pubs.acs.org/Langmuir © 2009 American Chemical Society
Controlling the Locus of Bubble Nucleation by Dissolved Gases in Heterogeneous Liquid-Liquid Systems Pramith Priyananda, Brian S. Hawkett, and Gregory G. Warr* Key Centre for Polymers and Colloids, School of Chemistry, F11, The University of Sydney, NSW 2006, Australia Received June 27, 2009. Revised Manuscript Received August 20, 2009 We have examined the nucleation of chemically generated nitrogen gas bubbles in microheterogeneous systems, using optical microscopy on a model system consisting of a single liquid-liquid interface. Results clearly show that bubble nucleation occurs in both the aqueous and oil phases, despite the nitrogen production reaction being a purely aqueous phase process. A theoretical model is developed which describes the time evolution of the nitrogen concentration profile, and this reveals that bubbles in the oil are a result of homogeneous nucleation of dissolved N2 transported across the interface into a (supersaturated) diffusion layer. We further show that bubble nucleation in the oil can be inhibited or eliminated by adding water-soluble surfactants, which facilitates aqueous phase bubble nucleation and then acts as highly effective nitrogen sinks, severely reducing the flux of dissolved gas across the water-oil interface.
Introduction Bubble nucleation is important in many natural processes and industrial applications.1 Some of the disastrous natural processes that have been caused by the formation of gas bubbles include the explosive degassing of magma in volcanoes,1 the sudden release of dissolved carbon dioxide in the deeper regions of Lake Nyos in 1986, which made a huge fountain causing over a thousand deaths,1,2 and the formation of nitrogen bubbles in blood and tissues of divers sometimes leading to pulmonary alveolar rupture.3 Bubble formation is important in both carbonated beverages, beer and soft drink,4 and liquid waste treatment1 and has been tested for cleaning dairy fouled ultrafiltration membranes.5 In addition, nucleation of bubbles is one of the major unit operations in making emulsion explosives. Ammonium nitrate-containing water-in-oil emulsions are commonly used in the mining industry as explosives. In order to make these detonable, these emulsions are often “gassed” by incorporating or generating small bubbles. Nitrogen bubbles are commonly generated in such emulsion explosives by dispersing a small amount of a NaNO2 solution in the emulsion to react with supersaturated aqueous NH4NO3 in the droplets to produce N2. Detonation is initiated by blasting a small amount of another high explosive, which is suitably placed in an emulsion column (or a cartridge).6,7 This generates a shockwave, which adiabatically *Corresponding author. E-mail:
[email protected]. (1) Jones, S. F.; Evans, G. M.; Galvin, K. P. Bubble nucleation from gas cavities - a review. Adv. Colloid Interf. Sci. 1999, 80, 27-50. (2) Evans, W. C. Lake Nyos, Knowledge of the fount and the cause of disaster. Nature 1996, 379, (6560), 21-22. (3) Mateer, J. Environmental Emergencies. In Emergency and Trauma Nursing, Curtis, K., Ramsden, C., Friends, J., Eds.; Elsevier: Australia, 2007. (4) Bisperink, C. G. J.; Prins, A. Bubble growth in carbonated liquids. Colloids Surf. A 1994, 85, 237-253. (5) Muthukumaran, S.; Kentish, S.; Lachandani, S.; Ashokkumar, M.; Mawson, R.; Stevens, G. W.; Grieser, F. The optimisation of ultrasonic cleaning procedures for dairy fouled ultrafiltration membranes. Ultrason. Sonochem. 2005, 12, 29-35. (6) da Silva, G.; Dlugogorski, B. Z.; Kennedy, E. M. An experimental and theoretical study of the nitrosation of ammonia and thiourea. Chem. Eng. Sci. 2006, 61, 3186-3197. (7) Bhattacharyya D. N.; Seshan, S.; Campbell, J. S.; Sen, S. A method for preparation of water-in-oil emulsion explosives and a method for the preparation of the same. U.S. Patent 4409044 10/11/1983 1983.
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compresses the N2 bubbles distributed throughout the emulsion, allowing them to act as hot centers, and propagates the detonation. The size and distribution of the bubbles, thus, affects the detonation properties of the emulsion. The partitioning of the bubbles between the continuous oil and dispersed aqueous phases of the emulsion also influences its rheological properties, particularly whether a tall column of gassed emulsion will collapse. In order to control these properties, it is important to understand the mechanism of bubble nucleation and the distribution between the oil and aqueous phases. This N2 “gassing” reaction is just one example of a large number of chemical reactions which yields a variety of dissolved gases including H2, O2, CO2, and CO in both aqueous and nonaqueous solvents, and in which, the gas bubbles are subsequently nucleated.8,9 Even in homogeneous solutions, bubble nucleation and dissolved gas transport can lead to complex kinetic behavior.10,11 However, these processes also find application across a diverse set of multiphase and microheterogeneous systems. The mechanism and kinetics of the reaction between NH4þ and NO2- ions to produce dissolved aqueous N2 have been extensively studied due to their widespread industrial importance. The reaction is exothermic, and its start can be delayed by controlling solution pH (a fused reaction). Exploitation of this feature to supply heat to melt solidified paraffin in undersea pipelines has been explored.12,13 Despite its importance, the mechanism of nucleation of the N2 bubbles in a heterogeneous system containing one or more oilwater interfaces is not well understood, and even the locus of (8) Rubin, M. B.; Noyes, R. M. Measurements of critical supersaturation for homogeneous nucleation of bubbles. J. Phys. Chem. 1987, 91, 4193-4198. (9) Rubin, M. B.; Noyes, R. M. Thresholds for nucleation of bubbles of nitrogen in various solvents. J. Phys. Chem. 1992, 96, 993-1000. (10) Bowers, P. G.; Bar-Eli, K.; Noyes, R. M. Unstable supersaturated solutions of gases in liquids and nucleation theory. J. Chem. Soc., Faraday Trans. 1996, 92, 2843-2849. (11) Smith, K. W.; Noyes, R. M. Gas Evolution Oscillators. 3. A computational model of the Morgan Reaction. J. Phys. Chem. 1983, 87, 1520-1524. (12) Nguyen, D. A.; Iwaniw, M. A.; Fogler, H. S. Kinetics and mechanism of the reaction between ammonium and nitrite ions: experimental and theoretical studies. Chem. Eng. Sci. 2003, 58, 4351-4362. (13) Singh, P.; Fogler, H. S., Fused chemical reactions: The use of dispersion to delay reaction time in tubular reactors. Ind. Eng. Chem. Res. 1998, 37, 2203-2207.
Published on Web 09/15/2009
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bubble nucleation has not been determined unequivocally. Although N2 is produced by the reaction in the aqueous phase of the emulsion, there is experimental evidence to suggest that bubbles nucleate in the oil phase14 and at the oil-water interface.15 Both the mathematical treatment and experiments to study the reaction and transport phenomena (diffusion, partition, and nucleation) in such a complex system as a concentrated, supersaturated emulsion harbor many difficulties. In this work, we have established and investigated a more convenient model system, comprising a rectangular capillary tube containing (vegetable or mineral) oil and an aqueous phase separated by a single oil-water interface. Nitrogen bubble nucleation, growth, and transport at this interface are followed by optical microscopy and compared with the predictions of a reaction-diffusion equation. N2 is generated in the aqueous side by introducing a small amount of a NaNO2 solution to the NH4Cl-rich aqueous phase, and the reaction kinetics are simply controlled through the concentrations of the two reagents. Bare oil-water interfaces are first examined, after which we investigate the effect of added surfactants.
Materials and Methods The oil-water interface for microscopic studies was made by contacting an aqueous solution and an oil in a flat capillary tube. About 3 mL of a NH4Cl (5% w/v at pH 4) solution was mixed with about 1 mL of a NaNO2 (5% w/v) solution in a small sample bottle, and a few drops of the mixture were immediately transferred to a flat capillary using a Pasteur pipet. Oil was introduced quickly to the capillary from the other end of the capillary to form the oil-water interface. Olive oil, hexadecane, and tetradecane were separately used in repeating experiments. The pH of the NH4Cl stock solution was adjusted by adding a few drops of 50% acetic acid. Experiments were carried out using a range of solution concentrations, NH4Cl (2-20% w/v) and NaNO2 (2-20% w/v). These concentrations were mixed in various ratios in repeat experiments. At high concentrations, bubbles formed rapidly, even before transferring the solution to the capillary. Therefore, in some experiments, NH4Cl and NaNO2 solutions were transferred to the capillary before acidifying, and then a drop of 20% acetic acid was injected in the water phase. Milli-Q water was used for all of the solutions and for washing the capillaries. The experiments were carried out at room temperature (20-25 C) and repeated several times over six months. The aqueous phase in the capillaries was typically about 1 cm long, and the length of the oil phase was 0.5-1 cm. The interface was about 1 cm wide. Two capillaries with different thicknesses were used, 0.017 and 0.1 cm. Capillary ends were not capped to allow for the expansion of the solution during the bubble formation. In some experiments, the ends were capped with oil. However, capping did not alter our observations. The capillaries were made by pasting microscope coverslips on glass slides. Rectangular pieces of a slide were first pasted on a slide. Then a coverslip was pasted on the pieces. Then the cell thickness was about 1 mm (see Figure 1). In order to make thinner capillaries, rectangular pieces of a coverslip were first pasted on a slide. The pieces were cut using a glass cutter, Araldite (fast-setting) glue was used to paste the coverslips. The capillaries (14) Turner, D.; Dlugogorski, B.; Palmer, T. Factors affecting the stability of foamed concentrated emulsions. Colloids Surf. A 1999, 150, 171-184. (15) Swayambunathan, V.; Mukesh, D.; Krishnan, S.; Chikhale, S. V.; Ghosh, P. K. Concentrated Emulsions: 4. Freeze Fracture SEM Studies of Chemically Generated Voids. J. Colloid Interface Sci. 1993, 156, 66-71.
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Figure 1. Schematic diagram of the capillary cell used to create the model oil-water interfaces for microscopy.
were immersed in Milli-Q water overnight, rinsed using a syringe, and dried before use. Some experiments were repeated using Vitrotube 1 10 mm and 0.2 4 mm flat capillaries. The commercial and homemade capillaries gave similar results; however, using a homemade capillary was much cheaper and easier, since the dimensions could be optimized to suit our requirements. Formation of gas bubbles was observed using an optical microscope (phase contrast) (Leica DM 2500P) fitted with a high-resolution, 3.3 mega pixel color CCD digital camera with real time viewing (RTV) (MicroPublisher RTV 3.3 Q-Imaging). The camera was packaged with QCapture Pro 5 software to capture images. Direct observations using eyepieces were made at the magnifications ranging from 100 to 500, as suited. In addition to phase contrast images, dark and bright field illuminations were made. Dark field illumination was very sensitive to small bubbles, which scattered light at oblique angles.16 However, for dark field illumination, the capillaries need to be completely free from dust because it scatters light. The mass transfer of nitrogen was theoretically examined by using a diffusion-reaction equation. Olive oil was used as the model oil for the theoretical investigations because data for olive oil have been well documented in literature. The related partial differential equations were solved using MATLAB (R2007a) pde toolbox. Effect of water-soluble surfactants on bubble nucleation was examined by adding a small amount of the anionic surfactant sodium dodecyl sulfate (SDS, Sigma) or the commercial nonionic surfactant polyoxyethelene(23) lauryl ether (Teric 12A23, Orica Australia) to the aqueous phase. Since SDS was insoluble in concentrated NH4Cl solutions, the surfactant could be tested only in more dilute (20 mM) NH4Cl solutions.
Results and Discussion Bare Oil-Water Interfaces. The nitrogen gassing reaction 1 was carried out in the aqueous phase in contact with a bare oil-water interface, and the evolution of N2 bubbles was observed by optical microscopy. NO2- ðaqÞ þ NH4þ ðaqÞ f 2H2 OðlÞ þ N2 ðaqÞ
ð1Þ
After 10-20 min, depending on the initial nitrite concentration and pH, bubbles formed and grew rapidly to diameters of 20 μm or more in the aqueous solution, as expected. However, we observed a bubble-depleted region extending from the interface into the aqueous phase between 300 and 800 μm in which no bubbles formed. Bubbles were also observed to form inside the oil phase very close to the interface at about the same time. These bubbles were (16) Yonit, D. E.; Gillary, E. W.; Hoffman, D. C. A microscopic investigation of bubble formation nuclei. J. Acoust. Soc. Am. 1984, 76, (5), 1511-1521.
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Figure 2. Dark field optical microscopy image showing the appearance of very small bubbles in hexadecane (left) and olive oil (right), close to the interface with aqueous NH4Cl. The oil-water interface in hexadecane appears diffuse because it exceeds the depth of the field on this scale.
this reaction to be pseudo first-order in NO2- and write the nitrite concentration in aqueous solution as ½NO2- ¼ ½NO2- 0 expð -ktÞ
ð2Þ
[NO-2]0
where is the initial concentration of nitrite and k is the pseudo first-order reaction rate constant. From the stoichiometry of the reaction, we can write the concentration of dissolved N2 as ½N2 ¼ ½NO2- 0 ð1 - expð -ktÞÞ
ð3Þ
and the rate of production of dissolved N2 in the aqueous phase, q, is Figure 3. Large bubbles formed in the aqueous phases approaching the interface and crossing to the oil (tetradecane) side. The interface appears wide due to optical distortion.
much smaller (d < 5 μm) than those formed in the aqueous phase and grew more slowly. A typical result is illustrated in Figure 2, using both hexadecane and olive oil as the oil. Similar results were found using all three oils. On some occasions, swarms of very small bubble like objects also appeared close to the interface in the oil (see below). After longer times, some bubbles that had formed in the aqueous phase then diffused into the depletion zone, up to the interface, and crossed to the oil phase. Figure 3 illustrates the difference in bubble sizes on the oil and aqueous sides of the interface, showing large bubbles that have approached the interface. After still longer times, bubble coalescence was observed in both phases. Both the coalescence of bubbles and their transport from the aqueous to the organic phases are expected in these systems, as both act to lower the surface free energy of the bubbles. Bubble nucleation in the oil phase was unexpected, however, as the N2generating reaction (1) occurs between the NH4þ and NO2- ions exclusively on the aqueous side of the interface. The intermediate steps involved and the rate constant for production of N2 by this reaction have been described by da Silva and others.12,17 Our concern here is with the overall rate of N2 production and consequent total volume of N2. In emulsion explosives and under the reaction conditions used in this model system, the ammonium ion concentration is much greater than the nitrite ion concentration, in which case the availability of NO2- ions will control the reaction rate. We, therefore, assume (17) da Silva, G.; Dlugogorski, B. Z.; Kennedy, E. M. Water-in-oil emulsion forming by thiourea nitrosation: reaction and mass transfer. AIChE J. 2006, 52, (4), 1558-1565.
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q ¼
d½N2 ¼ k½NO2- 0 expð -ktÞ dt
ð4Þ
The dissolved N2, thus, formed undergoes a mass transfer across the oil-water interface and is partitioned between the oil and water phases. The experimental configuration is shown schematically below, with the interface between the oil (1) and water (2) phases located at x = 0. For mathematical convenience, each phase will be treated as semi-infinite:
The instantaneous concentration of the dissolved nitrogen product in the aqueous phase is then described by a onedimensional reaction-diffusion equation written as18 Dc D2 c ¼D 2 þq Dt Dx
ð5Þ
where D = diffusion coefficient of solute, c = solute concentration, x = distance, t = time, and, in this system, q is given by eq 4. We can, thus, predict the N2 concentration in the system as a function of time and position as a result of mass transfer for different values of the reaction rate (k) and nitrite concentrations by solving eqs 4 and 5 simultaneously. The concentration of N2 dissolved in oil is c1, and, as there is no chemically generated N2, it satisfies the one-dimensional diffusion equation: D1
D2 c1 Dc1 ¼0 Dx2 Dt
x0
ð7Þ
where D1 and D2 are diffusion coefficients of N2 in oil and water, respectively. Equations 6 and 7 may be solved as coupled diffusion equations by using the following boundary conditions for the interface as proposed by Crank19 and others.20 If we assume that there is no resistance to mass transfer across the interface, the N2 flux across the interface is given by Figure 4. Calculated N2 concentration profiles on the water and
dc1 dc2 ¼ D2 D1 dx dx
when x ¼ 0
ð8Þ
The N2 concentrations in the layers of oil and water immediately adjacent to the interface are assumed to rapidly equilibrate,19 in which case c1 ¼ pc2
when x ¼ 0
ð9Þ
where p is the partition coefficient of N2 between water and oil. Do et al.20 have discussed a somewhat similar problem in the CO2 flooding of petroleum reservoirs. In those operations, CO2 is dissolved and allowed to diffuse into oil through a water plug. They have shown that when dissolved CO2 concentration increases in the bulk phase, the concentration at the oil-water interface varies with time. We can derive the time-dependent concentration of a chemically generated dissolved solute (in our case N2) in the aqueous solution immediately adjacent to the interface, c2I, to be (for details see Appendix (1))
c2I
0
1
B ¼ ½N2 @
1 C qffiffiffiffiffiA D1 1 þ p D2
when x ¼ 0
ð10Þ
where [N2] is the time-dependent bulk concentration of nitrogen in the aqueous phase (see eq 3). Using these boundary conditions in addition to the usual bulk limits c1 = 0 when x f -¥ and c2 = [N2] when x f þ¥ (and, therefore, DcDx2 ¼ 0, x f þ¥), the coupled partial differential equations were solved numerically using the Matlab pdetoolbox.18 Figure 4 shows the calculated development of the dissolved N2 concentration profile on both sides of the oil-water interface over time, with no dissolved N2 initially in either phase. For this example, olive oil was used for the calculation, as partitioning and diffusion coefficient data for N2 are available in literature. The calculated N2 concentration profile shows the development of a depletion layer several hundred micrometers thick on the aqueous side of the interface due to N2 diffusion across the interface into the oil. There is a corresponding layer of similar thickness on the oil side in which the N2 concentration is enriched due to the high value of the partition coefficient and the finite transport rate away from the interface. The layer is thinner on the oil side due to the lower diffusion coefficient of N2 in olive oil compared with that of water. (19) Crank, J. The Mathematics of Diffusion, 2 ed.; Clarendon Press: Oxford, 1975; p 28-43. (20) Do, H. D.; Pinczewski, W. V. Diffusion-controlled swelling of reservoir oil by indirect contact with injection gas. Chem. Eng. Sci. 1993, 48, 3243-3252.
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olive oil sides of the interface, as a function of reaction time obtained from the numerical solution of eqs 6 and 7 using D1 = 0.55 10-5 cm2 s-1,21 D2 =1.99 10-5 cm2 s-1,22 and p = 4.66.23
The theory of homogeneous nucleation of bubbles by a dissolved gas is well established.24 Bubble nucleation occurs when the dissolved N2 concentration reaches the limiting supersaturation concentration,10 which far exceeds the equilibrium solubility limit due to the work of creating the surface within the liquid.25 For N2 in pure water, the solubility limit is 6.4 10-4M, whereas the limiting supersaturation concentration is around 0.06M.10 The homogeneous nucleation condition24,26 is described by a critical radius, r*: r ¼
2σk ðcs - ceq Þ
ð11Þ
where σ is the surface tension, cs is the supersaturation concentration, and k is the Henry’s law constant for the dissolved gas. The critical radius has a corresponding (Helmholtz) free energy of activation for bubble formation, given by ΔF ¼
16πσ 3 k2 3ðcs - ceq Þ
2
¼
4πσr2 3
ð12Þ
Both the size of the critical nucleus and the height of the free energy barrier decrease as the dissolved gas concentration increases. Further, the free energy barrier varies in height as the cube of the surface tension. Rubin and Noyes8 have reported that the nucleation of threshold of N2, formed by the decomposition of ammonium nitrite, is sensitive to electrolyte concentration and decreases from 0.036 to 0.015 M in sodium perchlorate solutions, as the electrolyte concentration is increased from 2.82 to 5.90 M. (This data extrapolates to a critical nucleation concentration of 0.055 M in pure water, consistent with earlier work.)10 However, they reported that they were unable to reliably determine critical nucleation concentrations at lower ionic strengths, such as the approximately 2 M used here, as the reaction became too slow to (21) Davidson, D.; Eggleton, P.; Foggie, P. The diffusion of atmospheric gases through fats and oils. Experimental Physiology 1952, XXXVII, (2), 91-105. (22) Hayduk, W.; Laudie, H. Prediction of diffusion coefficients for nonelectrolytes in dilute aqueous solutions. AIChE J. 1974, 20, (3), 611-615. (23) Battino, R.; Evans, F. D.; Danforth, F. D. The solubilities of seven gases in olive oil with reference to theories of transport through the cell membrane. JOAC 1968, 45, 830-833. (24) Hodgson, A. W. Homogeneous nucleation. Adv. Colloid Interf. Sci. 1984, 21, 303-327. (25) Weatherford, W. D. J. Homogeneous nucleation of gas bubbles in liquids. J. Colloid Interface Sci. 1970, 34, 197-204. (26) Bowers, P. G.; Hofstetter, C.; Letter, C. R.; Toomey, R. T. Supersaturation limit for homogeneous nucleation of oxygen bubbles in water at elevated pressure: “Superhenry’s Law”. J. Phys. Chem. 1995, 99, 9632-9637.
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attain critical supersaturation.9 In an earlier study, Rubin and Noyes measured N2 bubble formation to occur at approximately 0.025 M in solutions with ionic strengths of about 1 or 1.5 M.8 We, therefore, expect bubble nucleation to occur when the dissolved aqueous N2 concentration reaches about 0.02 M. Our theoretical concentration profile (Figure 4) shows this bubble nucleation threshold is reached in just the bulk aqueous solution after 10 min. After 15 min, a depletion zone of about 0.5-1 mm wide, starting from the interface in the aqueous side, remains below the critical concentration in which no bubbles can be nucleated. This is consistent with the bubble depletion zone which was observed experimentally. The N2 concentration in the oil phase increases sharply near the interface, mainly due to the strong partitioning of N2 from water into oil. Near the interface it is, thus, possible to nucleate bubbles in the oil phase from dissolved N2, just as we observe under the microscope. Similar sharp discontinuities in dissolved solute profiles at liquid interfaces have also been observed previously due to partition of the solutes between the two phases. Do et al.20 have reported similar concentration profiles for CO2 diffusing through a water layer and into an oil, and Boderke et al.27 have described several-fold increases in the concentration of drugs in target tissues compared to the donor solutions. Our results indicate that the concentration of dissolved N2 in the oil near the interface is around 0.03-0.05 M when the bubbles begin to form, after 10-15 min of reaction. Is this a reasonable value for the critical saturation concentration? Rubin and Noyes9 have studied reactive generation of N2 in a variety of organic solvents. They consistently found that the nucleation concentration exceeds the equilibrium solubility by 30-50-fold. N2 has an equilibrium solubility of 0.0028 M in olive oil,23 which would lead us to expect a critical saturation concentration above 0.08 M (which might be reduced somewhat by surface active components in the olive oil). Alternatively, we can estimate the expected degree of supersaturation in the oil from Equation 12 by noting that ceq/k is just the equilibrium pressure of nitrogen, which is the same for both phases. For comparable values of the activation free energy in oil and water, the degree of supersaturation, cs/ceq, in oil should be less than in water by a factor of (σoil/σwater)3/2, leading to a critical saturation concentration around 0.03 M. Both approaches lead to concentrations consistent with our calculated values when bubbles begin to be observed in the oil. The rate of bubble nucleation depends on many factors, including surface tension.26,28,29 As Equation 12 describes an activation energy for nucleation, we would expect the rate of homogeneous nucleation to depend on its exponent and, hence, the exponent of the surface tension cubed. This has been verified by studies on bubble nucleation during boiling. This expectation is consistent with our observation that fewer, large bubbles are formed outside the depletion zone on the high surface tension, aqueous side of the interface, whereas more, smaller bubbles are formed near the interface on the oil side. We would also expect that a small reduction in surface tension of the aqueous solution should increase the number of bubbles nucleated.30 This is discussed further below. (27) Boderke, P.; Schittkowski, K.; Wolf, M.; Merkle, H. P. Modeling of diffusion and concurrent metabolism in cutaneous tissue. J. Theor. Biol. 2000, 204, 393-407. (28) Han, J. A.; Han, C. D. Bubble nucleation in polymeric liquids. J. Polym. Sci. B: Polym. Phys. 1990, 28, 743-761. (29) Blander, M.; Katz, J. L. Bubble nucleation in liquids. AIChE J. 1975, 21, (5), 833-848. (30) Cheng, L.; Mewes, D.; Luke, A. Boiling phenomena with surfactants and polymeric additives: A state-of-the-art review. Int. J. Heat Mass Transfer 2007, 50, 2744-2771.
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In addition to the small individual gas bubbles (Figure 2), swarms of small objects (Figures 2 and 3) appeared occasionally on the oil side and more often in the mineral oil than in the vegetable oil. We were unable to distinguish whether these were bubbles or emulsion droplets. Accumulation of impurities and the sharp rise in the N2 concentration at the interface may lead to heterogeneous nucleation of bubbles on impurity particles on the oil side. Emulsification of the interface may also occur during initial contact between the two phases. Such droplet formation at the pure oil-water interfaces has been reported by Tauer et al.31 Vegetable oil is more viscous, and the interface formed was more stable. Residual free fatty acids and other biomolecules in vegetable oils may also contribute to the stabilization of the interface. Such spontaneously formed aqueous droplets in the oil would contain NH4þ and NO2- ions, which would react to produce N2. However, bubbles would only result from such tiny droplets near the interface, which is rich in dissolved gas. As the concentration of N2 drops sharply on moving a short distance away from the interface (Figure 4), N2 would rapidly dissolve into the surrounding oil, preventing gas bubble nucleation. The formation and location of bubbles in both the oil and aqueous phases is, thus, a consequence of the aqueous phase chemical generation and transport of dissolved N2. The subsequent growth of the bubbles indicates that dissolved N2 is transported across the oil-water and gas-water interfaces into both the oil and existing bubbles. Effect of Gas Bubbles. The presence of bubbles on either side of the interface is expected to have a significant effect on the developing concentration profiles in both phases. We have examined this by numerically solving the reaction-diffusion equation in the absence and the presence of bubbles introduced into the aqueous side of our theoretical model. In addition to the planar oil-water interface (at x = 0), this includes two circular air-water interfaces in the aqueous phase. One bubble was about 400 μm from the interface (in the depletion layer) and the other was farther away. The two systems are shown in Figure 5. The N2 profile in the aqueous phase was determined by numerically solving the reaction-diffusion equation for a 4000 μm long, thin strip of the aqueous phase, while accounting for the presence of these two interfaces (oil-water and air-water) and the in situ generation of N2. This strip was considered sufficiently long that the boundary opposite the oil-water interface would remain at the bulk concentration. The N2 concentration at the bubble surface is calculated, using Henry’s law, and approximately equal to the equilibrium saturation concentration32,33 of N2 (0.00064 M).10 For bubbles such as these, with radii larger than 3 μm, the Laplace pressure is negligible. As we are interested in the N2 profile in the x-direction perpendicular to the oil-water interface, we have assumed ∂c/∂y = 0 at the boundaries parallel to the x-direction. A constant gas-water interfacial length (bubble perimeter) was also assumed, in order to simplify the bubble-wall boundary condition, permitting the solution of the reaction-diffusion equation. Figure 5 shows, on the left, the numerical solution to the concentration profile after 10 min with no bubbles present, which is identical to the result shown in Figure 4. The arrows show the (31) Taure, K.; Kozempel, S.; Rother, G. The interface engine: Experimental consequences. J. Colloid Interface Sci. 2007, 312, 432-438. (32) Srinivasan, R. S.; Gerth, W. A.; Powell, M. R. Mathematical models of diffusion-limited gas bubble dynamics in tissue. J. Appl. Physiol. 1999, 86, 731-741. (33) Frank, X.; Dietrich, N.; Jing Wu, R. B.; Li, H. Z. Bubble nucleation and growth in fluids. Chem. Eng. Sci. 2007, 62, 7090-7097.
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Figure 5. Dissolved N2 distribution in the water side in the presence of two gas bubbles (r = 100 μm and t =10 min). The arrows indicate the direction of N2 flux, which shows that the bubbles act as sinks, decreasing the mass transfer of N2 across the interface.
magnitude and the direction of the flux of dissolved N2, which is undergoing a net transport across the interface into the oil (sink). Figure 5 shows, on the right, the situation if two bubbles were also present in the aqueous side at different distances from the interface from beginning of the experiment. Similar results were obtained from the model when the bubbles were introduced to the water side after the N2 concentration at the interface had reached the bubble nucleation concentration (0.02 M). The subsequent concentration profile of the dissolved N2 and the flux lines (arrows) both show that the gas bubbles are more effective N2 sinks than the oil. Once the bubbles have formed in the aqueous phase, N2 transport into the oil is arrested and even reversed in their vicinity. That is, the bubbles are better sinks for N2 than oil. Once formed, the bubbles lower the surrounding dissolved gas concentration to its equilibrium saturation concentration in its vicinity, if no further, N2 is generated. This suggests that dissolved gas diffusion across the interface into the oil could be controlled by generating bubbles near the interface on the aqueous side and could prevent bubble nucleation from ever occurring in the oil. We have already demonstrated that nucleation of a bubble close to the interface in the water side does not occur in a pristine oil-water system, as N2 is depleted in this region (Figure 4). However, by the addition of a water-soluble surfactant, it may be possible to reduce the surface tension of the aqueous solution, and hence, the energy barrier for bubble nucleation sufficiently to nucleate bubbles at low N2 concentrations, before a substantial depletion layer has grown and well before the nucleation condition in the oil is approached. For example, the surface tension of water can be decreased below the surface tension of olive oil by addition of the surfactant sodium dodecyl sulfate (SDS). The surface tension of a 0.115 M NaCl solution decreased from about 65 to 30 mN m-1 when in a 1 mM SDS solution.34 Other methods, such as introducing heterogeneous nucleation sites, may also prove effective but were not examined as part of this work. Effect of Water-Soluble Surfactants on Dissolved N2 Diffusion and Bubble Nucleation. The formation of bubbles in the aqueous phase was significantly increased when either the anionic surfactant SDS or the commercial nonionic surfactant, polyoxyethylene-23-lauryl ether (Teric12A23) was added at concentrations between 1 and 15 mM. Bubble formation was rapid even at SDS concentrations less than its critical micelle concentration (CMC), which is about 1 mM in a 20 mM ammonium (34) Dean, D. S.; Sentenac, D. Surface charging mechanism for electrolytic soap films. Europhys. Lett. 1997, 38, 645-650. (35) Dutkiewicz, E.; Jakubowska, A. Effect of electrolytes on the physicochemical behaviour of sodium dodecyl sulphate micelles. Colloid Polym. Sci. 2002, 280, 1009-1014.
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Figure 6. Dark field optical microscopy image of the oil-water interfacial region in the presence of ∼15 mM SDS, showing many small bubbles formed in the aqueous phase. Rapid evolution of bubbles in the aqueous phase pushed some bubbles into the interface.
ion solution.35 However, the number of bubbles in the aqueous phase increased with the surfactant concentration. The bubbledepleted zone was much narrower, so that bubbles were observed to form near the interface (Figure 6) in the presence of these surfactants. The bubbles were also noticeably smaller than in the pristine system. This addition of surfactants also significantly decreased or completely eliminated small bubble formation in the oil phase, as predicted by our model. We attribute this to the consumption of N2 during formation of a large number of bubbles and uptake of N2 by the bubbles near the interface. The ability of surfactants to facilitate bubble nucleation has been reported previously by a number of researchers.30 Surfactants are expected to adsorb onto the surface of a growing bubble to form an oriented monolayer and lower the surface tension.36 However, the effect of this adsorbed layer on the transport of dissolved gas into the bubbles is not known, and previous studies (on O2) have been inconclusive. Rosso et al.37 determined that mass transfer of O2 from bubbles into water was decreased by adsorbed surfactants, whereas Sardeing et al.38 reported that it (36) Gosh, P. Coalescence of Air Bubbles at Air-Water Interface. Chem. Eng. Res. Des. 2004, 82, 849-854. (37) Rosso, D.; Huo, D. L.; Stenstrom, M. K. Effect of interfacial surfactant contamination on bubble gas transfer. Chem. Eng. Sci. 2006, 61, 5500-5514. (38) Sardeing, R.; Painmanakul, P.; Hebrard, G. Effect of surfactants on liquidside mass transfer coefficients in gas-liquid systems: A first step to modeling. Chem. Eng. Sci. 2006, 61, 6249-6260.
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was insensitive to adsorbed surfactant for bubbles smaller than ∼1500 μm in diameter. An adsorbed surfactant film is also expected to stabilize the bubbles against both coalescence and engulfment by the oilwater interface from normal colloidal stabilization forces, and this is also consistent with our observations of more smaller bubbles remaining in the aqueous phase. The presence of both very small and large bubbles in the water phase was particularly noticeable when the SDS concentration was greater than its critical micelle concentration (Figure 6). This may indicate that the micelles act as heterogeneous nucleation sites, further enhancing bubble formation in the aqueous phase. Solubilization of nonpolar gases in micellar solutions has been well documented in literature.39,40 Theoretical studies have suggested that the free energy barrier for a bubble nucleation from a micelle can be less than that in the absence of the micelle.41 That is, the micelle core, comprised of the hydrophobic tails of surfactants, may facilitate the formation of nanocavities and, hence, lead to heterogeneous nucleation of bubbles.1
Conclusions We have shown that N2 generated by the purely aqueous phase gassing reaction (1) NH4þ (aq) þ NO2- (aq) f N2 (aq) þ 2H2O nucleates N2 gas bubbles in both the oil and water phases of a heterogeneous system. A solution of the reaction-diffusion equation shows that dissolved N2 transport across the oil-water interface, due to diffusion and partitioning, leads to a bubbledepleted region on the aqueous side of the interface and a bubble nucleation within the oil in a narrow diffusion layer near the interface. Bubble nucleation loci can be controlled by manipulation of the concentration profile and the nucleation conditions. Bubbles are readily created closer to the aqueous side of interface by adding water-soluble surfactants, thus, lowering the energy barrier for nucleation. These bubbles are stronger N2 sinks than the oil phase and, therefore, retard N2 transport across the interface into the oil. Acknowledgment. This work was supported by the Australian Research Council and Dyno Nobel Asia-Pacific Ltd. We thank Jeff Gore and his team at Dyno Nobel Asia-Pacific Ltd for valuable discussions.
Appendix The time-dependent concentration of N2 at the interface can be evaluated by solving the diffusion equation using the Laplace transform method. The two phases meet at x = 0. The concentration of N2 in oil is denoted c1 and exists between -¥ and 0. That in water is c2, which exists between 0 and ¥. Then diffusion equation for the two phases can be written as D1
D2 c1 Dc1 ¼0 Dx2 Dt
x < 0 ðoilÞ
ðA1Þ
(39) King, A. D. Solubility of Gases in Micellar Solutions. In Encyclopaedia of Surface & Colloid Science; Hubbard, A. T., Ed.; Marcel Dekker Inc: 2002; Vol. 4, pp 4749-4759. (40) Roy, S.; Mehra, A.; Bhowmick, D. Prediction of solubility of nonpolar gases in micellar solutions of Ionic Surfactants. J. Colloid Interface Sci. 1997, 196, 53-61. (41) Apte, P. A.; Kusaka, I. Bubble nucleation in micellar solution: A density functional study. J. Phys. Chem. 2004, 121, (24), 12532-12542.
690 DOI: 10.1021/la902309f
D2
D2 c2 Dc2 þq ¼0 Dx2 Dt
x > 0 ðwaterÞ
q ¼ f ðtÞ
ðA2Þ ðA3Þ
where q is the rate of generation of N2 in the water phase, which is a function of time, t (see eq 4). D1 and D2 are diffusion coefficients of N2 in oil and water, respectively. Lets assume, when t = 0, c1= 0 and c2 = c0. Then, from a Laplace transformation42 of eqs A1 and A2: D1
D2
d 2 β1 - sβ1 ¼ 0 when x < 0 dx2
d 2 β2 - sβ2 þ c0 þ φðsÞ ¼ 0 when x > 0 dx2
ðA4Þ
ðA5Þ
where β1 and β2 are the Laplace transforms of c1 and c2, respectively, s is a parameter introduced by the transformation, and j(s) is the Laplace transformation of f(t) (for details please see Carslaw and Jegger42). A4 and A5 are ordinary differential equations which can be easily solved. From A4: d 2 β1 - q21 β1 ¼ 0 when x < 0 dx2
ðA6Þ
where q21 ¼ Ds1 . And from A5: D2
d 2 β2 c0 φðsÞ - q22 β2 ¼ D2 dx2 D2
when x > 0
ðA7Þ
where q22 ¼ Ds2 . Equation A7 has the solution: β2 ¼ A2 eq2 x þ B2 e - q2 x þ
c0 φðsÞ þ 2 q22 D2 q2 D2
which can be simplified to β2 ¼ A2 eq2 x þ B2 eq2 x þ
c0 φðsÞ þ s s
ðA8Þ
N2 is generated throughout in the aqueous phase; therefore, we may assume that the N2 concentration sufficiently farther from the interface is uniform. dβ2 2 Therefore as x f ¥,dc dx ¼ 0 and therefore, dx ¼ 0. By this we can show that A2 = 0. Therefore, the general solution A8 can be written as β2 ¼ B2 eq2 x þ
c0 φðsÞ þ s s
ðA9Þ
Similarly by assuming c1 = 0 as x f -¥, the general solution of A6 is ðA10Þ β1 ¼ A1 eq1 x The unknown parameters A1 and B2 can be determined by applying boundary conditions for the interface (x = 0). These parameters can be functions of t but not of x. (42) Carslaw, H. S.; Jaeger, J. C. Conduction of Heat in Solids, 2nd ed.; Oxford University Press: Oxford, 1959.
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If there is no accumulation of the solute at the interface,19 dc1 dc2 ¼ D2 D1 dx dx
when x ¼ 0
h
c0 s
þ
i
φðsÞ s
ðA11Þ
Assuming instantaneous equilibration between the two phases at the interface, we can write c1 ¼ pc2
Let θ ¼
ðA12Þ
B2 ¼
D1
dβ1 β ¼ D2 2 dx dx
and
β1 ¼ pβ2
ðA13Þ ðA14Þ
These boundary conditions were used in A9 and A10 to determine the parameters A1 and B2. FromðA9Þ
dβ2 ¼ B2 ð -q2 Þeq2 x dx dβ1 ¼ A1 ðq1 Þeq1 x dx
FromðA10Þ
ðA15Þ
ðA16Þ
Then by substitution of A15 and A16 in A13, we obtain D1 A1 ðq1 Þeq1 x jx ¼0 ¼ D2 A2 ð -q2 Þe - q2 x jx ¼0 which is simplified to D1 A1 ðq1 Þ ¼ D2 A2 ð - q2 Þ2 and therefore rffiffiffiffiffiffi D2 A1 ¼ B2 D1
ðA17Þ
Substituting A9 and A10 in A14 we obtain c0 φðsÞ þ A1 eq1 x jx ¼0 ¼ p B2 þ s x ¼0 s h Therefore, A1 ¼ p B2 þ A17:
c0 s
þ
i
φðsÞ s
and substituting this in
rffiffiffiffiffiffi D2 c0 φðsÞ B2 ¼ p B2 þ þ s D1 s
Langmuir 2010, 26(2), 684–691
ðA18Þ
- pθ qffiffiffiffiffi 2 pþ D D1
Now we can substitute this relation in eq A9 to determine the Laplace transform of the time-dependent concentration at x = 0. - pθ q2 x qffiffiffiffiffi e jx ¼0 þ θ ðA19Þ 2 pþ D D1 h i in A19 we Now by substituting the relation θ ¼ cs0 þ φðsÞ s obtain 0 1 c0 φðsÞ B 1 C qffiffiffiffiffiA β2 ¼ ðA20Þ þ @ D1 s s 1 þ p D2 β2 ¼
Then
where p is the partition coefficient of N2 between the two phases. From the Laplace transform of A11 and A12 we can write at x = 0:
. From A18:
and from inverse Laplace transform of this equation we get 0 1 Zt 1 B C qffiffiffiffiffiA f ðtÞdðtÞ@ ðA21Þ c2I ¼ ½c0 þ D1 1 þ p D 0 2 which gives the N2 concentration at the interface in the water side (= c2I). Interestingly, Z t Z t f ðtÞ dðtÞ ¼ q dðtÞ 0
0
is the increase in bulk concentration in the water side due to generation of N2 (see eqs 3 and 4). Therefore, 0 1 1 B C qffiffiffiffiffiA c2I ¼ ðc0 þ ½N2 Þ@ D1 1 þ p D2
ðA22Þ
Previously, Crank19 has shown that for a two phase composite system with a constant initial solute concentration in one of its phases (in our study c0) and when no generation occurs, the concentration at the interface is given by the initial concentration (c0) multiplied by the factor in the large brackets of A22. Hence, if no N2 generation occurs in the aqueous phase (i.e., when [N2] = 0), then A22 reduces to Crank’s solution. Equation A22 describes a more general situation than the example given by Crank because generation of the solute in one of the phases has been considered. This can now be used as the time-dependent boundary condition to numerically solve the diffusion eqs A1 and A2.
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