to an acoustic perturbation, and analysing their
response. The perturbation corresponds to a modulated signal with
frequencies F1 ± F2, where F1 acts as a carrier set at 1 MHz, and F2
corresponds to the modulating signal, which varies for each measurement from 1 kHz to 10 kHz with a step of 50 Hz. The configuration considers the use of a peristaltic pump to sample liquid and
bubbles from the flotation cell, which can be automated to operate
continuously and in such a way that no operator is needed. An
empirical relation was found between the average intensity of
the acoustic response of the bubbles, Imean, and d32. The relation
is linear and can be written as Imean ¼ m d32 þ n, with coefficients
m and n that are determined with the aid of an independent
method such as the MBSA. The acoustic technique allows determining d32 in the range between 0.75 and 3 mm, covering the
range of most interest of flotation, and represents an alternative
to the image analysis as a sensor to monitor the flotation process;
nevertheless, it does not completely replace image analysis, which
is still needed for calibration.
Acknowledgements
The authors would like to acknowledge the Chilean Economic
Development Agency (CORFO), project number 11IDL2-10687,
and the Chilean National Commission for Scientific and Technological Research (CONICYT), Basal Financing Program FB0809, for
funding this research. This work made use of the free software
package GNU Octave, and the authors are grateful for the support
of the Octave development community.
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