Langmuir 2008, 24, 9933-9936
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Particles Driven Up the Wall by Bursting Bubbles Alex D. Nikolov and Darsh T. Wasan* Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, Illinois 60616 ReceiVed March 28, 2008. ReVised Manuscript ReceiVed July 3, 2008 The phenomenon of particles being “driven up the wall” of a vessel by bursting bubbles at an air-water interface covered with hydrophobic nanoparticles is reported. Experiments have shown that the bubbles bursting at the interface give rise to the local surface pressure gradient, which pushes the particles to climb and coat the walls of the vessel. A theoretical model based on the lubrication approach to estimate the height and speed at which the particle layers climb up the walls yields values that are in fair agreement with the experimental measurements. The effects of the liquid viscosity, electrolyte strength, and particle wettability are also examined.
Introduction Bursting bubbles at free gas-liquid surfaces have fascinated scientists and technologists for a long time. Bursting bubbles on the surface of the sea lead to the introduction of sea-salt nuclei and organic particles from the ocean into the atmosphere. Air bubbles reaching the air-water interface burst and eject a number of liquid droplets to great heights into the air as a result of the Rayleigh instability in the jet. Various aspects of this jet motion have been extensively studied both experimentally and theoretically.1-4 Bubble dynamics (coalescing, shrinking, and collapsing) play an important role in chemistry (e.g., sonochemistry), physics (e.g., sonoluminescence), nature (e.g., fermentation), and technology.5-9 The nature of bubble dynamics amazes us with the unexpected formation of unusual structures.10,11 In many processes, the placement of a liquid layer on a solid (e.g., coatings) traps small air bubbles inside the coating layer. The entrapment of small bubbles inside the coating layer is expected to have an effect on the quality of the coating layer, but the role of the trapped bubbles in coating dynamics is still not well understood.12,13 Previously, Mayya and Sastry14 investigated the spontaneous growth of a gold-particle-laden film on a container wall from the oil-water interface. They suggested that the phenomenon was based on the conventional surface tension gradient mechanism (i.e., the Marangoni effect). Later, Binks, et al.15 provided additional evidence showing that the film growth phenomenon is driven by the coalescence of particle-coated emulsion drops * Corresponding author. E-mail:
[email protected]. (1) Rayleigh, R. J. S. On the Instability of Jets; Scientific Papers; Cambridge, England, 1899; pp 361-371. Rayleigh, R. J. S. On the Instability of Cylindrical Fluid Surfaces; Cambridge, England, 1902; pp 594-596. (2) Keintzler, C. F.; Blanchard, D. C.; Woodcock, A. H. Tellus 1954, 6, 1. (3) Longuet-Higgins, M. S. J. Fluid Mech. 1983, 127, 103. (4) Boulton-Stone, J. M.; Blake, J. R. J. Fluid Mech. 1993, 254, 437. (5) Lohse, D. Nature 2002, 418, 381. (6) Plesset, M. S.; Prosperetti, A. Annu. ReV. Fluid Mech. 1977, 9, 145. (7) Versluis, M.; Schmitz, B.; von der Heydt, A.; Lohse, D. Science 2000, 289, 2114. (8) Srinivasarao, M.; Collings, D.; Philips, A.; Patel, S. Science 2001, 292, 79. (9) Tsai, W. L.; et al. Nature 2002, 417, 139. (10) Lohse, D. Phys. Today 2003, 56, 36. (11) Liger-Belair, G. Sci. Am. 2003, 80. (12) Simpkins, P. G.; Kruck, V. J. Nature 2000, 403, 641. (13) Matheson, R. R. Science 2002, 297, 976. (14) Mayya, K. S.; Sastry, M. Langmuir 1999, 15, 1902. (15) Binks, B. P.; Clint, J. H.; Fletcher, I. D. P.; Timothy, J. G.; Taylor, P. Chem. Commun. 2006, 2531.
Figure 1. Sketch illustrating the dynamics of the breakage of the air-aqueous interface covered with a hydrophobic particle layer. (a) Generation of water droplets covered with a particle layer. (b) Air bubble covered with a particle layer forming in the aqueous phase.
at the oil-water interface. Binks et al.16 reported the phenomenon of particle film growth from foam bubble coalescence. We discussed the phenomenon in 2003.17 In the present letter, we report our observations of the phenomenon of bursting bubbles at a gas-liquid surface covered with tiny particles and a theoretical model based on the lubrication approximation to rationalize the observations.
Experimental Section Nanosized (20-30 nm) hydrophobic silica particles (a product of Wacker HDK) were placed on the surface of 50 mL of purified water (cleaned by the Millipore system) in a clean 250 mL graduated glass cylinder (3.8 cm i.d.). The glass cylinder was pretreated with chromic acid and then rinsed with deionized water. The walls of the glass cylinder were water wetted; a stable water film formed and drained on the glass surface when the cylinder with only water was shaken. The pyrogenic nanoparticles have an amorphous structure with a silica core and surface composed of 18% SiOH and 82% (16) Binks, B. P.; Clint, J. H.; Fletcher, I. D. P.; Lees, T. J. G.; Taylor, P. Langmuir 2006, 22, 4100. (17) Nikolov, A. D.; Wasan D. T. Paper presented at the American Chemical Societh meeting, 2003, Abstract U661, 345, Collected Part 1, p 225. (18) (a) Nikolov, A. D.; Dimitrov, A. S.; Kralchevsky, P. A. Opt. Acta 1986, 33, 359.19. (b) Menon, B.; Nikolov, A. D.; Wasan, D. T. J. Colloid Interface Sci. 1988, 124, 317.
10.1021/la8009817 CCC: $40.75 2008 American Chemical Society Published on Web 08/13/2008
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Letters of 25 ( 1 °C. An optical arrangement with a microscope, video camera, and recorder was used to observe the bubble-bursting phenomenon at the gas-liquid surface covered with the particle layer. The objective of the microscope was focused directly on the meniscus (i.e., water-glass-wall-aqueous film) region.
Results and Discussion
Figure 2. (a) The hydrophobic layer around the water droplet is located at the outer side of the air-aqueous interface; it isolates the droplet and prevents droplet coalescence with the air-aqueous homophase. The photograph depicts a single water droplet resting on an air-aqueous homophase interface. (b) The hydrophobic layer around the air bubble interface surface is located at its inner side and, as a result, cannot inhibit bubble coalescence with the homophase.
dichlordimethyl silane groups. During the chemical hydrophobization, the dichlordimethyl silane groups are not anchored uniformly over the particle surface; there are more silane groups anchored in some spots on the surface than on others. The surface energy of amorphous silica particles is not homogeneous, and particles tend to cluster into networks with void patterns. Consequently, some particle areas are more hydrophobic than others and have a “biphilic” nature. These particles are not the Janus type. These biphilic particles interact differently with the air and aqueous phases. When these particles are placed on the interface, a skinlike layer is formed because of the net result of the two types of forces, an attractive hydrophobic force between the hydrophobic parts (facing one another) in the air and a repulsive hydration force between the hydrophilic parts immersed in the water. The degree of hydrophobicity of the particles was determined by measuring the gas-liquid-solid contact angle between the water droplet and the hydrophobic particle layer at the surface using the sessile drop-shape method.18 A 0.01 g sample of hydrophobic particles was placed on the water-air surface inside the glass cylinder. The cylinder was shaken vigorously to generate small air bubbles and then was placed upright to rest. All of the experiments were conducted at a room temperature
Shaking the glass cylinder containing the aqueous phase covered with the nanoparticle layer causes the interface to oscillate and break up, simultaneously generating both water droplets and air bubbles covered with fine particles, as illustrated in Figure 1. The micrograph in Figure 2 shows a water droplet (0.27 cm in diameter) resting on the air-water interface covered with a skinlike layer of particles. Gentle horizontal shaking of the interface easily results in the water droplets’ run over the particle layer at the air-water interface. The interaction between the two particle layers, one layer on the water droplet surface and the other layer at the air-water surface, is mostly via the air film, which produces little resistance to the water droplet (Supporting Information movie, part I). Recently, Aussillous and Quere19 observed water droplets coated with hydrophobic particles (“liquid marbles”) run over a solid surface covered with a hydrophobic layer in a similar fashion. A different situation occurs when the air bubble with the particle layer inside it approaches the air-water interface. It interacts with the interface via an aqueous lamella that separates the bubble from the interface and appears as a small dot in the photomicrograph (Figure 3a). The lamella ruptures when it reaches a critical thickness, which is about 250-350 nm. After the lamella ruptures, the bubble shape changes from spherical to cratertype, and the gas from the cavity is released in the form of a jet (depicted in Figure 3b). Also, shortly after the ejection of the gas bubble, a liquid jet (often called a Worthington jet) bursts out and disintegrates into drops and a secondary bubble. A shock wave propagates at the interface. The photomicrographs in Figure 3b-d depict the phenomena. We used the capillary force balance, in conjunction with microinterferometry, to study the lamella film thickness stability.20 The particles were spread on the air-water interface by slightly
Figure 3. Time sequence of micrographs depicting bubble-bursting dynamics. (a) An air bubble arrives at the air-water surface covered with hydrophobic particles, and the white dot depicts the lamella formation. (b) The lamella ruptures, and the air from the bubble bursts, expelling small water droplets. (c) The bursting pressure forces particles to spread and move away from the bursting area. (d) The area of the air-water surface is not covered with particles.
Letters
shaking the vessel. A glass ring with an internal diameter of 0.2 cm was immersed in an aqueous phase and was then pulled out slowly. An aqueous drop with a double-concave meniscus covered with particles was formed. The liquid from the meniscus was slowly sucked out so that the two menisci approached each other to form a film. The thinning behavior of the film was monitored using reflected-light microinterferometry. The process of lamella rupture is triggered by the formation of a small circular hole inside the lamella. Hole formation is due to the local perturbation in the thickness promoted by thermal or mechanical perturbations. When bubbles smaller than 50 µm in diameter approach the air-water interface, they burst quickly in the absence of any surfactant, whereas the larger bubbles take a bit longer to collapse. The smaller bubbles have a higher capillary pressure, and the aqueous lamella thins faster and has a shorter lifetime. As a result of the bubble collapse at the interface, the particle layer at the surface of the collapsed bubble is more compressed than the particle layer at the air-water interface. The 2-D pressure difference drives particles from the compressed area to spread over the homophase. As more bubbles collapse at the air-water interface, the pressure in the 2-D layer increases and drives the particle layer to climb up and coat the walls of the container (Figure 4c and Supporting Information movie, part II). A skinlike layer (i.e., coated layer) of particles is formed at the air-water surface (Figure 4a). The particles adhere to the surface by a tiny three-phase contact line. The contact angle at the three-phase contact line is about 170°. Not all particles tend to form a skinlike layer. Some particles form microsized clusters, which appear as white dots in Figure 4b,c-2. We conducted a simple experiment to estimate the contribution of the capillary pressure of the bursting bubbles to the 2-D pressure gradient at the surface. The air-water surface was covered with enough particles to form a 2-D layer. A small bubble was expelled beneath the surface from a needle attached to a microspring. The experiment showed that at the time of the bubble collapse at the air-water surface the newly created area is about one-third of the initial bubble area (Figure 3d). We used this value to estimate the height and speed at which the particles climb up the walls. For a mean bubble size of 50 µm, as determined by measuring the bubble size distribution in our experiments, the capillary pressure for a spherical bubble estimated from the Laplace equation is
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P ) 2σ ⁄ Rb ≈ 6 × 103 Pa
(1)
Here Rb ) 25 µm and σ ) 72 mN/m as the surface tension of water at 25 °C. Therefore, the contribution of the capillary pressure to the 2-D particle layer spreading pressure is on the order of 2 × 103 Pa. Balancing this capillary pressure contribution with the hydrostatic pressure (∆FgH ) 2 × 103Pa), the height of the particle layer climbing up the walls is estimated to be H ) 21 cm. This value agrees well with the experimentally determined value of about 25 cm (Figure 4b). The maximum velocity at which the particle layer can climb up and coat the vessel walls can be estimated using Landau and Levich’s lubrication approach for the deep coating model.21 The Navier-Stokes equation representing the balance between the capillary force (given by the Laplace equation) and the viscous force for the case of capillary number Ca ) µU/σ ,1 and bond number ) FgR2/σ e 1 is
σ
d3δ d2u + µ )0 dx3 dy2
(2)
where u is the local vertical velocity of the fluid in the film, x is measured vertically upward from the meniscus level, y is measured perpendicular to the vessel wall, and δ(x) is the local film thickness (Figure 5). After integrating eq 2 with respect to y at constant x and subject to the no-slip condition, u ) U at the film meniscus, y ) 0, and the stress at the surface µ∂u/∂y ) 0 at y ) δ ) hf, where hf is the film thickness and the velocity, u, has a parabolic profile. Referring to Figure 5, the curvature at the meniscus surface is d2δ/dx2 ) -1/Rm; therefore, the interfacial curvature term is given by the expression
d3δ 1 ) 2 3 dx Rm
(3)
Because the radius of the collapsing bubble, Rb, is much smaller than the radius of curvature of the meniscus, Rm, the thickness of the film layer, hf, is governed by the radius of the collapsing bubble, hf ) Rb. Therefore, the expression for the maximum velocity of fluid climbing up the wall becomes
Figure 4. (a) Sketch of the optical arrangement for the experimental setup to monitor the meniscus region. (b) Photograph of the coated layer on the glass wall. (c) Micrograph of the texture of the coated particle layer on the glass wall: l. magnified view of the coated layer and 2. particles forming a cluster.
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hf2 σ Umax ≈ 3µ R 2
Letters
(4)
b
After introducing σ/Rb ) ∆P ) capillary pressure, eq 4 for the maximum velocity becomes
Umax ≈
hfσ hf ) ∆Ρ 3µRb 3µ
(5)
Assuming that the thickness of the aqueous film (hf) moving with the particle layer cannot exceed the particle diameter (25-30 nm), including the adhered water layer, and substituting for the viscosity of water (µ ) 0.01 P at 25 °C) and ∆P ) 2 × 103 Pa, the maximum climbing velocity of the particle layer is estimated to be 2.5 cm/s. The actual measured particle layer climb-up velocity was about 2 cm/s. The effects of the liquid-phase viscosity, electrolyte strength, and particle wettability were also examined. The liquid-phase
viscosity was increased 4 times by the addition of 40 vol % glycerol to the aqueous phase; the particle layer climb-up rate was reduced by a factor of about 3, which is in qualitative agreement with the simplified model predictions based on the lubrication approach. Increasing the electrolyte strength from 0.5 to 1.0 mL/L of NaCl did not result in any noticeable change in either the height or speed at which the particles climbed the walls of the vessel. The effect of particle hydrophobicity/hydrophilicity was also explored by using silica particles with different wetting characteristics (with contact angles of 45-60°). The particle layer did not climb up the walls as expected. In this particular case, the aqueous lamella (separating the air bubbles from the air-aqueous interface) is more stable (because the particles are located outside the air-water surface) and only the larger bubbles tend to burst, so the pressure gradient is small. There is insufficient force to drive the particles up the walls; consequently, the particle climbing-up-the-wall rate is low. In summary, the mechanism of a pressure gradient generated by bursting bubbles at an air-water interface (covered with hydrophobic nanoparticles) driving particles up the wet walls and the model predictions for the maximum climbing velocity of the particle were discussed here. The predicted value of the rate of the particle climb up the wall is in fair agreement with the measurements. Our present model may be applicable for small liquid droplets bursting (coalescing) at an oil-water interface laden with fine particles when no surfactant is present. Acknowledgment. This research was supported by the U.S. Department of Energy and by the National Science Foundation. Supporting Information Available: Movies I and II. This material is available free of charge via the Internet at http://pubs.acs.org. LA8009817
Figure 5. Schematic of the key parameters of the model for the climbingup-the-wall layer and the role of the meniscus and/or bubble curvature in the thickness of the lubrication layer.
(19) Aussillous, P.; Quere, D. Nature 2001, 411, 924. (20) Nikolov, A. D.; Wasan, D. T. J. Colloid Interface Sci. 1988, 133, 1. (21) Landau, L.; Levich, B. Acta Physicochim. USSR 1942, 17, 42.
