Langmuir 2008, 24, 6085-6091
6085
Coalescence of Bubbles Covered by Particles Seher Ata* Centre for Multiphase Processes, UniVersity of Newcastle, New South Wales, 2308, Australia ReceiVed February 12, 2008. ReVised Manuscript ReceiVed March 12, 2008 The interaction between two bubbles coated with glass particles in the presence of a cationic surfactant (cetyltrimethylammonium bromide, CTAB) was studied experimentally. The time taken for two bubbles to coalesce was determined as a function of the fractional coverage of the surface by particles. The results suggested that the coalescence time increases with the bubble surface coverage. Interestingly, it was found that although the particles did not have any physical role in film rupture at low surface coverage, they still added resistance to film drainage. For particle-loaded bubbles, the initial resistance was due to the lateral capillary interactions between particles on the interface, which hold the particles firmly together. The coalescence dynamics of bubbles was also observed to be affected by the presence of attached particles.
1. Introduction The interaction of solid-coated bubbles is an important phenomenon in many industrial applications such as mineral flotation, wastewater treatment, bubble columns, and food processing. The process is particularly important in froth flotation, where the recovery of particles ultimately depends on the survival chance of the bubbles during the interaction. Flotation is a process for separating valuable solids (values) from waste, based on the difference in the surface properties of the raw materials. In mineral flotation, the ore is finely ground and dispersed in water. Chemical agents are added to render the desired mineral surface hydrophobic while leaving the unwanted particles hydrophilic. Air is then pumped into the suspension in the form of small bubbles, which tend to adhere to only hydrophobic particles. The bubbles rise to the surface with their load, where they form a layer of closely packed bubbles. The froth gradually builds up by continuous arrival of the bubbles at the interface from the liquid beneath, and eventually it flows over the edge of the cell. The unattached hydrophilic solids remain in the cell. When two air bubbles approach each other, a thin liquid film is formed between them whose thickness decreases gradually due to the drainage of the liquid. The film eventually ruptures due to attractive molecular forces operating at the interfaces upon reaching a certain thickness. The situation may change if the surfaces of bubbles become coated with particles. The presence of particles in the interfilm may inhibit the liquid drainage by creating a steric barrier. The magnitude of the barrier depends on the particle size, concentration, shape, and contact angle and the orientation of the particles at the interface. Dippenaar1 studied the mechanism of the particle-film interaction using a highspeed camera focused on a thin film containing a single wellcharacterized particle and found that film stabilization largely depends on the contact angle. With contact angles of less than 90°, a stable film could be formed when the particle bridged both interfaces. His results also indicated that particle shape could affect the stability of film due to alignment of particles at the interface. An investigation of the influence of particle size and hydrophobicity on the stability of froth was made by Johansson and Pugh.2 Both dynamic and static froth stability measurements, * Tel +61 (2) 4921-5881; fax +61 (2) 4960-1445; e-mail Seher.Ata@ newcastle.edu.au. (1) Dippenaar, A. Int. J. Mineral Process. 1982, 9, 15. (2) Johansson, G.; Pugh, R. J. Int. J. Mineral Process. 1992, 34, 1.
as well as microinterferometric studies on thin aqueous films, were carried out on quartz particles having various sizes and degrees of hydrophobicity. With a 26-44 µm particle size fraction, the dynamic froth stability was maximized at a contact angle of 65° due to the attachment of particles at the solution/air interface. Particles with a low degree of hydrophobicity (θ < 40°) were found not to contribute to the stability of the froth film. This observation was supported by the work of Ata et al.3 and Schwarz and Grano,4 who demonstrated that the maximum froth stability occurs at contact angles between 63° and 66°. On the other hand, a study by Aveyard et al.5 indicated that the stabilization of foam required a much higher contact angle, 85°-90°. In connection with froth stability and particle hydrophobicity, the work of Moudgil and Gupta6 is relevant. They studied the effect of adding fine hydrophobic particles on the recovery of coarse phosphate particles in a Denver flotation cell. Size, amount, and hydrophobicity of the fines added were determined to have a major influence on the flotation efficiency of the coarse particles. It was found that fines with an optimum degree of hydrophobicity gave a maximum coarse flotation recovery, suggesting that there is an optimum particle hydrophobicity, which improves the stability of froth. Ata et al.7 investigated the effect of hydrophobic and hydrophilic particles on froth stability in a froth column and found that the water flow rate entering into the concentrate increases with an increase in hydrophilic solid concentration in the froth. This was attributed to inhibited liquid drainage due to particles retained in the films. The mechanism of film stabilization has been explained by ) 2pγ(cos the capillary pressure between bubbles, given by Pmax c θ)/R, where γ is the interfacial tension between air and water, R is the radius of the solid particle, θ is the contact angle of the particle, and p is a parameter that defines the geometric arrangement of particles at the interface. The theory was first proposed by Ivanov and co-workers8 and developed further by (3) Ata, S.; Ahmed, N.; Jameson, G. J. Int. J. Mineral Process. 2002, 64, 101. (4) Schwarz, S.; Grano, S. Colloids Surf., A 2005, 256, 157. (5) Aveyard, R.; Binks, B. P.; Fletcher, P. D. I.; Peck, T. G.; Rutherford, C. E. AdV. Colloid Interface Sci. 1994, 48, 93. (6) Moudgil, B.; Gupta, D. Flotation of coarse particles In AdVances in coal and mineral processing using flotation; Chander, S., Klimpel, R. R., Eds.; Society of Mining Engineers: Littleton, CO, 1989; p164. (7) Ata, S.; Ahmed, N.; Jameson, G. J. Minerals Eng. 2004, 17, 897. (8) Denkov, N. D.; Ivanov, I. B.; Kralchevsky, P. A.; Wasan, D. T. J. Colloid Interface Sci. 1992, 150, 589.
10.1021/la800466x CCC: $40.75 2008 American Chemical Society Published on Web 05/17/2008
6086 Langmuir, Vol. 24, No. 12, 2008
others.9–11 It implies that the stability of the liquid film is determined by the maximum capillary pressure drop, which is resisted by liquid menisci between the adsorbed particles. The film stability is very much dependent on the arrangement of particles confined in the interfilm. Therefore, according to the theory, a closely particle-packed interfilm is likely to give the highest resistance to film collapse. Recently, Kaptay10 extended the maximum capillary theory for various particle layers at the air-water interface. The optimum value of the contact angle for foam stabilization was found to be in the interval between 50° and 90°. Interestingly, his calculations showed that, to stabilize the thin films, the particles should be smaller than 3 µm, which is contradictory to the previous studies. In the majority of previous studies, the effect of particles on bubble stability has been carried out either on a single thin film or by use of a foam column to measure the froth volume generated. In the first approach, the particles are confined between two films, and their effect on the thinning of the film is monitored. In the latter, generally the volume of foam as a function of time is recorded, which is then taken an indication of stability of film. It should be noted that this method focuses only on the overall foam behavior and does not give any insight into processes operating in the system. In this study a different approach was taken to investigate the interaction between two solid-coated bubbles. Two bubbles of equal volumes were generated at the tips of adjacent capillaries and their coalescence behavior was investigated with regard to the fraction of surface occupied by particles. The time scale for coalescence was measured and linked to the stability of film. We also looked at the effect of attached particles on the bubble coalescence dynamic and at the surface elasticity, an important phenomenon that has not received much attention in the previous studies. Although the present work was carried out with particular focus on froth flotation, the outcome may be applicable in processes such as (anti)foaming and radioactive waste treatment, where interaction between bubbles and particles are frequently encountered.
2. Experimental Section 2.1. Materials. Cetyltrimethylammonium bromide (CTAB) was purchased from Aldrich Chemical Co., Australia, and used without further purification. Spherical soda-lime glass beads were supplied from Potters Industries Pty Ltd. (Melbourne, Australia). The average particle size (d50) was 66 µm; d90 was 92 µm, while the specific density of the particles was 2.5 g cm-3. The contact angle of glass was measured by pressing a bubble against a glass plate immersed in CTAB solution by use of a DataPhysics OCA 20 (DataPhysics Instruments, Germany). The contact angle value obtained with glass plates was between 27° and 30°. The ζ potential of the particles was measured with a Zetasizer (Malvern Instruments) and found to be -40 mV for the surfactant system employed in this study. Due to their large size, a small amount of sample particles was ground in a clean ceramic ball mill to below 10 µm. The ground sample was then cleaned as explained below and used in the measurement of ζ potential. The size reduction was necessary because the glass particles were virtually free of particles smaller than 20 µm, thus making the ζ potential measurement impossible due to particle settling in the measurement cell. It is noted that the newly exposed surface area of ground glass would be several orders of magnitude larger than the area of the original surface, which may result in an increase in the ζ potential. It also noted that no aggregation of spherical glass particles was observed in the present system, suggesting the particles had sufficient charge to prevent them from aggregation. All the (9) Nushtayeva, A. V.; Kruglyakov, P. M. MendeleeV Commun. 2001, 235. (10) Kaptay, G. Colloids Surf., A 2003, 230, 67. (11) Kaptay, G. Colloids Surf., A 2006, 282/283, 387.
Ata
Figure 1. Experimental arrangement.
glassware, the cell, and the glass particles were cleaned by soaking in ammonia-H2O2 solution for several hours and then rinsing with deionized water repeatedly until the pH returned to the pH of pure water. The absence of contamination was checked by measuring the coalescence time between two bubbles growing side by side. In a clean, contamination-free system this time was very small, on the order of milliseconds. The water used in the work was cleaned via a Milli-Q Ultra Pure water system, to a resistivity of 18.2 mΩ/m. All experiments were performed at ambient temperature, 22 °C. The pH of the solution in the presence of particles was always around 9 due to the nature of the glass particles. 2.2. Equipment. All experiments were performed in a rectangular Perspex cell of width 100 mm and height 220 mm, fitted with a removable divider (Figure 1). The divider served to separate the cell into two identical compartments (50 mm × 220 mm), in which bubbles could be individually conditioned and mineralized with different particle types, if necessary. In the present work, the divider was not used since only one type of particles was employed. Two stainless steel capillary needles were used to form bubbles inside the cell. The needles had an inner diameter of 0.69 mm and an outer diameter of 1.07 mm and were connected to two microsyringes driven by separate programmable microsyringe pumps. Before each experiment the needles were cleaned carefully in acetone and then rinsed with ethanol and finally with water. An insert composed of vertical Perspex tubes was fitted to the inside of the cell, in order to better control mixing and turbulence, as well as to increase the suspension height of particles. The tubes were 80 mm tall, with an outer diameter of 6 mm and a wall thickness of 1 mm. Underneath each compartment of the cell was a magnetic stirrer, used to initiate particle suspension in the cell and to ensure reagent uniformity throughout the cell. One of the needles could be moved by means of a three-dimensional MicroFlex micropositioner that permitted precise movements in three dimensions. This was used to move the needles with bubbles from compartment to compartment, to align the needles at the beginning of each series of experiments, and to set the distance between needles for experiments. The entire setup was placed on a vibration-free table to minimize the disturbance. The experiments were focused on the visual record of the particle behavior during the coalescence process. A Phantom 5 high-speed camera (Vision Research) coupled with a Nicor lens and two magnification rings was used to capture images at the desired magnification and depth of field. The capture rate varied from 100 to 3700 frames/s. Phantom Video software (version 630) was used to record videos, as well as all bubble-sizing and observation. 2.3. Methodology. Before each experiment was started, the absence of contamination was checked by observing coalescence of two bubbles in pure water and in the absence of reagents. The particles were conditioned with CTAB to make sure the surface of particles was coated with reagents properly before they were added into the cell. The concentration of CTAB was 1.4 × 10-4 mM unless stated. Two grams of glass particles together with reagents were added into a beaker containing 15 mL of water and stirred for 15 min with a magnetic stirrer. The suspension was then transferred to the cell,
Coalescence of Bubbles CoVered by Particles
Langmuir, Vol. 24, No. 12, 2008 6087
Figure 2. Effect of coverage of particles on the coalescence time with both bubbles coated (9) and one bubble coated ([) at various surface coverages. The arrow indicates the coalescence time of bubble pairs not coated with the particles; the particles treated with surfactant were still present in the cell. Surface coverage corresponds to the bubble size at the time of coalescence.
which was filled with water up to 800 mL. The ionic strength of the suspensions was set to 1.3 mM by use of purity-grade KCl. Bubbles were grown at the ends of the two capillaries to a diameter of approximately 2 mm by means of microsyinge pumps, with the grids on the CCD camera software used as a guide. The magnetic stirrer was then turned on so that the particles would start to suspend and cover the surface of the bubbles. Depending on the experiment being undertaken, the stirrer was turned off once the bubbles were coated to the required amount. Once the particles had settled under gravity and the liquid became clear, which took about 10-20 s, one of the bubbles was slowly moved adjacent to the other bubble with the aid of the micropositioner. Then the bubbles were slowly grown at a constant flow rate of 0.3 mL/h. They were allowed to continue growing until they made contact, and finally they either coalesced or one or both of them detached from the capillary. The bubble size at the time of coalescence was 2.1 ( 0.2 mm in diameter. In the case of detachment, the result recorded was “did not coalesce”. In the case of coalescence, the video was played back at a much slower rate (between 2% and 10% of normal speed), so that the time between initial contact of the bubbles and the beginning of coalescence could be determined visually. Between 20 and 30 experiments were performed under each condition, and the average was taken as the result. Each experiment was repeated at least twice. The measurements were done with one and two bubbles coated at various fractional surface coating. The coalescence time reported was the time measured from the first contact until the liquid film between them broke down. The mineralization of bubbles at various fractions at the time of coalescence initially was estimated visually, with the grids on the CCD’s software as a guide. The exact fraction of the bubble(s) covered by the particles in each system was then determined by use of Optimas imaging software (Media Cyberbetics Inc., Silver Spring, MD) within ranges of (5%. It should be noted that, in this study, the surface tension of the solutions was essentially that of pure water, due to the low concentrations of CTAB used. This was not surprising as CTAB starts to affect the interfacial tension of aqueous solutions at above a certain concentration, 1 × 10-2 mM,12 which is well above the concentration used here, 1.4 × 10-4 mM.
3. Discussion of Results 3.1. InfluenceofCoverageofParticlesonBubbleCoalescence. Figure 2 shows the experimental values of the coalescence time
between two bubbles as a function of bubble surface coverage which ranges from 25% ((5%) to 90% ((5%) coverage for one-bubble and two-bubble coated systems. The error associated with each experiment is given in the figure. It is noted that the surface coverage corresponds to the bubble size at the time of coalescence. As can be seen from the graph, in both systems, the total coalescence time increased monotonically with increasing surface coverage. Clearly, when two bubbles were coated, it took more time for coalescence to take place at all surface coverages, and eventually at 90% ((5%) coating, the highest surface coverage employed in this study, scarcely any pairs collapsed, with the probability of coalescence less than 2%. Instead, in this system, in most cases it was observed that the particle-laden bubbles detached from the capillaries individually and rose up to the surface, where they burst. It has been reported in the literature13,14 that very stable foam and liquid films can be formed if their surfaces are coated densely with closely packed particle layers. The presence of particles at the film surface is believed to reduce film thinning by preventing liquid drainage and creating a steric barrier at the interface. The high stability of bubbles coated with particles observed here is consistent with the above findings. Although it is more likely that the increase in bubble coalescence time with increasing surface coverage is due to particles attached to the bubble surface, the contribution of CTAB to the film stability should also be considered. CTAB was used to facilitate the bubble-particle attachment in the present study. It is well-known that this surfactant has the ability to absorb at an air-water interface,12 providing a resistance to premature film rupture. It is not possible, however, to assess the contribution of particles and surfactant to the coalescence time separately in this study. The role of CTAB on the bubble stability is discussed below. Observations also revealed that the mechanism of coalescence of coated bubble pairs differed from that of uncoated pairs. It (12) Ravera, F.; Santini, E.; Loglio, G.; Ferrari, M.; Liggieri, L. J. Phys. Chem. B 2006, 110, 19543. (13) Horozov, T. S.; Aveyard, R.; Clint, J. H.; Neumann, B. Langmuir 2005, 21, 2330. (14) Pugh, R. J. Langmuir 2007, 23, 7972.
6088 Langmuir, Vol. 24, No. 12, 2008
Ata Table 1. Coalescence Times for Various Systems in the Presence of 1.3 mM KCl
a
Figure 3. Sequences of coalescence for (a) both uncoated bubbles, (b) coated and uncoated bubbles, and (c) both coated bubbles. The surface coverage of coated bubble(s) (b, c) was about 94%, and the time between photographs was approximately 0.5 ms.
is noted that the concentration of CTAB in these tests was 1.1 × 10-3 mM to observe the influence of attached particles on the bubble oscillation more clearly. Figure 3a is a sequence of images showing the coalescence of two uncoated bubbles. The process begins with the rupture of the thin liquid film that separates the two bubbles at their contact point. A neck is seen to form between the two bubbles, while the remainder of their surfaces is not immediately affected. The neck extends as an expansion wave along the surface of the newly created single bubble. As the wave reaches the farthest point, the bubble bulges, increasing in width in the horizontal plane. This bulge then collapses as the wave returns in the reverse direction, increasing the vertical height. The process repeats itself in a damped oscillatory pattern, alternating between width and height, until the bubble settles to a spherical shape and finally detaches from the capillaries (also see Supporting Information). This action is analogous to the coalescence of two liquid drops and bubbles as observed previously.15,16 The dynamics of coalescence when only one of the bubbles is coated proceeds differently than the case when both bubbles are coated (see Supporting Information). In the case where only one bubble is coated, as soon as the film between the bubbles is broken (Figure 3b), a large wave moves horizontally from the point of rupture along the surface of the naked bubble toward the undisturbed far end, causing a bulge due to the localized inertial pressure as observed previously with the coalescence of two naked bubbles. Initially, the coated bubble experiences no (15) Stover, R. L.; Tobias, C. W.; Denn, M. M. AIChE J. 1997, 43, 2385. (16) Menchaca-Rocha, A.; Martinez-Davalos, A.; Nunez, R.; Popinet, S.; Zaleski, S. Phys. ReV. E: Stat., Nonlinear, Soft Matter Phys. 2001, 63, 046309/1.
system
coalescence time (s)
only CTAB CTAB + particles, uncoated bubbles CTAB + particles, one bubble coated sparsely (25% ( 5%) CTAB + particles, both bubbles coated sparsely (25% ( 5%)
14.55 a 1.62 3.56
On the order of milliseconds.
deformation at all. As the surface wave recoils and moves back toward the coated end of what is now a single bubble, particles are seen to move to the center of the bubble, to form a belt of particles around the surface, leaving each of the ends uncoated. The amplitude of the expansion and contraction of the wave decreases in a damped oscillatory pattern until it reaches a stable stationary state. With the merging of two coated bubbles, coalescence appears to progress very smoothly with no indication of horizontal bulging at the end of the bubbles at all (Figure 3c; also see Supporting Information). Although the resultant bubble pulsates until it settles, the motion happens more slowly, probably due to the damping effect of the particles on the surface, which adds some rigidity to the interfacial region and contributes to the dissipative processes that slow the progress of the waves. 3.2. Comparing Uncoated Bubbles with Sparingly Coated Bubbles. Table 1 shows the coalescence times of uncoated and sparingly coated bubbles (25% ( 5%). For comparison, the coalescence time of bubble pairs in the presence of 1.4 × 10-4 mM CTAB is also given in the table. It is seen that when the bubbles were not covered with particles the coalescence time was rapid, on the order of milliseconds (see also Figure 2, indicated with an arrow). It is important to note that glass particles including the surfactant were still present in the cell with this system. This result strongly implies that most of the CTAB molecules were adsorbed on the surface of particles or on the walls of the cell and the solution was essentially depleted of surfactant. An analysis of the surfactant take-up on the surface of the particles may provide further conformation. If monomolecular coverage is assumed, and if the surface area of the particles and the area occupied by each CTAB molecule on the surface is taken to be 0.035 m2/g (calculated with the assumption of spherical particle geometry) and 60 Å, respectively, it can be calculated that approximately 56% of the solid surface would be covered by the surfactant. Note that the actual surface coverage by CTAB is probably less than that, as the surfactant take-up by the walls of the cell as well as the insert that was fitted in the cell to aid a uniform turbulence were ignored in the calculation. So it is reasonable to assume that in the presence of particles almost all CTAB is adsorbed at the solid-water interface and the solution may be regarded as surfactant-free. Of course, the assumption of monolayer alignment of surfactant molecules on the solid surface may not be necessarily valid. However, at such a low concentration it is more likely the particles would be covered by an unsaturated CTAB monolayer, as may be evident from the study of Rutland and Parker.17 It is also evident from Table 1 that when the bubbles were sparsely coated, the lifetime of the film appeared to increase enormously compared to the system where the bubbles were uncoated (see also Figure 2). It is also interesting to see that the (17) Rutland, M. W.; Parker, J. L. Langmuir 1994, 10, 1110.
Coalescence of Bubbles CoVered by Particles
time scale for coalescence of two coated bubbles is higher than for one coated bubble and one uncoated bubble, suggesting that the number of particles is crucial in the latter system as well. This behavior is unexpected and difficult to explain when it is considered that the particles resided only at the bottom part of the bubbles, far away from the contact point of the bubbles. Close inspection of video footage showed that the particles did not cause any visual deformation at the interfaces of the bubbles when brought into contact with each other, as observed previously with approaching oil droplets.18 No evidence of particle migration to the initial point of contact between bubbles was observed during the film rupture processes. Our first impression was that once the particles attached to bubbles, the surfactant molecules that had adsorbed on the surface of glass particles previously, migrated from the solid-water interface to the air-water interface and therefore hindered bubble coalescence in the present system. Migration of surfactants from one phase to another has been reported previously. Ravera et al.12 investigated the effect of nanosized silica particles on the interfacial properties of air-water and water-hexane interfaces in the presence of CTAB and found that the dynamic surface tension of both systems decreased as a function of time. The conditions were such that the bulk solutions did not contain any free surfactant, and it was concluded that the particles acted as carriers of surfactant to the interface. Once at the interface, the surfactant molecules and particles underwent rearrangement, leading to a reduction in the surface tension. Similar conclusions were derived by Gonzenbach et al.19 and Nushtayeva and Kruglyakov9 to explain a dramatic drop in the surface tension in the presence of a mixture of particles and surfactants. Wang et al.20 observed that in the presence of ionic surfactants the interfacial tension of an oil-water interface dropped significantly with the addition of colloidal particles into the aqueous phase. The authors explained this phenomenon in terms of transfer of surfactant from the oil-water interface to the oppositely charged surfaces of the particles. The electric field around the particles was believed to be the main reason for the transportation of surfactant from one phase to another. Dong and Johnson21 studied the gas-liquid interfacial tensions of aqueous suspensions of charged-stabilized titania at various bulk solid concentrations. Their results indicated an optimum particle concentration where the surface tension was a minimum. It was believed that at higher concentrations the capillary forces acting between the particles caused an increase in the effective surface tension, because deformations of the interface would require work to be done in rearranging the menisci around and between the particles, therefore adding to the work done when the apparent surface area is changed. To eliminate the effect of CTAB and determine only the role of particles on the bubble coalescence time in the present study, some tests have been carried out with artificially hydrophobized glass particles. The particles were treated with trimethylchlorosilane to a known degree of hydrophobicity, and no reagents other than electrolyte were used in these tests. Interestingly, initial results have indicated a similar trend to that observed earlier with the CTAB surfactant system. Bubbles sparingly coated with the particles have been found to be more stable once again than completely naked bubbles. This result strongly suggests that it was not the CTAB molecules, but rather the presence of (18) Stancik, E. J.; Kouhkan, M.; Fuller, G. G. Langmuir 2004, 20, 90. (19) Gonzenbach, U. T.; Studart, A. R.; Tervoort, E.; Gauckler, L. J. Angew. Chem., Int. Ed. 2006, 45, 3526. (20) Wang, W.; Zhou, Z.; Nandakumar, K.; Xu, Z.; Masliyah, J. H. J. Colloid Interface Sci. 2004, 274, 625. (21) Dong, L.; Johnson, D. Langmuir 2003, 19, 10205.
Langmuir, Vol. 24, No. 12, 2008 6089
Figure 4. (a) Interparticle interaction between two arbitrary spheres at the air-water interface arising from (2) van der Waals force, (9) electrostatic force, and ([) capillary force as a function of separation distance. (b) Replot of van der Waals and electrostatic forces.
particles, that made the bubbles resistant to coalescence in the case where the particles occupied only the lower part of the bubbles and did not take an active role on the film drainage process. It has been shown22,23 that the presence of particles on an interface is sufficient to create a gradient of surface tension, which may cause fluid motion.24 Whether this would have any influence on the bubble stability is not known. We are currently continuing our studies in this area.
4. Mechanism of Stability 4.1. Interparticle Interactions. From the above considerations it is clear that the particle shell around the interface provides a dynamic resistance to film rupture. For coalescence to occur, the forces that hold the particles together at the air-water interface must be overcome. Accordingly, it is interesting to estimate the interaction energy operating between the particles. Figure 4shows the interaction potentials between two particles at the air-water interface. Three forcessthe van der Waals force, the electrostatic force, and the capillary forceswere considered. The van der Waals force was estimated from the relationship FvanderWaals ) -Aeff∂f(P)12L2, where Aeff is the modified effective Hamaker (22) Menon, V. B.; Nikolov, A. D.; Wasan, D. T. J. Colloid Interface Sci. 1988, 124, 317. (23) Levine, S.; Bowen, B. D. Colloids Surf. 1992, 65, 273. (24) Casson, K.; Johnson, D. J. Colloid Interface Sci. 2001, 242, 279.
6090 Langmuir, Vol. 24, No. 12, 2008
constant based on the immersion of particles at the air-water interface, ∂ is the radius of the particles, f(P) is an adjustable parameter, and L is the separation distance between two identical spheres.25,26 The electrostatic interaction was calculated according to Felectrostatic ) 6εairq2water/4πε0ε2waterκ2L4, where ε0 is the permittivity of free space, εair and εwater are the relative dielectric constants of air and water, qwater is the charge of the water-immersed section of the particle, and κ-1 is the Debye screening length.27 The capillary force between two arbitrary particles was computed from the expressions derived by Chan et al.28 This force arises because of the local deformation of the interface between the particles at close distances of separation and is found by solving the Young-Laplace equation with the appropriate contact angle at the glass-air-solution contact line. The measured ζ potential and contact angle were used in the relevant expressions. The data reported in Figure 4a show that the lateral capillary forces arising from the deformation of the gas-liquid interface are the key controlling elements in the interaction of two approaching bubbles, over separation distances up to 40 µm. The presence of capillary forces is more likely to initiate a closely packed layer formation in the interfilm as well as at the surface of the bubbles. In order for coalescence between the two bubbles to take place, the interaction energy of the particles needs to be overcome. When the particles are very close to touching, the electrostatic forces arising from Coulombic interaction are more likely to operate between the particles, as suggested by Figure 4b. As this force is repulsive, it should resist the closer approach of the bubbles and the coalescence time will increase. At this stage the coating of particles may also strongly hinder the expansion of the bubbles and will try to prevent the coalescence from initiating. In the present system, the bubbles were grown side by side by continuous addition of air. If the bubbles resist expansionsfor example, when the surfaces of the bubbles are coated completely with particlessthen the pressure inside the bubbles will increase to a point where the interaction energy of solid particles can no longer resist the growing pressure. At this stage, the particles will be either expelled from the interface or pushed aside until the surfaces of the two bubbles make contact. The removal of a particle from the air-water interface requires considerable energy,29 so it is more likely that the latter will be the case. This point will be explained below. 4.2. Changes in Surface Area with Time. Further insight into the effect of attached particles on the coalescence behavior may be obtained by looking at the change in the surface area as a function of time, immediately following coalescence. The surface area of the bubbles, before and after coalescence, was measured as a function of time by use of Optimas, and the results are presented as the percentage change in the superficial area relative to the initial surface area of the bubbles just before coalescence. Such an analysis is given in Figure 5 for (a) both uncoated bubble pairs, (b) coated and uncoated bubble pairs, and (c) both coated bubble pairs. It can be seen that after coalescence begins, the superficial surface area initially increases slightly followed by a dramatic drop in the area, with a reduction of up to 20% with coated bubbles and even more with uncoated bubbles. In the experiments, (25) Tarimala, S.; Dai, L. L. Langmuir 2004, 20, 3492. (26) Van de Ven, T. G. M. Colloidal Hydrodynamics; Academic Press: San Diego, CA, 1989. (27) Aveyard, R.; Binks, B. P.; Clint, J. H.; Fletcher, P. D. I.; Horozov, T. S.; Neumann, B.; Paunov, V. N.; Annesley, J.; Botchway, S. W.; Nees, D.; Parker, A. W.; Ward, A. D.; Burgess, A. N. Phys. ReV. Lett. 2002, 88, 246102/1. (28) Chan, D. Y. C.; Henry, J. D., Jr.; White, L. R. J. Colloid Interface Sci. 1981, 79, 410. (29) Binks, B. P. Curr. Opin. Colloid Interface Sci. 2002, 7, 21.
Ata
Figure 5. Percent change in the total bubble surface area relative to the initial area following coalescence for (a) both uncoated bubble pairs, (b) coated and uncoated bubble pairs, and (c) both coated bubble pairs.
some particles detached from the bubble surface under the action of the oscillatory waves. One reason for detachment might be the reduction in the total surface area after coalescence, and indeed this may be the particular case for the system in which two coated bubbles merge together. If both bubbles are initially fully coated, and the surface area after coalescence is reduced following simple geometric considerations, then some of the particles have to be expelled from the interface, being surplus to the number needed for total coverage on the resulting single bubble. The initial fractional coverage of coated bubbles was about 94%. As seen from the figures, with all three systems, the bubble undergoes oscillations, with percentage change relative to its
Coalescence of Bubbles CoVered by Particles
initial size decreasing as time passes, until it reaches its final shape. The frequency of oscillation is highest with uncoated bubbles and lowest with coated bubbles, suggesting that the particles cause viscous damping additional to that of the viscous resistance in the surrounding fluid, which is the main reason for the uncoated bubble oscillation pattern. Interestingly, the presence of particles at the interface seems to have a retarding effect on the period of oscillation. 4.3. Ejection of Particles from Interface. It is easy to show on geometric grounds that the diameter D of the single large bubble formed from the coalescence of two smaller bubbles of equal diameters d is D ) 21/2d, while the ratio of the surface area of the large single bubble to that of the two smaller bubbles combined is 2-1/3 or 0.794. Thus, if the small bubbles are coated to an extent greater than 79.4% of their area, it is inevitable that some particles will be rejected during the coalescence process, simply because there is insufficient room for them to fit on the available surface area. When we come to the case where one bubble is essentially fully coated and the other is devoid of particles, there is clearly an excess of surface area over that required to accommodate the particles. The reason for the ejection of particles during coalescence of a coated and an uncoated bubble is probably due to the violent nature of the wave formed immediately following the rupture of the thin liquid film between the bubbles. During the initial postrupture period, the bubble undergoes repeated compression and expansion, resulting in the breakdown of the long-range lateral capillary forces and short-range structure of the particle layer. Obviously, to be able to remove a particle from the air-water interface, the surface energy released during an oscillation should be larger than the detachment energy. An estimate of the energy required to remove a particle from an interface may be made from the expression30 WA ) γLVπR2(1 - cos θ), where R is the radius of the particle, γLV is the water-air interfacial tension, and θ is the contact angle. The effect of gravity can be neglected for the size of the particles employed here.31 The measured surface tension and contact angle were used in the calculation of the adhesion energy. From the relationship, the detachment energy to remove a particle from the bubble surface is on the order of 5.6 × 10-11 J. The corresponding capillary interaction energy (approximated by use of the expressions developed by Chan et al.28) is on the order of 1 × 10-12 J for separation distances up to 3 µm. It can be seen that the energy required to remove a particle from the air-water interface is much greater than that which is necessary to separate two adjacent particles while they remain at the interface. The energy needed to remove the particles from the surface must come from the surface waves, which leads to rapid changes in the direction of the underlying liquid.
5. General Discussions of Coalescence and Relevance to Flotation These analyses reveal that a comprehensive understanding of the phenomenon of coalescence of particle-laden bubbles requires observations from first contact to final damped equilibrium. This aspect of coalescence has not been well represented in the literature. The nature and high rate of coalescence are generally not considered in discussions of bubble coalescence. Further (30) Morrison, I. D.; Ross, S. Colloidal Dispersions: Suspensions, Emulsions, and Foams; Wiley: New York, 2002. (31) Princen, H. M. Surf. Colloid Sci. 1969, 2, 1.
Langmuir, Vol. 24, No. 12, 2008 6091
study in this area could prove to be very valuable since this action may very well play a significant role in detachment during coalescence, which is an important feature of the flotation process. The effect of oscillation on the detachment of particles is the subject of future study. The consequences of this research are particularly relevant to the flotation process for the separation of valuable minerals from waste materials. After the floatable particles have risen on the surfaces of the bubbles into the froth phase, it is common for the bubbles to coalesce. During coalescence, some of the particles that had been attached to the bubbles are lost from the bubble’s surfaces and pass into the liquid surrounding them, subsequently draining back into the contents of the flotation cell. It would be reasonable to assume that the particles that detach are in some respects less likely to adhere than those that remain on the surfaces of the bubbles. The latter of course will pass out of the flotation cell as the product. From a separation point of view, it would be desirable for particles that were less hydrophobic, or were formed as composites of hydrophobic and hydrophilic materials, to be depleted from the froth, because these would presumably be of lower purity or grade than the particles of highest sticking ability. Thus the rejection of particles from bubbles during coalescence described here probably contributes to the selectiVity of the flotation process as practiced industrially.
6. Conclusions The interaction between two particle-coated bubbles growing by side by side at the tip of capillaries has been investigated as a function of bubble surface coverage. The coalescence time between two bubbles was measured and was taken as an indication of bubble stability. The coalescence time was found to be a monotonically increasing function of the fractional area occupied by the adsorbed particles. Interestingly, the time scale for coalescence for sparsely coated bubbles is typically longer than that for coalescence of uncoated bubbles, although the particles physically did not take part in the rupture of the thin film between the bubbles, which was a necessary precursor to coalescence. In the presence of particles at the initial rupture point, the coalescence of the bubbles was resisted mainly by lateral capillary force between the particles at the gas-liquid interface, while the electrostatic forces and van der Waals were found to be secondary. The coalescence dynamics of bubbles coated with monolayers of particles exhibited behavior quite different from that of uncoated bubbles. The presence of the particles had a strong damping effect on the waves observed during bubble coalescence. Acknowledgment. Thanks are due to K. Harding and Y. Chang (McGill University, Canada) for their contributions to the experimental work. Thanks are also due to Professor R. J. Pugh of YKI (Sweden) for his invaluable comments on the paper and to Professor G. J. Jameson for many useful discussions. I acknowledge the University of Newcastle for an Independent Investigator Grant, and also the Australian Research Council for its support for the Special Research Centre for Multiphase Processes. Supporting Information Available: Three movies showing the coalescence behavior of two bubbles with both uncovered, covered and uncovered, and both covered. This material is available free of charge via the Internet at http://pubs.acs.org. LA800466X
