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Effect of surface electrical charge on microbubbles’ terminal velocity and gas holdup
Minerals Engineering 119 (2018) 166–172
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Effect of surface electrical charge on microbubbles’ terminal velocity and gas holdup
T
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Roberto Pérez-Garibaya, , Arturo Bueno-Tokunagab, Rosa H. Estrada-Ruizc, Luis F. Camacho-Ortegónb a
Cinvestav-IPN, Industria Metalúrgica No. 1062, Parque Industrial Saltillo-Ramos Arizpe, Ramos Arizpe, Coahuila C.P. 25900, Mexico Escuela Superior de Ingeniería de la Universidad Autónoma de Coahuila, Blvd. Adolfo López Mateos, Nueva Rosita, Coahuila, Mexico c Instituto Tecnológico Nacional de México, Instituto Tecnológico de Saltillo, Venustiano Carranza No. 2400, Col. Tecnológico, Saltillo CP. 25280, Coahuila Mexico. Departamento de Ingeniería Mecánica-Mecatrónica, Mexico b
A R T I C L E I N F O
A B S T R A C T
Keywords: Microbubbles Terminal velocity Double layer charge The boundary layer thickness
The objective of this research was to study the effect of the electrical charge of microbubbles on their terminal velocity when they are conditioned with typical flotation reagents. Some of the contrasting collectors studied were potassium ethyl xanthate (anionic) and dodecylamine (cationic), and the studied frothers were terpinol, methyl-isobutyl-carbinol (MIBC), and 2-ethylhexanol. It was found that the microbubbles’ terminal velocity is mainly affected by their diameter, but the electrical charge has a significant effect, as it can change the boundary layer thickness of water surrounding each bubble. This behaviour is explained by considering that the attraction between the potential-determining ions and the counterions [e.g., hydrated proton (+) and xanthate (–)] shrinks and compacts the boundary layer thickness, which can reach high density, decreasing the microbubble terminal velocity. The opposite occurs when the bubble charge has the same sign as the counterions [e.g., hydroxyls (–) and xanthate (–)]; in this case, the diffuse layer and the boundary layer do not grow and the bubble terminal velocity increases.
1. Introduction It is known that in the froth flotation process, the bubble size has a significant effect on particle recovery, as it is recognized that for each particle size distribution, there exists a bubble size distribution that increases its collection efficiency (Han et al., 2007; Pease et al., 2005). For example, fine particles require small bubble sizes with low terminal velocity, not only because they need a long induction time to traverse the boundary layer thickness of water surrounding the bubbles in order to make contact with the air surface but also because they provide a high specific bubble surface area to carry a sufficient mass of fines particles. In this case, the bubble terminal velocity, bubble charge, and boundary layer thickness should be interesting variables for the optimization of the fine particles’ froth-flotation, as demonstrated in this paper. As mentioned by other researchers (Parkinson et al., 2008), so far there are few studies about microbubbles’ terminal velocity (diameter < 100 μm; Re < 1), and this lack of information is caused by the lack of sophisticated technology to visualize each individual floating microbubble. Fortunately, in recent years this technology has
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become available, which has permitted the realization of this study. This paper explains that in bubbling reactors, the gas holdup is not only a function of the bubble diameter and gas flow rate; in fact, other phenomena such as the effect of the double layer charge, the boundary layer thickness, and the friction between the adsorbed surfactant and the liquid side can be the origin of these gas holdup changes. This is a novel contribution to the knowledge of gas–liquid dispersion that can be used to explain the reasons why bubbles of the same diameter conditioned with different collectors can have different flotation velocities, affecting the gas holdup in the bubbling reactor. This paper is original and contributes new information to the fundamental knowledge of surfactant adsorption on bubble surfaces, the electrical charge of microbubbles, and microbubbles’ terminal velocity. 2. Background 2.1. Effect of surfactants and electrolytes on bubbles’ terminal velocity This section discusses why some physicochemical phenomena can affect the hydrodynamics of microbubbles and conventional bubble
Corresponding author. E-mail address: [email protected] (R. Pérez-Garibay).
https://doi.org/10.1016/j.mineng.2018.01.026 Received 6 June 2017; Received in revised form 23 December 2017; Accepted 18 January 2018 0892-6875/ © 2018 Elsevier Ltd. All rights reserved.
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bubble terminal velocity, as was also observed by Rafiei et al. (2011), who noted that bubbles with the same diameter conditioned with NaCl ascended more rapidly than those conditioned with methyl-isobutylcarbinol (MIBC), producing gas holdup increments.
sizes similarly. For example, the forces that define the bubbles’ rise velocity are the gravity, drag, and buoyancy, and once these forces are present for bubbles of both sizes (microbubbles and conventional bubbles), their rise velocities can be affected by the force balance. Independently of the bubble size, one of the variables of the bubbling reactors which is directly associated with changes in rise velocity is the gas holdup. In this context, the rise velocity can also be modified at both bubble sizes, because the double electrical layer is equally present in both cases, which affects the boundary layer volume and the drag force, as proposed in this paper. However, the hydrodynamics of microbubbles will be more affected than those of conventional bubbles. Kracht and Finch (2010) studied the effect of F150 frother and NaCl on the sphericity and velocity of bubbles. They observed that initially the bubbles accelerated up to a maximal velocity, after which there was a period with frequent velocity oscillations, and finally the bubbles reached their terminal velocity. They also found that when the bubbles are spherical, which is due to increased frother adsorption, they float slowly. Several authors (Dukhin et al., 1998; Krzan et al., 2007; Maldonado et al., 2013) discuss this phenomenon, explaining that surfactants reduce the terminal velocity of floating bubbles for two reasons: because they reduce the bubble diameter and because they increase the friction between the bubble surface and the liquid side. As evidence of this phenomenon, Fig. 1(a) shows the effect of frother concentration on bubble diameter, where it can be seen that the frother concentration decreases the bubble size, but this effect is different for each frother (Tan et al., 2013). A detailed description of the mechanism related to the effect of the frother type and concentration on the bubble diameter is outside of the scope of this paper, but it involves some factors such as molecular sizes, molecular orientation and packing at the bubble surface, surface mobility, surface tension gradients, and so on. The frothers can also affect the bubble rise velocity because they increase the bubble–liquid friction, as shown by the same authors in Fig. 1(b). Similar results were obtained by Kracht and Finch (2010), and Maldonado et al. (2013).they Krzan et al. (2004) also studied the bubble terminal velocity, the effect of the distance travelled, and the bubble sphericity. They found that the bubble terminal velocity decreased with the increment of reagent additions, and reported changes from 35 to 15 cm/s, even when the bubble diameter changed by only 10%. Analysing the literature, in general it is observed that the authors consider that a bubble reaches this velocity after travelling a distance of 100 times its diameter (Navarra et al., 2009; Rafiei et al., 2011; Tan et al., 2013). Another phenomenon resulting from the effect of surfactant adsorption is that bubbles of the same diameter conditioned with different surfactants have different flotation velocities, affecting the gas holdup in bubbling reactors. Azgomi et al. (2007) attempted to explain this observation, postulating that this effect is due to the changes of the
2.2. Effect of the microbubble electrical charge on the boundary layer thickness and the bubble terminal velocity It is known that the electric force of aqueous solutions has a strong effect on the electric double layer, as explained by Derjaguin, Landau, Verwey and Overbeek (DLVO) theory. This signifies that when the microbubbles are present in an aqueous solution with a strong concentration of counterions they produce a compact double layer, which may be related to their increased rise velocity, whereas a low concentration of counterions produces low compaction and possibly more friction during movement. It should be mentioned that a dense and heavy double layer also decreases the speed of the bubble. It is interesting that in the case of one microbubble, the volume of its boundary layer may be significant, in contrast to the gas volume, which is the reason why its rice velocity can be considerably affected by the surfactant adsorption. Gélinas et al. (2005), using the ultravioletvisible spectrophotometric technique, estimated the boundary layer thickness of the bubbles and found that this thickness increases with surfactant adsorption. Depending on the charge of the surface immersed in the electrolytic solution, it will attract a layer of ions with the opposite sign. When the Stern layer is covered (positive or negative), it will attract other approaching ions of opposite charge, forming a diffuse layer of counterions and eventually reaching a dynamic equilibrium and neutrality. This physical phenomenon is related to the boundary layer thickness of the microbubbles and may be the origin of the change of the microbubbles’ terminal velocity. Because this work deals with the relationship between the terminal velocity and the electrical charge of the microbubbles, some references and results regarding the characterization of the zeta potential of microbubbles conditioned with typical froth flotation reagents are presented. Kubota and Jameson (1993) estimated the zeta potential of fine bubbles in the presence of surfactants in aqueous solution and observed that the surfactant adsorption density changes with different chemical reagents. In another work, Nguyen and Schulze (2003) studied the effect of the electrolytes NaCl and KCl; they found that at pH > 3, the hydroxyl ions are adsorbed on the bubble surface, acquiring a negative charge, and suggested that the Na+, K+, and Cl− ions remain as indifferent electrolytes. Fig. 2(a) shows the zeta potential values measured by BuenoTokunaga et al. (2015) for air bubbles as a function of pH in the presence of typical froth flotation collectors at 25 ppm. Based on this
Fig. 1. Effect of frother concentration on bubble diameter (a) and bubble rise velocity (b) (Tan et al., 2013).
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30
10
(a)
(b)
NaCl 10 -2 M
20
0
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Z-Potential, mV
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NaCl 10 -2 M Deionized water
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Terpinol, 25 ppm.
Xanthate, 25 ppm.
-50 -60
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Deionized water
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Dodecylamine, 25 ppm.
2 Ethylhexanol, 30 ppm.
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0
2
4
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8
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12
14
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2
4
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Fig. 2. (a) Effects of typical froth flotation collectors on the zeta potential of air bubbles [dithiophosphinate 25 ppm (9.46E-5 M); xanthate 25 ppm (1.56E-4 M); dodecylamine 25 ppm (1.35E-4 M); 2-mercaptobenzothiazole 25 ppm (1.49E-4 M)]. (b) Effects of typical froth flotation frothers (25 ppm) on the zeta potential of air bubbles [terpinol 25 ppm (1.62E-4 M); MIBC 25 ppm (2.45E-4 M); 2-ethylhexanol 30 ppm (2.30E-4 M)]. . Adapted from Bueno-Tokunaga et al. (2015)
figure, the collectors can be ranked in the following order from more anionic to more cationic: xanthate, dithiophosphinate, deionized water, mercaptobenzothiazole, and dodecylamine. Fig. 2(b) compares the effects of typical froth flotation frothers (at 25 ppm) on the zeta potential of air bubbles. Contrary to what was observed for the collectors, the frothers have only a minimal effect on the zeta potential.
function was to prevent visualization of the bubbles passing behind this zone. A small white-light lamp (7 W) was placed near the semi-opaque plaque to illuminate the microbubbles. Once the displacement distance of the bubble and the time required for the displacement had been registered, the bubble velocity was estimated.
4. Methodology 3. Experimental The froth flotation reagents that were investigated were a) potassium ethyl xanthate (C3H5KOS2, 96%; Sigma-Aldrich), b) dodecylamine (C12H27N, 98%; Sigma-Aldrich), c) terpinol (C10H18O, 98%; Sigma-Aldrich), and d) methyl-isobutyl-carbinol (MIBC, 98%; SigmaAldrich). When the aqueous solution had been prepared, the pH, temperature, and electrical conductivity were recorded. To provide a controlled ionic strength, a sufficient quantity of NaCl was added to the aqueous solution for it to reach a concentration of 10−3 M. This solution was poured into the bubbling cell, and the remainder was put in the air saturator. To facilitate air dissolution, the saturator was manually mixed until the saturation point was reached. Once the solution was saturated with air, the valve located at the output of the saturator was opened to introduce the solution into the bubbling cell, initiating the microbubble nucleation. Fig. 4 shows a sequence of images depicting the vertical displacement of the microbubble. Each figure includes a semi-transparent wire of a known size (a thin Nylon® wire, 230 μm in diameter), which was placed close to the front wall of the cell and used as a size reference. The images also include the file names used in the format
3.1. Equipment The experimental setup is composed of three major components: the air-saturation reactor (where water is saturated with air), the bubbling cell, and the image-acquisition system (see Fig. 3). The image acquisition system includes a digital camera equipped with a macro lens (Navitar® 12X). The video camera (Toshiba 3-CCD RGB; resolution 1024 × 768 pixels; 90 frames/s) permitted the user to register the bubble displacement and the time through a MATHLAB® library that linked the video camera to the computer. The saturation reactor was constructed from polyvinyl chloride (PVC, 40; internal diameter = 10 cm; height = 20 cm). To saturate the aqueous solution with air, this gas was injected at a pressure of 100 PSI and mixed manually to promote the air–liquid contact and saturation. The bubbling cell was made from transparent acrylic, and the video camera was placed in the central section facing the cell wall. The visualization screen was constructed from one acrylic semiopaque sheet placed 0.2 cm behind the transparent front wall, and its
Input: Air and solution Visualization
zone Bubbling cell
Camera
Image acquisition Fig. 3. Experimental setup.
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Saturator Microbubbles injection
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15 : 43 : 33 : 828
(a)
15 : 43 : 34 : 545
250 μm
(b)
15 : 43 : 35 : 295
250 μm
250 μm
(c)
15 : 43 : 36 : 218
(d)
250 μm
Fig. 4. Sequence of images depicting the route and vertical displacement of a bubble measured at 20 cm after its release.
“HH_MM_SS_FFF” to record the hours, minutes, seconds, and milliseconds. Several images were collected to permit the selection of at least 20 single microbubbles, moving with free flotation in front of the visualization zone. After measuring the time and displacement of the bubble, the bubble velocity could be estimated, which was possible because the video file could be replayed offline. To obtain reliable images, a photograph of a single microbubble ascending through free flotation was selected. The registered images and video (converted to images) were analysed using IMAGEPRO® software. Each bubble diameter and terminal velocity, presented in the “Results and Discussion” section, is the average of 20 or 30 measurements of bubbles of very similar diameters, where the standard deviation oscillated between 35 and 60 µm/s, at the terminal velocity. The following sequence of images illustrates the bubbles’ movement [see Fig. 4(a) to (d)]:
5.2. Effect of bubble size and frother addition on microbubbles’ terminal velocity Fig. 6(a) shows the effect of the bubble diameter and MIBC concentration on the bubble terminal velocity at a pH close to 5.7. It is important to specify that each point represents the average of the velocity measurements of bubbles with similar diameters ( ± 3 µm, approximately). As observed in this figure, the terminal velocity decreases with the increment of MIBC concentration, which may be related to the augmentation of friction, as mentioned by Detwiler and Blanchard (1978) or to the growth in the boundary layer thickness. It should be noted that a similar effect is observed in Fig. 6(b) when the terpinol frother is added. It is known that frothers do not modify the zeta potential of the bubbles significantly (Bueno-Tokunaga et al., 2015), and consequently the change in the terminal velocity is mainly due to the change in the friction with the water side, as shown in Fig. 4.
5. Results and discussion 5.3. Effect of pH, bubble diameter, and ionic collector type on bubble terminal velocity
5.1. Validation of the microbubble terminal velocity measurement In the first instance, this work aimed to prove that the microbubble terminal velocity was measured in all of the tests, and as evidence, Fig. 5 shows the monitoring of one of these measurements where the flotation bubble velocity was kept constant in the visualization zone. Also, the values of the terminal velocity observed in this work are similar to those reported in the literature (Parkinson et al., 2008; Takahashi, 2005; Kelsall et al., 1996). It is noteworthy that this work was carried out with microbubbles whose maximum diameter was 73 µm and whose terminal velocity was measured at 20 cm after their release, which represents more than 2600 times the bubble diameter.
Fig. 7(a) and (b) compare the effects of bubble diameter, pH, and ionic collector type (anionic and cationic) on the microbubble terminal velocity. It is noteworthy that when working with xanthate (anionic) at an alkaline pH, the terminal velocity is greater than that obtained at an acidic pH, even when the bubble diameter is similar. In contrast, it should be noted that when working with dodecylamine (cationic) at alkaline pH, the terminal velocity is smaller than that obtained at acidic pH. It is important to note that, although 30 ppm (1.62E-4 M) of dodecylamine was added, at pH 11.6 dodecylamine solubility (pKb) is 10.6, which signifies that a part of this reagent is not solubilized (ionic state); however, it is believed that the solubilized part is responsible for the enlargement of the double layer engrossment and the diminution of the terminal velocity. Fig. 8 shows that when the microbubbles are conditioned with xanthate or dodecylamine at a pH close to neutrality (between 6.2 and 7.02), the bubbles ascend with almost the same velocity with both collectors. It should be noted that when the pH values are similar in the two cases, the terminal velocities are also similar. These results may be explained by the fact that at neutral pH (pH 7), a high concentration of determinant ions (protons or hydroxyls) does not exist, which decreases the attractive forces for the counterions or the diffuse layer, as described in this paper. To explain these results, it is proposed that when an anionic collector (xanthate) is adsorbed under an acidic pH, the bubbles float more slowly for two reasons: (1) the boundary layer reaches a greater thickness for the formation of an expanded diffuse layer and (2) the expanded diffuse layer also increases the friction with the liquid side. The fact that the boundary layer may increase its volume in acidic conditions [as illustrated in Fig. 9(a)] can be explained by the following mechanism: Initially the water dipoles are placed on the air surface,
Experimental Vt (μm/s)
1000 950 900 850 800 750 700 650 600 0
1
2
3
Time (s) Fig. 5. Monitoring of the rise velocity of one microbubble in the visualization zone (20 cm after its release).
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1800 1600
Agua desionizada Deionized water
MIBC 30 ppm (2.94E-04 M), pH=5.7 MIBC;30ppm.,pH=5.7
Experimental Vt (μm/s)
Experimental Vt (μm/s)
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MIBC;7ppm.,pH=5.8 MIBC 7 ppm (6.85E-05 M), pH=5.8
1400 1200 1000 800 600
Terpinol, ppm (1.62E-4 Terpinol, 2525 ppm.
2500
M)
pH=7
2000 1500 1000
400 500
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(a)
(b)
0 0
10
20
30
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Bubble diameter (μm)
20
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80
Bubble diameter (μm)
Fig. 6. Effect of diameter and frother concentration on microbubbles’ terminal velocity, measured at 20 cm after their release: (a) for MIBC; (b) for terpinol and deionized water. 3,500
Experimental Vt(μm/s)
exposing their negative end (oxygen atoms) toward the air side, and via charge–dipole interaction occurs the attraction of the zeta potential determining ions (H+ and/or OH−, depending on the pH). It should be mentioned that this zone may include several layers, as proposed by Zhang and Finch (1996). Then, on the proton layer, the counterions or the xanthate anions are adsorbed, finally imposing a negative charge on the bubble, as proposed by several authors (Nguyen and Schulze, 2003; Ushikubo et al., 2010; Takahashi, 2005). When a strong acid and a strong base (HCl and NaOH) were used as pH modifiers, their protons and bases were completely hydrolyzed, becoming potential-determining ions for the double electrical layer. However, these are not the only ions that act on the interphase, because the collector decomposition due to the effect of pH can produce other ionic products with the capacity to interact with the water molecules, as donors or receptors of protons or bases. It is known that the chemical decomposition of xanthate (−OCS2−) is greater in acidic than in alkaline pH (Shen et al., 2016). For example, in acidic medium, the xanthate produces carbon disulfide (CS2), while in alkaline solutions it can produce alcohol (R−OH ), trithiocarbonate (CS3−2) , xanthic acid (R−OCS2 H ), xanthic acid compound (R−OCS2−H+) , dixanthogen (R−OCS2)2 , perxanthate (R−OCS2 O−) , monothiocarbonate (CO2 S 2 −) , dithiocarbonate (CS22 −) , and sulfide (S 2 −) . All of these products can act as weak bases, competing with all the other species to take a space at the bubble interphase and contributing a low and negative electrical charge to the bubble. As a result of this complex interaction between protons, basic ions, and water molecules, a double layer is formed on the bubble surface, indirectly affecting the bubble terminal velocity. Contrarily, under an alkaline pH, the bubbles ascend rapidly because they apparently transport a boundary layer with a minor volume,
Xantato,30 Xanthate,ppm.,pH=6.2 30 ppm (1.87E-4 M),
2,500
Dodecylamine, ppm.,pH=7.02 30 ppm (1.62E-4 M), Dodecilamina,30
pH=6.2 pH=7.02
2,000 1,500 1,000 500 0 0
20
40
60
80
Bubble diameter(μm) Fig. 8. Effect of bubble diameter and collector type on microbubble terminal velocity measured at 20 cm after release and pH = 7.
as illustrated in Fig. 9(c). In this case, it is proposed that the first layer of water molecules inverts its polarity, orienting its positive pole toward the liquid side due to the high concentration and adsorption of hydroxyl ions. Once the hydroxyl ions have been adsorbed, the bubble intensifies its negative charge, decreasing the adsorption of the xanthate due to the electrostatic repulsive forces and producing a zeta potential like bubbles in water at alkaline pH. A similar explanation can be given when the bubbles are conditioned with a cationic collector such as dodecylamine. In acidic pH, the protons are adsorbed on the first layer of water molecules, which
2,500
1,800
(a)
Xanthate,ppm.,pH=12 30 ppm (1.87E-4 M), Xantato,30 2,000
Dodecylamine, 30 ppm (1.62E-4 M), pH=11.6 Dodecylamine, 30 ppm, Dodecilamina,30 ppm.,pH=2.3 pH=2.3
1,500
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Dodecilamina,30 ppm.,pH=11.6
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pH=12 Xanthate,ppm.,pH=2.4 30 ppm, pH=2.4 Xantato,30
Experimental velocity (μm/s)
Experimental velocity (μm/s)
3,000
1,400 1,200 1,000 800 600 400 200
0
0 0
20
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80
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0
20
40
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Bubble diameter (μm)
Fig. 7. Effect of pH and bubble diameter on microbubble terminal velocity, measured at 20 cm after release: (a) with xanthate; (b) with dodecylamine.
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pH
3
7
-
+-
+
+
-
X
+-
+ +-
± = H2O Dipole
-
+-
Na+
X
X
Cl-
-
-
+-
+-
+ X-
-
+-
+
-
X-
-
-
+ X-
-
X- = Xanthate ion
-
-
-
+ = H+
Na+
+-
X-
+ +-
+-
-
-
X-
X-
+
+-
+ +
+ +-
+-
+
-
X
X-
X
-
- = OH
Cl-
Anionic collector
14
Na+ = Sodium ion Na+
Cl- = Cloride ion
Cl-
(a)
(c)
(b)
Fig. 9. Schematic representation of boundary layer thickness with xanthate.
+-
+
+
D+
+
D
-
+
D
+
-
+
D+
+ +-
+
+-
(b)
D+ = Dodecylamine
+
Na+ = Sodium ion
-
Na+
(a)
± = H2O Dipole
- D+
D
D+
+ = H+
D+
-
+-
+-
-
+-
+
D
+
-D +
-
+ +-
-
Cl-
-
-
- = OH
Na+
+
+-
+
+
D
-
D
+
+-
Cationic collector
+ +-
+-
+ +
Na+
Cl-
+-
Cl-
Cl- = Cloride ion
(c)
Fig. 10. Schematic representation of boundary layer thickness with dodecylamine.
velocity. The extrapolated curves of dodecylamine and water zeta potential converge in the acid region, whereas the extrapolated curves for water and xanthate converge in the alkaline region. In contrast, the differences between the zeta potential curves of the collectors increase in the alkaline region for dodecylamine and in the acidic region for xanthate. From these observations, it is possible to conclude that when the curves converge, an attraction force that would cause growth of the diffuse layer thickness (short boundary layer) does not exist, whereas when the difference between the zeta potential curves increases, an attractive force exists, which increases the diffuse layer thickness (big boundary layer). Certainly, the double layer is not the only factor that affects the bubble rise velocity. It is well known that there is a proportionality between the size of the hydrocarbon chain and the hydrophobicity of the surfactant (Tan and Finch, 2016), from which it is deduced that the hydrophobicity also increases the friction with the liquid phase, indirectly causing a decrease in the bubble terminal velocity. With regard to the effect of the frother’s surface activity, the frother molecule has
expose their negative dipole toward the liquid side, acquiring a positive potential [see Fig. 10(a)]. The ionic nature of this weak electrolyte is predominantly nonionic at high pH (10 < pH < 13) (Xu et al., 2015), forms ionic–nonionic pairs at intermediate pH, and is only truly cationic at low pH (1–9). Thus, the pH will also affect the surface activity of such a weak base as dodecylamine, leading to competition between species to take space at the bubble interphase. However, as shown in the “Background” section, a low positive charge predominates on the bubbles, even at alkaline pH. When this occurs, the positive dodecylamine cations are repelled, impeding the growth of the diffuse boundary layer and producing a similar potential with acidic pH. In the case where the microbubbles are conditioned with dodecylamine at alkaline pH (see Fig. 10(c)), the hydroxyl anions adsorbed on the bubble attract the cations of the collector, increasing the boundary layer thickness and decreasing its negative potential. Fig. 11 shows some experimental data, extracted from BuenoTokunaga et al. (2015), that support the presented explanation concerning the effect of the bubble electrical charge on the bubble terminal 30
(a) Dodecylamine Na+
+
D
(b) Water
-
-10
D
|pZ-pZ(H2O)|
-20
(c) Xanthate
0
2
+
+D
+ +-
-40 -50
-
+
D
-30
-
+
4
6
8
10
D+
-
+-
+-
+
+
Cl-
0
Na+
+
+-
+
Zeta potencial (mV)
+
-
+ +-
+-
+ +
D
-
10
+
- D+
-
Cl-
+-
20
D
+
-
12
pH
Fig. 11. Convergence of zeta potential curves of water and dodecylamine for the acid region and curves of water and xanthate for the alkaline region (pZ refers to the zeta potential).
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two parts: a hydrophobic (non-polar) hydrocarbon (usually alkyl) chain and a hydrophilic (polar) head. The general understanding is that the frother molecule adsorbed at the water/air interface with the polar group oriented to the water side and the hydrocarbon chain oriented to the air side (Tan and Finch, 2016), which also contributes to the increment of bubble–water friction. Ionic collectors also have a polar part and a hydrocarbon chain and when they are adsorbed on the particles, the non-polar part is oriented toward the water. Contrarily, when it is adsorbed on the bubble surface, the non-polar part is oriented toward the air. Once the hydrophilic part has been oriented to the water, it is possible for the hydration to increase the friction and decrease the bubble rise velocity. All of that promotes competition between the repulsive forces of the double layer and the hydrophilic and polar parts of the collector, producing a stable water film that decreases the bubble rise velocity, as observed by other authors investigating hydrophobic particles (Pan and Roe-Hoan Yoon, 2016; Meyer et al., 2006).
Detwiler, A., Blanchard, D.C., 1978. Aging and bursting bubbles in trace-contaminated water. Chem. Eng. Sci. 33 (1), 9–13. Dukhin, S.S., Miller, R., Loglio, G., 1998. Physico-chemical hydrodynamics of rising bubble. In: MÖbius, D., Miller, R. (Eds.), Studies in Interface Science. Elsevier, pp. 367–432. Gélinas, S., Finch, J.A., Gouet-Kaplan, M., 2005. Comparative real-time characterization of frother bubble thin films. J. Colloid Interface Sci. 291 (1), 187–191. Han, M., Kim, T., Kim, J., 2007. Effects of flock and bubble size on the efficiency of the dissolved air flotation (DAF) process. Water Sci. Technol. 56 (10), 109–115. Kelsall, G.H., Tang, S., Yurdakul, S., Smith, A.L., 1996. Electrophoretic behaviour of bubbles in aqueous electrolytes. J. Chem. Soc. Faraday Trans. 92 (20), 3887–3893. Kracht, W., Finch, J.A., 2010. Effect of frother on initial bubble shape and velocity. Int. J. Miner. Process. 94 (3–4), 115–120. Krzan, M., Lunkenheimer, K., Malysa, K., 2004. On the influence of the surfactant's polar group on the local and terminal velocities of bubbles. Colloids Surf. A: Physicochem. Eng. Asp. 250 (1–3), 431–441. Krzan, M., Zawala, J., Malysa, K., 2007. Development of steady state adsorption distribution over interface of a bubble rising in solutions of n-alkanols (C5, C8) and nalkyltrimethylammonium bromides (C8, C12, C16). Colloids Surf. A: Physicochem. Eng. Asp. 298 (1–2), 42–51. Kubota, K., Jameson, G.J., 1993. A study of the electrophoretic mobility of a very small inert gas bubble suspended in aqueous inorganic electrolyte and cationic surfactant solutions. J. Chem. Eng. Jpn. 26 (1), 6. Maldonado, M., Quinn, J.J., Gomez, C.O., Finch, J.A., 2013. An experimental study examining the relationship between bubble shape and rise velocity. Chem. Eng. Sci. 98, 7–11. Meyer, E.E., Rosenberg, K.J., Israelachvili, J., 2006. Recent progress in understanding hydrophobic interactions. Proc. Natl. Acad. Sci. U.S.A. 103, 15739–15746. Navarra, A., Acuña, C., Finch, J.A., 2009. Impact of frother on the terminal velocity of small bubbles. Int. J. Miner. Process. 91 (3–4), 68–73. Nguyen, A., Schulze, H.J., 2003. Colloidal Science of Flotation. Taylor & Francis. Pan, L., Roe-Hoan Yoon, R.H., 2016. Measurement of hydrophobic forces in thin liquid films of water between bubbles and xanthate-treated gold surfaces. Miner. Eng. 98, 240–250. Parkinson, L., Sedev, R., Fornasiero, D., Ralston, J., 2008. The terminal rise velocity of 10–100 μm diameter bubbles in water. J. Colloid Interface Sci. 322 (1), 168–172. Pease, J., Curry, D., Young, M., 2005. Designing flotation circuits for high fines recovery. Miner. Eng. 19, 831–840. Rafiei, A.A., Robbertze, M., Finch, J.A., 2011. Gas holdup and single bubble velocity profile. Int. J. Miner. Process. 98 (1–2), 89–93. Shen, Y., Nagaraj, D.R., Farinato, R., Somasundaran, P., 2016. Study of xanthate decomposition in aqueous solutions. Miner. Eng. 93, 10–15. Takahashi, M., 2005. ζ potential of microbubbles in aqueous solutions: electrical properties of the gas−water interface. J. Phys. Chem. B 109 (46), 21858–21864. Tan, Y.H., Finch, J.A., 2016. Frother structure–property relationship: effect of alkyl chain length in alcohols and polyglycol ethers on bubble rise velocity. Miner. Eng. 95, 14–20. Tan, Y.H., Rafiei, A.A., Elmahdy, A., Finch, J.A., 2013. Bubble size, gas holdup and bubble velocity profile of some alcohols and commercial frothers Int. J. Miner. Process. 119, 1–5. Ushikubo, F.Y., Furukawa, T., Nakagawa, R., Enari, M., Oshita, S., 2010. Evidence of the existence and the stability of nano-bubbles in water. Colloids Surf. A: Physicochem. Eng. Asp. 361 (1–3), 31–37. Xu, S., Kou, J., Sun, T., Jong, K., 2015. A study of adsorption mechanism of dodecylamine on sphalerite. Colloids Surf. A: Physicochem. Eng. Asp. 486, 145–152. Zhang, Y., Finch, J., 1996. Terminal velocity of bubbles: approach and preliminary investigation. Column 96, 63–69.
6. Conclusions It was shown that frothers do not affect the electrical charge of the microbubbles significantly, but their effect on the terminal velocity may be due to the increase in viscous forces between the adsorbed frother and the liquid side. When the potential-determining ions at the surface of the bubble (protons and hydroxyls) have the opposite charge to the ionic surfactant (anionic or cationic), the diffuse layer is expanded and then the boundary layer thickness increases. It is proposed that besides the effect of bubble diameter and surfactant addition, the electrical charge of the bubble affects the terminal velocity and the boundary layer thickness of the microbubbles. Acknowledgements The authors are grateful to CONACYT (Mexico) for scholarships and funding and to Carmelita Yamamoto Chavarria for assistance with the data collection. This study was also funded by Cinvestav internal projects (928, 1032). References Azgomi, F., Gomez, C.O., Finch, J.A., 2007. Correspondence of gas holdup and bubble size in presence of different frothers. Int. J. Miner. Process. 83 (1–2), 1–11. Bueno-Tokunaga, A., Pérez-Garibay, R., Martínez-Carrillo, D., 2015. Zeta potential of air bubbles conditioned with typical froth flotation reagents. Int. J. Miner. Process. 140, 50–57.
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Effect of surface electrical charge on microbubbles’ terminal velocity and gas holdup
T
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Roberto Pérez-Garibaya, , Arturo Bueno-Tokunagab, Rosa H. Estrada-Ruizc, Luis F. Camacho-Ortegónb a
Cinvestav-IPN, Industria Metalúrgica No. 1062, Parque Industrial Saltillo-Ramos Arizpe, Ramos Arizpe, Coahuila C.P. 25900, Mexico Escuela Superior de Ingeniería de la Universidad Autónoma de Coahuila, Blvd. Adolfo López Mateos, Nueva Rosita, Coahuila, Mexico c Instituto Tecnológico Nacional de México, Instituto Tecnológico de Saltillo, Venustiano Carranza No. 2400, Col. Tecnológico, Saltillo CP. 25280, Coahuila Mexico. Departamento de Ingeniería Mecánica-Mecatrónica, Mexico b
A R T I C L E I N F O
A B S T R A C T
Keywords: Microbubbles Terminal velocity Double layer charge The boundary layer thickness
The objective of this research was to study the effect of the electrical charge of microbubbles on their terminal velocity when they are conditioned with typical flotation reagents. Some of the contrasting collectors studied were potassium ethyl xanthate (anionic) and dodecylamine (cationic), and the studied frothers were terpinol, methyl-isobutyl-carbinol (MIBC), and 2-ethylhexanol. It was found that the microbubbles’ terminal velocity is mainly affected by their diameter, but the electrical charge has a significant effect, as it can change the boundary layer thickness of water surrounding each bubble. This behaviour is explained by considering that the attraction between the potential-determining ions and the counterions [e.g., hydrated proton (+) and xanthate (–)] shrinks and compacts the boundary layer thickness, which can reach high density, decreasing the microbubble terminal velocity. The opposite occurs when the bubble charge has the same sign as the counterions [e.g., hydroxyls (–) and xanthate (–)]; in this case, the diffuse layer and the boundary layer do not grow and the bubble terminal velocity increases.
1. Introduction It is known that in the froth flotation process, the bubble size has a significant effect on particle recovery, as it is recognized that for each particle size distribution, there exists a bubble size distribution that increases its collection efficiency (Han et al., 2007; Pease et al., 2005). For example, fine particles require small bubble sizes with low terminal velocity, not only because they need a long induction time to traverse the boundary layer thickness of water surrounding the bubbles in order to make contact with the air surface but also because they provide a high specific bubble surface area to carry a sufficient mass of fines particles. In this case, the bubble terminal velocity, bubble charge, and boundary layer thickness should be interesting variables for the optimization of the fine particles’ froth-flotation, as demonstrated in this paper. As mentioned by other researchers (Parkinson et al., 2008), so far there are few studies about microbubbles’ terminal velocity (diameter < 100 μm; Re < 1), and this lack of information is caused by the lack of sophisticated technology to visualize each individual floating microbubble. Fortunately, in recent years this technology has
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become available, which has permitted the realization of this study. This paper explains that in bubbling reactors, the gas holdup is not only a function of the bubble diameter and gas flow rate; in fact, other phenomena such as the effect of the double layer charge, the boundary layer thickness, and the friction between the adsorbed surfactant and the liquid side can be the origin of these gas holdup changes. This is a novel contribution to the knowledge of gas–liquid dispersion that can be used to explain the reasons why bubbles of the same diameter conditioned with different collectors can have different flotation velocities, affecting the gas holdup in the bubbling reactor. This paper is original and contributes new information to the fundamental knowledge of surfactant adsorption on bubble surfaces, the electrical charge of microbubbles, and microbubbles’ terminal velocity. 2. Background 2.1. Effect of surfactants and electrolytes on bubbles’ terminal velocity This section discusses why some physicochemical phenomena can affect the hydrodynamics of microbubbles and conventional bubble
Corresponding author. E-mail address: [email protected] (R. Pérez-Garibay).
https://doi.org/10.1016/j.mineng.2018.01.026 Received 6 June 2017; Received in revised form 23 December 2017; Accepted 18 January 2018 0892-6875/ © 2018 Elsevier Ltd. All rights reserved.
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bubble terminal velocity, as was also observed by Rafiei et al. (2011), who noted that bubbles with the same diameter conditioned with NaCl ascended more rapidly than those conditioned with methyl-isobutylcarbinol (MIBC), producing gas holdup increments.
sizes similarly. For example, the forces that define the bubbles’ rise velocity are the gravity, drag, and buoyancy, and once these forces are present for bubbles of both sizes (microbubbles and conventional bubbles), their rise velocities can be affected by the force balance. Independently of the bubble size, one of the variables of the bubbling reactors which is directly associated with changes in rise velocity is the gas holdup. In this context, the rise velocity can also be modified at both bubble sizes, because the double electrical layer is equally present in both cases, which affects the boundary layer volume and the drag force, as proposed in this paper. However, the hydrodynamics of microbubbles will be more affected than those of conventional bubbles. Kracht and Finch (2010) studied the effect of F150 frother and NaCl on the sphericity and velocity of bubbles. They observed that initially the bubbles accelerated up to a maximal velocity, after which there was a period with frequent velocity oscillations, and finally the bubbles reached their terminal velocity. They also found that when the bubbles are spherical, which is due to increased frother adsorption, they float slowly. Several authors (Dukhin et al., 1998; Krzan et al., 2007; Maldonado et al., 2013) discuss this phenomenon, explaining that surfactants reduce the terminal velocity of floating bubbles for two reasons: because they reduce the bubble diameter and because they increase the friction between the bubble surface and the liquid side. As evidence of this phenomenon, Fig. 1(a) shows the effect of frother concentration on bubble diameter, where it can be seen that the frother concentration decreases the bubble size, but this effect is different for each frother (Tan et al., 2013). A detailed description of the mechanism related to the effect of the frother type and concentration on the bubble diameter is outside of the scope of this paper, but it involves some factors such as molecular sizes, molecular orientation and packing at the bubble surface, surface mobility, surface tension gradients, and so on. The frothers can also affect the bubble rise velocity because they increase the bubble–liquid friction, as shown by the same authors in Fig. 1(b). Similar results were obtained by Kracht and Finch (2010), and Maldonado et al. (2013).they Krzan et al. (2004) also studied the bubble terminal velocity, the effect of the distance travelled, and the bubble sphericity. They found that the bubble terminal velocity decreased with the increment of reagent additions, and reported changes from 35 to 15 cm/s, even when the bubble diameter changed by only 10%. Analysing the literature, in general it is observed that the authors consider that a bubble reaches this velocity after travelling a distance of 100 times its diameter (Navarra et al., 2009; Rafiei et al., 2011; Tan et al., 2013). Another phenomenon resulting from the effect of surfactant adsorption is that bubbles of the same diameter conditioned with different surfactants have different flotation velocities, affecting the gas holdup in bubbling reactors. Azgomi et al. (2007) attempted to explain this observation, postulating that this effect is due to the changes of the
2.2. Effect of the microbubble electrical charge on the boundary layer thickness and the bubble terminal velocity It is known that the electric force of aqueous solutions has a strong effect on the electric double layer, as explained by Derjaguin, Landau, Verwey and Overbeek (DLVO) theory. This signifies that when the microbubbles are present in an aqueous solution with a strong concentration of counterions they produce a compact double layer, which may be related to their increased rise velocity, whereas a low concentration of counterions produces low compaction and possibly more friction during movement. It should be mentioned that a dense and heavy double layer also decreases the speed of the bubble. It is interesting that in the case of one microbubble, the volume of its boundary layer may be significant, in contrast to the gas volume, which is the reason why its rice velocity can be considerably affected by the surfactant adsorption. Gélinas et al. (2005), using the ultravioletvisible spectrophotometric technique, estimated the boundary layer thickness of the bubbles and found that this thickness increases with surfactant adsorption. Depending on the charge of the surface immersed in the electrolytic solution, it will attract a layer of ions with the opposite sign. When the Stern layer is covered (positive or negative), it will attract other approaching ions of opposite charge, forming a diffuse layer of counterions and eventually reaching a dynamic equilibrium and neutrality. This physical phenomenon is related to the boundary layer thickness of the microbubbles and may be the origin of the change of the microbubbles’ terminal velocity. Because this work deals with the relationship between the terminal velocity and the electrical charge of the microbubbles, some references and results regarding the characterization of the zeta potential of microbubbles conditioned with typical froth flotation reagents are presented. Kubota and Jameson (1993) estimated the zeta potential of fine bubbles in the presence of surfactants in aqueous solution and observed that the surfactant adsorption density changes with different chemical reagents. In another work, Nguyen and Schulze (2003) studied the effect of the electrolytes NaCl and KCl; they found that at pH > 3, the hydroxyl ions are adsorbed on the bubble surface, acquiring a negative charge, and suggested that the Na+, K+, and Cl− ions remain as indifferent electrolytes. Fig. 2(a) shows the zeta potential values measured by BuenoTokunaga et al. (2015) for air bubbles as a function of pH in the presence of typical froth flotation collectors at 25 ppm. Based on this
Fig. 1. Effect of frother concentration on bubble diameter (a) and bubble rise velocity (b) (Tan et al., 2013).
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Fig. 2. (a) Effects of typical froth flotation collectors on the zeta potential of air bubbles [dithiophosphinate 25 ppm (9.46E-5 M); xanthate 25 ppm (1.56E-4 M); dodecylamine 25 ppm (1.35E-4 M); 2-mercaptobenzothiazole 25 ppm (1.49E-4 M)]. (b) Effects of typical froth flotation frothers (25 ppm) on the zeta potential of air bubbles [terpinol 25 ppm (1.62E-4 M); MIBC 25 ppm (2.45E-4 M); 2-ethylhexanol 30 ppm (2.30E-4 M)]. . Adapted from Bueno-Tokunaga et al. (2015)
figure, the collectors can be ranked in the following order from more anionic to more cationic: xanthate, dithiophosphinate, deionized water, mercaptobenzothiazole, and dodecylamine. Fig. 2(b) compares the effects of typical froth flotation frothers (at 25 ppm) on the zeta potential of air bubbles. Contrary to what was observed for the collectors, the frothers have only a minimal effect on the zeta potential.
function was to prevent visualization of the bubbles passing behind this zone. A small white-light lamp (7 W) was placed near the semi-opaque plaque to illuminate the microbubbles. Once the displacement distance of the bubble and the time required for the displacement had been registered, the bubble velocity was estimated.
4. Methodology 3. Experimental The froth flotation reagents that were investigated were a) potassium ethyl xanthate (C3H5KOS2, 96%; Sigma-Aldrich), b) dodecylamine (C12H27N, 98%; Sigma-Aldrich), c) terpinol (C10H18O, 98%; Sigma-Aldrich), and d) methyl-isobutyl-carbinol (MIBC, 98%; SigmaAldrich). When the aqueous solution had been prepared, the pH, temperature, and electrical conductivity were recorded. To provide a controlled ionic strength, a sufficient quantity of NaCl was added to the aqueous solution for it to reach a concentration of 10−3 M. This solution was poured into the bubbling cell, and the remainder was put in the air saturator. To facilitate air dissolution, the saturator was manually mixed until the saturation point was reached. Once the solution was saturated with air, the valve located at the output of the saturator was opened to introduce the solution into the bubbling cell, initiating the microbubble nucleation. Fig. 4 shows a sequence of images depicting the vertical displacement of the microbubble. Each figure includes a semi-transparent wire of a known size (a thin Nylon® wire, 230 μm in diameter), which was placed close to the front wall of the cell and used as a size reference. The images also include the file names used in the format
3.1. Equipment The experimental setup is composed of three major components: the air-saturation reactor (where water is saturated with air), the bubbling cell, and the image-acquisition system (see Fig. 3). The image acquisition system includes a digital camera equipped with a macro lens (Navitar® 12X). The video camera (Toshiba 3-CCD RGB; resolution 1024 × 768 pixels; 90 frames/s) permitted the user to register the bubble displacement and the time through a MATHLAB® library that linked the video camera to the computer. The saturation reactor was constructed from polyvinyl chloride (PVC, 40; internal diameter = 10 cm; height = 20 cm). To saturate the aqueous solution with air, this gas was injected at a pressure of 100 PSI and mixed manually to promote the air–liquid contact and saturation. The bubbling cell was made from transparent acrylic, and the video camera was placed in the central section facing the cell wall. The visualization screen was constructed from one acrylic semiopaque sheet placed 0.2 cm behind the transparent front wall, and its
Input: Air and solution Visualization
zone Bubbling cell
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Image acquisition Fig. 3. Experimental setup.
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Fig. 4. Sequence of images depicting the route and vertical displacement of a bubble measured at 20 cm after its release.
“HH_MM_SS_FFF” to record the hours, minutes, seconds, and milliseconds. Several images were collected to permit the selection of at least 20 single microbubbles, moving with free flotation in front of the visualization zone. After measuring the time and displacement of the bubble, the bubble velocity could be estimated, which was possible because the video file could be replayed offline. To obtain reliable images, a photograph of a single microbubble ascending through free flotation was selected. The registered images and video (converted to images) were analysed using IMAGEPRO® software. Each bubble diameter and terminal velocity, presented in the “Results and Discussion” section, is the average of 20 or 30 measurements of bubbles of very similar diameters, where the standard deviation oscillated between 35 and 60 µm/s, at the terminal velocity. The following sequence of images illustrates the bubbles’ movement [see Fig. 4(a) to (d)]:
5.2. Effect of bubble size and frother addition on microbubbles’ terminal velocity Fig. 6(a) shows the effect of the bubble diameter and MIBC concentration on the bubble terminal velocity at a pH close to 5.7. It is important to specify that each point represents the average of the velocity measurements of bubbles with similar diameters ( ± 3 µm, approximately). As observed in this figure, the terminal velocity decreases with the increment of MIBC concentration, which may be related to the augmentation of friction, as mentioned by Detwiler and Blanchard (1978) or to the growth in the boundary layer thickness. It should be noted that a similar effect is observed in Fig. 6(b) when the terpinol frother is added. It is known that frothers do not modify the zeta potential of the bubbles significantly (Bueno-Tokunaga et al., 2015), and consequently the change in the terminal velocity is mainly due to the change in the friction with the water side, as shown in Fig. 4.
5. Results and discussion 5.3. Effect of pH, bubble diameter, and ionic collector type on bubble terminal velocity
5.1. Validation of the microbubble terminal velocity measurement In the first instance, this work aimed to prove that the microbubble terminal velocity was measured in all of the tests, and as evidence, Fig. 5 shows the monitoring of one of these measurements where the flotation bubble velocity was kept constant in the visualization zone. Also, the values of the terminal velocity observed in this work are similar to those reported in the literature (Parkinson et al., 2008; Takahashi, 2005; Kelsall et al., 1996). It is noteworthy that this work was carried out with microbubbles whose maximum diameter was 73 µm and whose terminal velocity was measured at 20 cm after their release, which represents more than 2600 times the bubble diameter.
Fig. 7(a) and (b) compare the effects of bubble diameter, pH, and ionic collector type (anionic and cationic) on the microbubble terminal velocity. It is noteworthy that when working with xanthate (anionic) at an alkaline pH, the terminal velocity is greater than that obtained at an acidic pH, even when the bubble diameter is similar. In contrast, it should be noted that when working with dodecylamine (cationic) at alkaline pH, the terminal velocity is smaller than that obtained at acidic pH. It is important to note that, although 30 ppm (1.62E-4 M) of dodecylamine was added, at pH 11.6 dodecylamine solubility (pKb) is 10.6, which signifies that a part of this reagent is not solubilized (ionic state); however, it is believed that the solubilized part is responsible for the enlargement of the double layer engrossment and the diminution of the terminal velocity. Fig. 8 shows that when the microbubbles are conditioned with xanthate or dodecylamine at a pH close to neutrality (between 6.2 and 7.02), the bubbles ascend with almost the same velocity with both collectors. It should be noted that when the pH values are similar in the two cases, the terminal velocities are also similar. These results may be explained by the fact that at neutral pH (pH 7), a high concentration of determinant ions (protons or hydroxyls) does not exist, which decreases the attractive forces for the counterions or the diffuse layer, as described in this paper. To explain these results, it is proposed that when an anionic collector (xanthate) is adsorbed under an acidic pH, the bubbles float more slowly for two reasons: (1) the boundary layer reaches a greater thickness for the formation of an expanded diffuse layer and (2) the expanded diffuse layer also increases the friction with the liquid side. The fact that the boundary layer may increase its volume in acidic conditions [as illustrated in Fig. 9(a)] can be explained by the following mechanism: Initially the water dipoles are placed on the air surface,
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exposing their negative end (oxygen atoms) toward the air side, and via charge–dipole interaction occurs the attraction of the zeta potential determining ions (H+ and/or OH−, depending on the pH). It should be mentioned that this zone may include several layers, as proposed by Zhang and Finch (1996). Then, on the proton layer, the counterions or the xanthate anions are adsorbed, finally imposing a negative charge on the bubble, as proposed by several authors (Nguyen and Schulze, 2003; Ushikubo et al., 2010; Takahashi, 2005). When a strong acid and a strong base (HCl and NaOH) were used as pH modifiers, their protons and bases were completely hydrolyzed, becoming potential-determining ions for the double electrical layer. However, these are not the only ions that act on the interphase, because the collector decomposition due to the effect of pH can produce other ionic products with the capacity to interact with the water molecules, as donors or receptors of protons or bases. It is known that the chemical decomposition of xanthate (−OCS2−) is greater in acidic than in alkaline pH (Shen et al., 2016). For example, in acidic medium, the xanthate produces carbon disulfide (CS2), while in alkaline solutions it can produce alcohol (R−OH ), trithiocarbonate (CS3−2) , xanthic acid (R−OCS2 H ), xanthic acid compound (R−OCS2−H+) , dixanthogen (R−OCS2)2 , perxanthate (R−OCS2 O−) , monothiocarbonate (CO2 S 2 −) , dithiocarbonate (CS22 −) , and sulfide (S 2 −) . All of these products can act as weak bases, competing with all the other species to take a space at the bubble interphase and contributing a low and negative electrical charge to the bubble. As a result of this complex interaction between protons, basic ions, and water molecules, a double layer is formed on the bubble surface, indirectly affecting the bubble terminal velocity. Contrarily, under an alkaline pH, the bubbles ascend rapidly because they apparently transport a boundary layer with a minor volume,
Xantato,30 Xanthate,ppm.,pH=6.2 30 ppm (1.87E-4 M),
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as illustrated in Fig. 9(c). In this case, it is proposed that the first layer of water molecules inverts its polarity, orienting its positive pole toward the liquid side due to the high concentration and adsorption of hydroxyl ions. Once the hydroxyl ions have been adsorbed, the bubble intensifies its negative charge, decreasing the adsorption of the xanthate due to the electrostatic repulsive forces and producing a zeta potential like bubbles in water at alkaline pH. A similar explanation can be given when the bubbles are conditioned with a cationic collector such as dodecylamine. In acidic pH, the protons are adsorbed on the first layer of water molecules, which
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X-
+ +-
+-
-
-
X-
X-
+
+-
+ +
+ +-
+-
+
-
X
X-
X
-
- = OH
Cl-
Anionic collector
14
Na+ = Sodium ion Na+
Cl- = Cloride ion
Cl-
(a)
(c)
(b)
Fig. 9. Schematic representation of boundary layer thickness with xanthate.
+-
+
+
D+
+
D
-
+
D
+
-
+
D+
+ +-
+
+-
(b)
D+ = Dodecylamine
+
Na+ = Sodium ion
-
Na+
(a)
± = H2O Dipole
- D+
D
D+
+ = H+
D+
-
+-
+-
-
+-
+
D
+
-D +
-
+ +-
-
Cl-
-
-
- = OH
Na+
+
+-
+
+
D
-
D
+
+-
Cationic collector
+ +-
+-
+ +
Na+
Cl-
+-
Cl-
Cl- = Cloride ion
(c)
Fig. 10. Schematic representation of boundary layer thickness with dodecylamine.
velocity. The extrapolated curves of dodecylamine and water zeta potential converge in the acid region, whereas the extrapolated curves for water and xanthate converge in the alkaline region. In contrast, the differences between the zeta potential curves of the collectors increase in the alkaline region for dodecylamine and in the acidic region for xanthate. From these observations, it is possible to conclude that when the curves converge, an attraction force that would cause growth of the diffuse layer thickness (short boundary layer) does not exist, whereas when the difference between the zeta potential curves increases, an attractive force exists, which increases the diffuse layer thickness (big boundary layer). Certainly, the double layer is not the only factor that affects the bubble rise velocity. It is well known that there is a proportionality between the size of the hydrocarbon chain and the hydrophobicity of the surfactant (Tan and Finch, 2016), from which it is deduced that the hydrophobicity also increases the friction with the liquid phase, indirectly causing a decrease in the bubble terminal velocity. With regard to the effect of the frother’s surface activity, the frother molecule has
expose their negative dipole toward the liquid side, acquiring a positive potential [see Fig. 10(a)]. The ionic nature of this weak electrolyte is predominantly nonionic at high pH (10 < pH < 13) (Xu et al., 2015), forms ionic–nonionic pairs at intermediate pH, and is only truly cationic at low pH (1–9). Thus, the pH will also affect the surface activity of such a weak base as dodecylamine, leading to competition between species to take space at the bubble interphase. However, as shown in the “Background” section, a low positive charge predominates on the bubbles, even at alkaline pH. When this occurs, the positive dodecylamine cations are repelled, impeding the growth of the diffuse boundary layer and producing a similar potential with acidic pH. In the case where the microbubbles are conditioned with dodecylamine at alkaline pH (see Fig. 10(c)), the hydroxyl anions adsorbed on the bubble attract the cations of the collector, increasing the boundary layer thickness and decreasing its negative potential. Fig. 11 shows some experimental data, extracted from BuenoTokunaga et al. (2015), that support the presented explanation concerning the effect of the bubble electrical charge on the bubble terminal 30
(a) Dodecylamine Na+
+
D
(b) Water
-
-10
D
|pZ-pZ(H2O)|
-20
(c) Xanthate
0
2
+
+D
+ +-
-40 -50
-
+
D
-30
-
+
4
6
8
10
D+
-
+-
+-
+
+
Cl-
0
Na+
+
+-
+
Zeta potencial (mV)
+
-
+ +-
+-
+ +
D
-
10
+
- D+
-
Cl-
+-
20
D
+
-
12
pH
Fig. 11. Convergence of zeta potential curves of water and dodecylamine for the acid region and curves of water and xanthate for the alkaline region (pZ refers to the zeta potential).
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R. Pérez-Garibay et al.
two parts: a hydrophobic (non-polar) hydrocarbon (usually alkyl) chain and a hydrophilic (polar) head. The general understanding is that the frother molecule adsorbed at the water/air interface with the polar group oriented to the water side and the hydrocarbon chain oriented to the air side (Tan and Finch, 2016), which also contributes to the increment of bubble–water friction. Ionic collectors also have a polar part and a hydrocarbon chain and when they are adsorbed on the particles, the non-polar part is oriented toward the water. Contrarily, when it is adsorbed on the bubble surface, the non-polar part is oriented toward the air. Once the hydrophilic part has been oriented to the water, it is possible for the hydration to increase the friction and decrease the bubble rise velocity. All of that promotes competition between the repulsive forces of the double layer and the hydrophilic and polar parts of the collector, producing a stable water film that decreases the bubble rise velocity, as observed by other authors investigating hydrophobic particles (Pan and Roe-Hoan Yoon, 2016; Meyer et al., 2006).
Detwiler, A., Blanchard, D.C., 1978. Aging and bursting bubbles in trace-contaminated water. Chem. Eng. Sci. 33 (1), 9–13. Dukhin, S.S., Miller, R., Loglio, G., 1998. Physico-chemical hydrodynamics of rising bubble. In: MÖbius, D., Miller, R. (Eds.), Studies in Interface Science. Elsevier, pp. 367–432. Gélinas, S., Finch, J.A., Gouet-Kaplan, M., 2005. Comparative real-time characterization of frother bubble thin films. J. Colloid Interface Sci. 291 (1), 187–191. Han, M., Kim, T., Kim, J., 2007. Effects of flock and bubble size on the efficiency of the dissolved air flotation (DAF) process. Water Sci. Technol. 56 (10), 109–115. Kelsall, G.H., Tang, S., Yurdakul, S., Smith, A.L., 1996. Electrophoretic behaviour of bubbles in aqueous electrolytes. J. Chem. Soc. Faraday Trans. 92 (20), 3887–3893. Kracht, W., Finch, J.A., 2010. Effect of frother on initial bubble shape and velocity. Int. J. Miner. Process. 94 (3–4), 115–120. Krzan, M., Lunkenheimer, K., Malysa, K., 2004. On the influence of the surfactant's polar group on the local and terminal velocities of bubbles. Colloids Surf. A: Physicochem. Eng. Asp. 250 (1–3), 431–441. Krzan, M., Zawala, J., Malysa, K., 2007. Development of steady state adsorption distribution over interface of a bubble rising in solutions of n-alkanols (C5, C8) and nalkyltrimethylammonium bromides (C8, C12, C16). Colloids Surf. A: Physicochem. Eng. Asp. 298 (1–2), 42–51. Kubota, K., Jameson, G.J., 1993. A study of the electrophoretic mobility of a very small inert gas bubble suspended in aqueous inorganic electrolyte and cationic surfactant solutions. J. Chem. Eng. Jpn. 26 (1), 6. Maldonado, M., Quinn, J.J., Gomez, C.O., Finch, J.A., 2013. An experimental study examining the relationship between bubble shape and rise velocity. Chem. Eng. Sci. 98, 7–11. Meyer, E.E., Rosenberg, K.J., Israelachvili, J., 2006. Recent progress in understanding hydrophobic interactions. Proc. Natl. Acad. Sci. U.S.A. 103, 15739–15746. Navarra, A., Acuña, C., Finch, J.A., 2009. Impact of frother on the terminal velocity of small bubbles. Int. J. Miner. Process. 91 (3–4), 68–73. Nguyen, A., Schulze, H.J., 2003. Colloidal Science of Flotation. Taylor & Francis. Pan, L., Roe-Hoan Yoon, R.H., 2016. Measurement of hydrophobic forces in thin liquid films of water between bubbles and xanthate-treated gold surfaces. Miner. Eng. 98, 240–250. Parkinson, L., Sedev, R., Fornasiero, D., Ralston, J., 2008. The terminal rise velocity of 10–100 μm diameter bubbles in water. J. Colloid Interface Sci. 322 (1), 168–172. Pease, J., Curry, D., Young, M., 2005. Designing flotation circuits for high fines recovery. Miner. Eng. 19, 831–840. Rafiei, A.A., Robbertze, M., Finch, J.A., 2011. Gas holdup and single bubble velocity profile. Int. J. Miner. Process. 98 (1–2), 89–93. Shen, Y., Nagaraj, D.R., Farinato, R., Somasundaran, P., 2016. Study of xanthate decomposition in aqueous solutions. Miner. Eng. 93, 10–15. Takahashi, M., 2005. ζ potential of microbubbles in aqueous solutions: electrical properties of the gas−water interface. J. Phys. Chem. B 109 (46), 21858–21864. Tan, Y.H., Finch, J.A., 2016. Frother structure–property relationship: effect of alkyl chain length in alcohols and polyglycol ethers on bubble rise velocity. Miner. Eng. 95, 14–20. Tan, Y.H., Rafiei, A.A., Elmahdy, A., Finch, J.A., 2013. Bubble size, gas holdup and bubble velocity profile of some alcohols and commercial frothers Int. J. Miner. Process. 119, 1–5. Ushikubo, F.Y., Furukawa, T., Nakagawa, R., Enari, M., Oshita, S., 2010. Evidence of the existence and the stability of nano-bubbles in water. Colloids Surf. A: Physicochem. Eng. Asp. 361 (1–3), 31–37. Xu, S., Kou, J., Sun, T., Jong, K., 2015. A study of adsorption mechanism of dodecylamine on sphalerite. Colloids Surf. A: Physicochem. Eng. Asp. 486, 145–152. Zhang, Y., Finch, J., 1996. Terminal velocity of bubbles: approach and preliminary investigation. Column 96, 63–69.
6. Conclusions It was shown that frothers do not affect the electrical charge of the microbubbles significantly, but their effect on the terminal velocity may be due to the increase in viscous forces between the adsorbed frother and the liquid side. When the potential-determining ions at the surface of the bubble (protons and hydroxyls) have the opposite charge to the ionic surfactant (anionic or cationic), the diffuse layer is expanded and then the boundary layer thickness increases. It is proposed that besides the effect of bubble diameter and surfactant addition, the electrical charge of the bubble affects the terminal velocity and the boundary layer thickness of the microbubbles. Acknowledgements The authors are grateful to CONACYT (Mexico) for scholarships and funding and to Carmelita Yamamoto Chavarria for assistance with the data collection. This study was also funded by Cinvestav internal projects (928, 1032). References Azgomi, F., Gomez, C.O., Finch, J.A., 2007. Correspondence of gas holdup and bubble size in presence of different frothers. Int. J. Miner. Process. 83 (1–2), 1–11. Bueno-Tokunaga, A., Pérez-Garibay, R., Martínez-Carrillo, D., 2015. Zeta potential of air bubbles conditioned with typical froth flotation reagents. Int. J. Miner. Process. 140, 50–57.
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