Factors Controlling the Formation and Stability of Air Bubbles

Aug 25, 2004 - formed by shaking water with the particles, but a much higher volume fraction of bubbles was obtained by pressurizing the aqueous phase...
2 downloads 0 Views 423KB Size
Download PDF
Langmuir 2004, 20, 8517-8525

8517

Factors Controlling the Formation and Stability of Air Bubbles Stabilized by Partially Hydrophobic Silica Nanoparticles Eric Dickinson, Rammile Ettelaie, Thomas Kostakis, and Brent S. Murray* Food Colloids Group, Procter Department of Food Science, University of Leeds, Leeds LS2 9JT, United Kingdom Received April 30, 2004. In Final Form: July 9, 2004 Air bubbles have been formed using partially hydrophobic silica nanoparticles as the stabilizer. The particles were of primary particle size 20 nm, chemically treated to different degrees with dichlorodimethylsilane to render them partially hydrophobic. Above a certain bubble size range (typically 80-µm diameter), the bubbles seemed to be almost indefinitely stable, while for any size above 20 µm their stability against disproportionation is far better than bubbles stabilized by any protein film investigated in previous studies. A possible theoretical justification for this observation is presented. Bubbles could be formed by shaking water with the particles, but a much higher volume fraction of bubbles was obtained by pressurizing the aqueous phase to 5 atm overnight followed by suddenly releasing the pressure to nucleate bubbles within the silica dispersion. Sonicating the silica dispersion before nucleation also gave more bubbles, which were also found to be more stable. There appeared to be an optimum degree of surface hydrophobicity that gave maximum foamability and foam stability, where around 20-33% of the silanol groups on the silica surface had been converted to dimethylsilane groups. However, a sharp increase in stability occurred when between 1.8 and 2 mol dm-3 NaCl was also included in the aqueous phase. The change in stability due to inclusion of salt can be rationalized in terms of changes occurring in the value of the particle contact angle. The effects of increasing sonication and an optimum surface chemical treatment can be explained by the need to make the particles sufficiently hydrophobic so that they adsorb strongly enough, while at the same time minimizing their tendency to aggregate in the bulk aqueous phase, which hinders their adsorption. Furthermore, confocal laser scanning microscopy of the bubble dispersions suggests that a large volume fraction of stable bubbles is only formed when the particles adsorbed to the bubbles are also part of a spanning silica particle network in the bulk aqueous solution, forming a weak gel with a finite yield stress.

Introduction Broad interest has recently been re-awakened in the study of solid particles as stabilizers of dispersed systems.1-4 Much of this activity has been stimulated by the research of Binks and co-workers,5a-e though the principles of such stabilization were observed at least 100 years ago.6 There are many practical examples in which particles are implicated in emulsion stability, such as the presence of wax crystals in water-in-crude oil emulsions and triglyceride fat crystals in food emulsions.7 However, compared to oil-in-water and water-in-oil emulsions, up to now there have been relatively few studies of the stabilization of foams by particles.8,9 The key to the colloid stabilizing mechanism by particles is that, if the surface energy (or contact angle) of the * Author for correspondence. Tel.: 44 (0)113 3432962. Fax: 44 (0)113 3432982. E-mail: [email protected]. (1) Rousseau, D. Food Res. Int. 2000, 33, 3. (2) Tambe, D. E.; Sharma, M. M. Adv. Colloid Interface Sci. 1994, 52, 1. (3) Zhai, Z.; Efrima, S. J. Phys. Chem. 1996, 100, 11019. (4) Midmore, B. R.; Herrington, T. M. Prog. Colloid Polym. Sci. 1999, 112, 115. (5) (a) Binks, B. P.; Lumsdon, S. O. Langmuir 2000, 16, 8622. (b) Binks, B. P.; Clint, J. H. Langmuir 2002, 18, 1270. (c) Binks, B. P.; Lumsdon, S. O. Langmuir 2000, 16, 2539. (d) Ashby, N. P.; Binks, B. P. Phys. Chem. Chem. Phys. 2000, 2, 5640. (e) Binks, B. P. Curr. Opin. Colloid Interface Sci. 2002, 7, 21. (6) Ramsden, W. Proc. R. Soc. London 1903, 72, 156. (7) Walstra, P. In Food Structure and Behaviour; Blanshard, J. M. V., Lillford, P., Eds.; Academic Press: London, 1987. (8) Kam, S. I.; Rossen, W. R. J. Colloid Interface Sci. 1999, 213, 329. (9) Du, Z.; Bilbao-Montoya, M. P.; Binks, B. P.; Dickinson, E.; Ettelaie, R.; Murray, B. S. Langmuir 2003, 19, 3106.

particles with the aqueous phase is in the correct range, then the adsorption energy per particle can be up to several thousand kT,5b,10 where k is the Boltzmann constant and T is the absolute temperature. Thus, once particles are adsorbed at the interface of a droplet, it is almost impossible to force them out of the interface, either by shrinkage of the droplet or through coalescence between droplets. Practically, this tends to put the desired contact angle in the region of 90°, so that the particles are not particularly preferentially wetted by either the dispersed or the continuous phase. However, for emulsion formation, the particles can be adequately dispersed in either bulk phase using high energy homogenization and/or ultrasonication, followed by mixing of the particle-containing phase prior to homogenization. It is then possible to obtain emulsion droplets coated in a layer of particles that prevents coalescence or Ostwald ripening. With foams, as our own preliminary work9 has shown, there seems to be the problem that the particles have to be reasonably hydrophobic, but then the option of dispersing them in the hydrophobic (air) phase is not there. Consequently, the particles tend to become highly aggregated in the aqueous phase and at the air-water interface, although some very stable bubbles can be formed under certain conditions.9 What is far from clear, however, is the detailed structure of the particle film stabilizing the bubbles, for example, whether this consists of a closepacked monolayer of small, primary particles plus adventitiously attached aggregates, a rigid network of (10) Aveyard, R.; Clint, J. H.; Nees, D. Colloid Polym. Sci. 2000, 278, 155.

10.1021/la048913k CCC: $27.50 © 2004 American Chemical Society Published on Web 08/25/2004

8518

Langmuir, Vol. 20, No. 20, 2004

Dickinson et al.

aggregates, or both. Indeed the balance between the necessity of strong attractive particle-particle interaction versus strong particle adsorption to the interface is still not entirely clear for all the particle-stabilized colloids studied so far, including emulsions. In this paper, we extend our earlier work on silicaparticle-stabilized foams to explore how variations in particle aggregation and hydrophobicity affect foam formation and stability. Varying the aqueous-phase solvent conditions as a way of optimizing the balance of the adsorption tendency versus the aggregation tendency in the bulk was adopted as a convenient formulation tool in making the particle-stabilized foams. Materials and Methods Materials. Fumed silica particles were used, of nominal diameter 20 nm, that had been treated with a silylating reagent to different extents. The particles were specially made by WackerChemie GmbH (Munich, Germany). They had been subjected to different degrees of dichlorodimethylsilane treatment. In this work, two particular samples were mainly used: one with 33% of the surface Si-OH groups treated (33% SiOR) and another with 20% of the surface Si-OH groups treated (20% SiOR), the latter, therefore, being less hydrophobic than the former. In some preliminary measurements, particles with 43, 53, and 60% SiOR were also investigated. Water from a Milli-Q system (Millipore, Ltd., Watford, U.K.), free from surface active impurities and with a conductivity of less than 10-7 S cm-1, was used throughout. AnalR grade NaCl was from Sigma (Poole, Dorset). Methods. Three different particle concentrations were investigated: 0.01, 0.08, and 1 wt %. The particles were added to a small volume of water in a glass sample bottle containing variable concentrations of NaCl, in the range of 0-4 mol dm-3. In preliminary measurements to identify the optimum conditions for bubble stability, sample bottles containing 0.01 or 0.08 wt % dispersions of the particles were sealed with a clean polyproylene lid and shaken vigorously by hand for 15 s, and the approximate lifetime of the bubbles in the bottle was recorded by eye. In more controlled measurements of stability, sample bottles containing 0.08 or 1 wt % dispersions of the particles were sonicated for 10 min in a Grant model XB14 ultrasound bath (Grant Instruments, Ltd., Shepreth, U.K.) with an operating frequency of 38 kHz, 162 W RMS power. In some experiments, the sonication was applied for 1 h. These dispersions were then foamed as follows. As described elsewhere,9 the bubbles were generated by applying a pressure drop to the aqueous suspension of particles, and the behavior of the resulting bubbles was observed at a planar air-water interface, which is especially convenient for quantitative study, both experimentally and theoretically.11 The bubble cell apparatus used to generate and observe the bubbles in this way, illustrated schematically in Figure 1, was constructed in the workshop of the Procter Department of Food Science, University of Leeds. It consists of two stainless steel chambers connected together via a steel tube. The larger chamber, the observation chamber, has a 12.7-mm plate glass at the top end and a 12.7-mm poly(vinyl chloride) PVC plate at the bottom. The two plates are optically polished to enable clear illumination from below via a Schott KL 1500 cold light source and fiber optic cable. The observation of the interface is made through the top plate via a Nikon microscope fitted with a Nikon Mplan 40x long-working-distance lens and Hitachi KP-MIEK/K chargecoupled device video camera. The window on the top can be easily removed and sealed again to enable pressurization up to approximately 5 bar. The small chamber, the pressurization one, is designed to be sealed by a stainless steel piston as it travels past the O-ring, pressurizing the whole system. The chambers were filled with the required dispersion up to approximately 90% of the capacity of the observation chamber. The piston was manually screwed down a pre-set distance into the pressurization chamber cylinder to produce a pressure of 5 bar. For convenience, the dispersion was left overnight (ap(11) Dickinson, E.; Ettelaie, R.; Murray, B. S.; Du, Z. J. Colloid Interface Sci. 2002, 252, 202.

Figure 1. Schematic representation of bubble apparatus for generating bubbles via the pressure drop method: (a) microscope, (b) upper glass window, (c) observation chamber, (d) aqueous dispersion, (e) air-water interface, (f) lower PVC window, (g) light source, (h) pressurization chamber, (i) O-ring, and (j) piston. proximately 12 h) to ensure that the aqueous phase became saturated with air at 5 bar. Then the excess pressure was suddenly (i.e., in less than 1 s) reduced by releasing the piston. Because of difficulties in generating and stabilizing bubbles to different degrees, depending on the system, we have found this in situ method of generating bubbles is more reproducible because it avoids the problems of trying to form and transfer unstable bubbles to the cell prior to observations. Image Capture and Analysis. For relatively short (approximately less than 2 h) sequences of images, the pressure release and post pressure release changes were recorded directly via a Perception digital video recorder (PVR) system and software (Digital Processing System, Inc., Farnham, U.K.) at an appropriate time-lapse rate. For longer sequences, the whole experimental sequence was recorded to videotape, and then selected frames, or sequences of frames, were played back to the digital video recorder for subsequent analysis. The sizes of the individual bubbles were measured via the software Image Tool v2.00a3 (University of Texas, U.S.A.), after appropriate contrast adjustment, thresholding, and calibration to a standard-sized object. Bubbles that were touching had to be specified as separate objects by the user of the software. When there were many bubbles in the field of view, and particularly when many particle aggregates were visible as well, the process of identifying and sizing all the visible bubbles as a function of time became difficult and time-consuming. Therefore, as an alternative, in some instances the bubble stability was represented in terms of the stable bubble fraction, F. This was defined as the ratio of the number of bubbles still visible after a certain time to the original number of bubbles present at the start, that is, immediately after their formation. In this case, the number of bubbles (and, hence, F) was determined by manual counting. The field of view was typically 8 × 8 mm. Bulk Rheology. Dispersions of 33% SiOR particles in 3 mol dm-3 NaCl were investigated by creep rheometry using a Bohlin CVO-R controlled stress rheometer (Bohlin Instruments, Cirencester, U.K.). A concentric cylinder measurement cell with 24/27 double gap geometry (outer gap 1.25 mm diameter, inner gap 1.1 mm) was used, with a total sample volume of 10 mL. The temperature was maintained at 25 ( 1 °C. The dispersions were sonicated for 1 h as described above and left overnight before gently transferring them to the rheometer, to have the same conditions as when the bubbles were formed via the pressure drop method. Rheology measurements commenced 30 min after transfer to the rheometer. Confocal Laser Scanning Microscopy (CLSM). CLSM was carried out with a Leica TCS SP2 unit combined with a Leica model DM RXE microscope, utilizing a ×20 dry objective lens of 0.7 numerical aperture. A 0.1 vol % solution of Rhodamine B (Sigma Chemicals, Poole, Dorset) was used to stain the silica particles. Samples were excited with the 543-nm line of a HeNe laser. Dispersions of 1.0 wt % of 33% SiOR particles in 3 mol dm-3 NaCl, sonicated for 1 h, were aerated by pressurization and then pressure release as described above. A small volume of the aerated dispersion was transferred carefully via a plastic

Formation and Stability of Air Bubbles

Langmuir, Vol. 20, No. 20, 2004 8519

Table 1. Approximate Bubble Lifetimes after Hand-Shaking with the 33% SiOR Particles at Different NaCl Concentrations and Particle Concentrations bubble lifetime NaCl, mol dm-3

0.01 wt % particle concentration

0.08 wt % particle concentration

0 1 2 3

few s 10-15 s 1-2 min 1-2 min

few s 2 min-few h 3 min-24 h >24 h

pipet from the bubble cell to a welled slide immediately after the release of pressure. The welled slides consisted of a glass ring (15 mm diameter, 1.75 mm thick) fused to glass microscope slides (26 mm × 76 mm × 1.75 mm thick). The sample contained within the ring was sealed with a microscope coverslip. Confocal images were recorded approximately 5 min after the release of pressure.

Results and Discussion Preliminary Measurements Using Manual Shaking. Table 1 shows the stability results from the method of simple hand-shaking with the 33% SiOR particles at the two different particle concentrations. With the 20% SiOR particles, even at high particle concentrations and high NaCl concentrations, any bubbles that were formed did not survive for more than a few seconds, but coalesced soon after their formation. With all the other particles tested that had a higher % SiOR content (i.e., more hydrophobic than 33% SiOR), at the same particle concentrations and NaCl concentrations, virtually no bubbles were formed at all and the silica remained in a highly aggregated state in the aqueous phase. For this reason, the more detailed measurements (see below) concentrated on the use of the 33% SiOR particles and to a lesser extent the 20% SiOR particles. It is interesting to note in Table 1 how the stability appeared to increase considerably as the salt concentration was increased. We note that at 1 mol dm-3, virtually all the electrostatic repulsion between the particles is screened out, so that although one expects an increasing tendency for particle aggregation due to loss of double-layer repulsion below 1 mol dm-3, not much further change might be expected between 1 and 3 mol dm-3. However, Deryaguin has demonstrated12,13 an explicit relationship between contact angle and pair interaction energy, and so at these high salt concentrations (>1 mol dm-3) there could still be changes in solvation forces, and so forth, that explain the apparent change in the contact angle on silica. Thus, the addition of these high concentrations of salt is a way of fine-tuning the particle surface hydrophobicity to obtain optimum foaming behavior. Because it is difficult to control precisely the degree of silylization or to be sure of the uniformity of the degree of modification to individual particle surfaces, the technique of altering the surface hydrophobicity via the composition of the continuous solution phase is a convenient alternative for optimizing formulation conditions for both emulsions and foams. Further detailed work was, therefore, performed on these high-ionic-strength systems. Measurements Using the Pressure Drop Method. Figure 2 illustrates the typical images obtained using the in situ method of generating bubbles via the pressure drop method (in this case for 0.08 wt % of 33% SiOR particles in 3 mol dm-3 NaCl). The efficiency of this method in generating stable bubbles may be noted by the fact that, (12) Deryaguin, B. V. Kolloidn. Zh. 1940, 14, 137. (13) Churaev, N. V.; Sobolev, V. D. Adv. Colloid Interface Sci. 1995, 61, 1.

Figure 2. Typical images of bubbles at the planar air-water interface obtained with the in situ method of generating bubbles involving the pressure drop method, in this case for 0.08 wt % of 33% SiOR particles in 3 mol dm-3 salt: (a) 1 h and (b) 14 h after pressure drop. Examples of two bubbles illustrating the static nature of the bubbles and the interface are surrounded by rectangular boxes.

in our earlier work,9 we were able to produce stable bubbles using even more hydrophobic silica particles (40% SiOR) using this method. Figure 2 also illustrates the presence of aggregates of particles at the air-water interface. Figure 2a shows that a range of bubble sizes was initially produced, and Figure 2b shows that some bubbles, both large and small, could be remarkably stable, continuing to exist for several hours. Other bubbles either coalesced with the planar air-water interface or slowly shrank because of disproportionation between the bubble and the interface,11,14,15a the planar interface in effect acting as a bubble of infinite radius. It was also seen, in this case, that the bubbles and interface remained relatively static, in that some stable bubbles did not appear to have moved after several hours. To obtain the subsequent results, such images, with at least 100 bubbles initially present, were analyzed to give the fraction (F) of remaining stable bubbles as a function of time (t) or to give the radii (R) of a representative selection of individual bubbles measured as a function of time. Only individual bubbles that were well separated from neighboring bubbles were included in this analysis, to avoid the complications of bubble-to(14) Ettelaie, R.; Dickinson, E.; Du, Z.; Murray, B. S. J. Colloid Interface Sci. 2003, 263, 47. (15) (a) Murray, B. S.; Dickinson, E.; Du, Z.; Ettelaie, R.; Maisonneuve, K.; So¨derberg, I. In Food Colloids, Biopolymers and Materials; Dickinson, E., van Vliet, T., Eds.; Royal Society of Chemistry: Cambridge, 2003. (b) Fryillas, M. M.; Kloek, W.; van Vliet, T.; Mellema, J. Langmuir 2000, 16, 1014.

8520

Langmuir, Vol. 20, No. 20, 2004

Dickinson et al.

Figure 5. Plots of bubble radius (R) versus time (t) in a densely covered particle region at the planar interface, with 0.08 wt % of 33% SiOR particles + 3 mol dm-3 NaCl. The different symbols are for three representative bubbles of different starting bubble size. Shown for comparison as dashed lines are examples of the most stable protein-stabilized bubbles from earlier work.11

Figure 3. Typical image of the planar air-water interface obtained with the in situ method of generating bubbles via the pressure drop method for 0.08 wt % of 33% SiOR particles in 3 mol dm-3 NaCl, illustrating regions of high (A) and low (B) densities of particles + bubbles.

Figure 4. Effect of extent of particle aggregation on stability for 33% SiOR particles + 3 mol dm-3 NaCl. Fraction of stable bubbles (F) versus time (t) in regions of high (b) and low (O) particle density at the same interface.

bubble disproportionation.11,14,15a On a theoretical basis, this minimum separation was chosen as at at least twice the mean bubble diameter of a pair of bubbles. Figure 3 illustrates another aspect of the relationship between bubble stability and particle aggregation, in this case for bubbles formed in 0.08 wt % of 33% SiOR particles by the pressure drop method. The density of the particle film at the planar interface was often nonuniform, with some regions that appeared to be fairly uniformly covered with particles, while other areas were relatively sparsely covered. It was generally noticeable that those areas that contained more particles also contained more bubbles and that bubbles in the more densely particle-covered regions were also more stable, as illustrated in Figure 4. As a result of the rather violent nature of the initial bubble nucleation process, when the pressure was suddenly lowered, it was possible to obtain clear images beginning only a few seconds or so after the pressure had restabilized at 1 atm. This time is the “zero” time in the plots of F and R versus t. However, on carefully checking the video recordings of some experiments, other types of behavior were occasionally observed. Sometimes hardly any bubbles were formed at all, and occasionally the bubbles seemed to be formed on the bottom window of the cell. Also, occasionally a large, coherent raft of particles, containing some bubbles, appeared to rise up to the planar interface from somewhere within the cell. Presumably, therefore, aggregates of particles were also present on the bottom of the cell and perhaps on its walls, within which bubbles were subsequently nucleated or entrapped. Hence, it is unproven whether the particle + bubble regions observable at the planar interface were formed

there or whether they were formed elsewhere in the system and subsequently rose to the surface. Figure 5 indicates the stability of individual bubbles in a densely covered particle region at the planar interface. The data are representative of the behavior of the three different starting bubble sizes. For comparison, the stability toward disproportionation (i.e., bubble shrinkage) of some protein-stabilized bubbles of the same initial starting size is shown, the data being taken from our earlier work.11 The protein is β-lactoglobulin, at a bulk protein concentration of 0.05 wt % at pH 7 and 0.1 mol dm-3 ionic strength. These conditions were found to produce some of the most stable protein-stabilized bubbles,11 but it can be seen that these bubbles were still far less stable than the particle-stabilized bubbles investigated here. In some instances a slight growth in the radius (R) of particle-stabilized bubbles was detected at early times (see Figure 5). This was possibly due to the presence of smaller bubbles beneath the larger bubble or present in the adjacent particle layer (and, hence, not so visible), “feeding” the larger bubble via disproportionation. Another characteristic feature, illustrated by the examples shown in Figure 5, is the tendency for bubbles below a certain size to shrink, while those above a particular size hardly shrink at all. The critical size range above which shrinkage was much slower or insignificant was in the range 60-80 µm. The tendency for particlestabilized bubbles to shrink slightly and then stabilize was noted earlier.9 Our explanation put forward is that a certain amount of shrinkage is required before a bubble becomes completely surrounded by a solid shell of particles. This explains why fewer stable bubbles are formed in regions of low particle density, because locally there are not enough particles to form a stabilizing shell. Note that the adsorbed particle layer around a bubble may allow easy expansion of the bubble (e.g., by absorption of gas from surrounding bubbles) but not contraction, due to strong resistance to compaction of the network of particles on the bubble on compression but not on expansion. However, it is still not clear from these experiments whether the bubbles are nucleated within the adsorbed particle layer at the planar interface or, alternatively, if nucleation takes place within the aqueous phase or at the walls of the cell, and then the bubbles rise up beneath the adsorbed particle layer. The different histories of formation of adsorbed particle layers around the bubbles might be expected to affect their stability. Because smaller bubbles are inherently more unstable to disproportionation due to their higher Laplace pressure, they shrink faster, and this may mean that there is less time for them to collect sufficient particles in the bulk aqueous phase to form a rigid shell. Hence, a critical minimum stable size can be envisaged, whose value is

Formation and Stability of Air Bubbles

Langmuir, Vol. 20, No. 20, 2004 8521

dependent upon the relative rates of bubble shrinkage, particle aggregation, and transport of particles (and aggregates) to the bubble surface. Theoretical Description of the Kinetics of Bubble Stabilization by Particles. It is constructive to consider a newly formed bubble, with a given initial size, and ask how far such a bubble will shrink, due to diffusion of gas out of the bubble and into the bulk aqueous phase, before a sufficient level of bubble surface coverage by particles is achieved, preventing further dissolution. It must be stressed that, in reality, following the nucleation of bubbles in the solution, the main mechanism of short-time instability is bubble coalescence. Therefore, the analysis below refers to experiments under rather idealized conditions of a very low concentration of bubbles, distributed evenly throughout a large volume of dispersing fluid. The driving force for diffusion of gas from the bubbles to the aqueous phase, that is, disproportionation, is the Laplace pressure, the bulk aqueous phase in this case acting as an infinite sink with a constant overall concentration of dissolved gas. A freshly formed bubble, under the above conditions, is known to shrink according to the equation11

R3(t) ) R03 - (t/τ)

(1)

where R0 and R(t) are the initial radius of the bubble and that after a time t. The constant τ in eq 1 has dimensions of s m-3 and is related to the ambient temperature and pressure, T and P0, the gas diffusion coefficient in the fluid, Dg, the gas-water interfacial tension, γ, and Henry’s solubility constant, S, for the gas comprising the bubble. It is given by11

τ)

P0 6γSDgRgT

(2)

The constant Rg in eq 2 is the ideal gas constant. Provided the rate of shrinkage is not too fast, the diffusion rate of particles onto the surface of bubbles can be considered as a quasi-stationary flux of particles, given by

Q ) 4πDpnpR(t)

(3)

at any given time t. Notice that, as the surface area of the bubble shrinks, the flux, Q, also decreases. In eq 3, np represents the concentration of individual stabilizing particles or aggregates of such particles, if these are not dispersed down to the primary size. Similarly, Dp is the diffusion coefficient of the particles (or aggregates). Because no particle, once adsorbed, is assumed to leave the gas-water interface, it is clear that with time the coverage of the surface of a bubble increases, partly because of bubble shrinkage and partly because it gathers more particles. Combining these two effects, then, the fractional surface coverage of particles on the bubble, λ, varies in such a way as to satisfy the equation below:

[

]

d[4πR2(t)] λ πr2 dλ ) 4πDpnpR(t) dt dt 4πR2(t) 4πR2(t) )

πDpnpr2 R(t)

-

λ dR(t) R(t) dt

(4)

In deriving eq 4, we have made use of eq 3 and also assumed that each particle (or aggregate of particles) occupies an area of πr2, where r is the radius of the particle/aggregate on the surface of the bubble. This last assumption amounts

Figure 6. Theoretical ratio (Rf/R0) of radius of the final stable bubble to that of initial bubble radius (R0), assuming adsorbing particle aggregates of radius 100 nm and a critical area packing fraction of 0.5 for stability. Other solution parameters are defined in the text. The inset gives the actual final radius (Rf) versus R0 for the same conditions.

to taking the particle-solution contact angle to be 90°, but the analysis could easily be generalized to other angles. Substituting eq 1 into the above expression, we arrive at the following differential equation for λ:

dλ 2λ 3 t R dt 3τ 0 τ

(

)

-1

(

) πDpnpr2 R03 -

t τ

)

-1/3

(5)

Equation 5 is straightforward to solve and, combined with the initial condition λ(t ) 0) ) 0, yields the following time dependence for λ:

λ(t) )

{

}

4/3 4 3 1 R0 - [R0 - (t/τ)] Rc2 [R03 - (t/τ)]2/3

(6)

where we have defined Rc ) (3πτDpnpr2/4)-1/2, having dimensions of length. This is the critical radius at which a bubble ceases to shrink further, because a sufficiently closely packed layer of particles, defined by the surface coverage λ*, is formed on its surface. From eq 6, this occurs when R4 + λ*Rc2R2 + R04 ) 0; this leads to a final radius for the bubble given by

R)

[(λ*2Rc4 + 4R04)1/2 - λ*Rc2]1/2 2

(7)

It is noticed that when λ*Rc2 . R02 then the radius of the bubble changes little from its initial value and we have R ≈ R0. On the other hand, if λ*Rc2 , R02, the final radius varies as the square of the initial radius R ≈ (2/λ*)(R02/Rc) and decreases rapidly as the initial size of the bubble becomes smaller. Therefore, in practice, one would expect that a bubble with an initial radius R0 much smaller than Rc would be rather hard to stabilize against disproportionation via the particle adsorption mechanism. Such bubbles shrink too quickly to allow adequate particle surface coverage to be established. A graph of the ratio of the final to the initial radius, plotted against the latter, is shown in Figure 6. These values were calculated for adsorbing particle aggregates of r ) 100 nm, npDp ) kT/(6πηr) ) 2.2 × 10-12 m2 s-1. The gas solubility S, the gas diffusion coefficient in water, and the pressure P0 are taken as 6.9 × 10-6 mol m-1 N-1, 1.99 × 10-9 m2 s-1, and 1 × 105 Pa, respectively, following the values used in our previous work.11 We arbitrarily assume that the critical surface coverage required to stop further shrinkage of the bubble is λ* ) 0.5. The actual value of λ* for any particular system is quite uncertain, being no doubt sensitive to such factors as the shape of the aggregates, their polydispersity, and the nature of the interactions between aggregates. Although the assumed value of λ* influences the predicted value of Rc, it does not

8522

Langmuir, Vol. 20, No. 20, 2004

Dickinson et al.

Figure 7. Effect of NaCl concentration on the fraction (F) of stable bubbles as a function of time (t) with 33% SiOR particles: 3 mol dm-3 (b), 2 mol dm-3 (O), 1.8 mol dm-3 (2), and 1 mol dm-3 (4).

Figure 8. Comparison of the effect of particle hydrophobicity on the fraction (F) of stable bubbles as function of time (t) for 0.08 wt % dispersions of 33% SiOR (b) and 20% SiOR (O) in 3 mol dm-3 NaCl.

Figure 10. Typical image of bubbles formed with 1 wt % of 33% SiOR particles after 10 min sonication and the pressure drop method.

Figure 9. Comparison of the effect of particle concentration on the fraction (F) of stable bubbles as function of time (t) for 33% SiOR particles in 3 mol dm-3 NaCl, after 10 min sonication: 1 wt % particles (b) and 0.08 wt % (O) particles.

Figure 11. Bubble radius (R) versus time (t) of bubbles formed with 33% SiOR particles in 3 mol dm-3 NaCl after 10 min sonication and the pressure drop method for 1 wt % (2, b) and 0.08 wt % (O) particles. For comparison, examples of the most stable protein-stabilized bubbles from earlier work11 are shown (dashed lines).

alter the qualitative conclusions. As Figure 6 shows, rapid shrinkage of small bubbles, coupled with a relatively slow diffusion of aggregated particles to the bubble interface, sets a lower limit to the bubble size at which stabilization by particles is feasible. Of course, all the above assumes diffusive mass transport of bubbles, particles, and gas molecules. Stirring, convection, sonication, and so forth would change the kinetics. Effects of Salt Concentration. The clear effect of increasing bubble stability with increasing salt concentration above 1 mol dm-3 NaCl is shown in Figure 7, for the case of a dispersion of 0.08 wt % of 33% SiOR particles. A similar effect is seen for a 0.08 wt % dispersion of 20% SiOR particles, though overall the bubbles were less stable with the 20% SiOR particles, as measured by the rate of decrease of F(t). This is made more clear in Figure 8, where F(t) is plotted for 0.08 wt % dispersions of both 20% SiOR and 33% SiOR particles at the same salt concentration (3 mol dm-3). Effects of Particle Concentration and Sonication Time. Figure 9 illustrates the substantial increase in bubble stability on increasing the particle concentration from 0.08 to 1 wt %, in this case for the 33% SiOR particles in 3 mol dm-3 NaCl. Even more striking was the appearance of the bubbles, as shown in Figure 10. The bubbles formed at 1 wt % particle concentration seem to be smaller and much more uniform in size, with some bubbles at the planar interface (in focus) and some below the interface (out of focus). In fact, on focusing up and

down through the cell, the bubbles seemed to be uniformly distributed throughout the whole system. The image of the bubbles shown in Figure 10 is not very clear because the underlying bubbles scatter much of the illuminating light. It would appear, then, that a silica particle gel had formed under these conditions, with the bubbles being formed throughout this gel. The gel network was apparently strong enough to prevent the upward movement of most of the bubbles, because very few new bubbles appeared at the planar interface once the pressure had stabilized. Although the bubbles formed at the interface at the lower particle concentration (0.08 wt %) were static, clearly any bubbles that formed within the bulk phase were only static in the sense that they appeared to be formed within fairly rigid particle aggregates. The fact that these aggregates, or “rafts”, could sometimes move up to the surface, as stated above, indicates that a true spanning network, or gel of particles, was not formed at 0.08 wt % silica. It is quite possible, however, that the dense layer of particles that always forms at the planar interface is also in some sort of “two-dimensional” gel state. Figure 11 emphasizes the enhanced stability of these bubbles compared to those formed at the lower concentration of particles or with a good protein foam stabilizer. The data are representative of the behavior of the three different starting bubble sizes. Finally, Figure 12 shows the effect of increasing the sonication time from 10 to 60 min for 33% SiOR particles in 3 mol dm-3 NaCl. The longer

Formation and Stability of Air Bubbles

Figure 12. Effect of sonication time on the fraction (F) of stable bubbles as a function of time (t) for 33% SiOR particles in 3 mol dm-3 NaCl: 1 wt % particles, 60 min sonication time (b); 1 wt % particles, 10 min sonication time (O); 0.08 wt % particles, 60 min sonication time (2); and 0.08 wt % particles, 10 min sonication time (4).

sonication time gave a higher bubble stability, most notably for the 0.08 wt % dispersion. In addition, there was virtually no movement of individual bubbles or particle rafts with associated bubbles, as was sometimes observed with 0.08 wt % particles after lower sonication times. Bulk Rheology. A question that arises is whether the formation of a particle gel network is a prerequisite for the formation of a stable dispersion of bubbles. Fyrillas et al.15b have clearly shown from a theoretical point of view that, if the storage modulus of such a gel is high enough, this alone could inhibit diffusional disproportionation. The retardation of bubble movement by the particle network may provide greater time for the bubbles to become covered with primary particles (or their aggregates) via diffusion and so aid stability. It is well-known that, when fumed silica is dispersed in liquids, adjacent aggregates can interact with each other via silanol-silanol hydrogen bonding, giving rise to large flocs.16 Flocculated structures (at high silica concentrations) can form a three-dimensional network throughout the volume of the suspension: this type of network is sometimes referred to as a “physical gel”.17,18 The creation of this network increases the viscosity of the liquid at small deformations, that is, the liquid becomes thixotropic. By applying a shearing force to it, the network is easily destroyed, resulting in a drop in viscosity, but once the force is removed the network is rapidly reformed and the viscosity increases again.18 On the other hand, it is still an open question whether such a particle network is continuous with the adsorbed particle layer. In the latter case, the rigidity of the threedimensional particle network as a whole may be the factor that imparts bubble stability, rather than simply the rigidity of the quasi-two-dimensional particle layer around the bubble. For these reasons it was considered important to try to establish whether the low volume fraction of silica particles used under the conditions of the bubble experiments was capable of forming a network that possessed a high enough yield stress to prevent bubble movement due to buoyancy. Figure 13 shows a plot of creep compliance versus time at different constant shear stresses for a dispersion of 1 wt % dispersion of 33% SiOR particles in 3 mol dm-3 NaCl (previously sonicated for 1 h). The dispersion was formed under the same conditions as for the bubble experiments but in the absence of incorporated air bubbles. The compliance curve for 0.13 Pa is slightly above that for 0.15 and 0.18 Pa, but this is probably due to experimental error at these quite low stresses. The key (16) Yan, N. X.; Gray, M. R.; Masliyah, J. H. Colloids Surf., A 2001, 193, 97. (17) Einslauer, J.; Killmann, E. J. Colloid Interface Sci. 1979, 74, 108. (18) Addona, T.; Munz, R. J. Can. J. Chem. Eng. 1994, 72, 476.

Langmuir, Vol. 20, No. 20, 2004 8523

Figure 13. Creep compliance (J) versus time (t) for a 1 wt % dispersion of 33% SiOR particles in 3 mol dm-3 NaCl (previously sonicated for 1 h) at different constant shear stresses: 0.13 (b); 0.15 (O); 0.18 (2); and 0.20 Pa (4).

difference is the big change at 0.20 Pa, indicating yielding of the structure. Clearly, on the basis of the data in Figure 13, a self-supporting network of particles can be formed, having a low but finite yield stress in the region of 0.180.20 Pa. Measurements were also made (results not shown) on dispersions of a lower concentration of the same particles (0.6 wt %). The yield stress seemed to be lower (≈0.05 Pa), but the results were not so reproducible. It should noted that the presence of bubbles could contribute to the magnitude of the yield stress, with small bubbles acting as active filler particles. CLSM. To gain further understanding of the nature of the bubble-particle network and of the adsorbed particle layers around the bubbles, CLSM was performed on a selection of systems aerated via the pressure drop method. While it was difficult to transfer samples from the bubble cell to the CLSM well slides without destroying most of the bubbles, a sufficient number of bubbles remained to obtain acceptable representative images. Figure 14 shows typical examples of pictures obtained for systems consisting of 1 wt % of 33% SiOR particles in 3 mol dm-3 NaCl (previously sonicated for 1 h). The maximum resolution of the CLSM is at least 1 order magnitude less than the supposed primary silica particle size (20 nm), so that any particulate entities observed must be particle aggregates. Some bubbles appear to be surrounded by a thinner layer of particles than others. In fact, some bubbles, at first sight, do not seem to have any aggregates attached at all, whereas others clearly have very large aggregates of primary particles attached, these aggregates often apparently extending outward, presumably to the silica particle network in the bulk. A principal advantage of CLSM over conventional microscopy is the ability to scan, or section, a turbid sample at different heights. When this was done for each bubble observed, it was found that there was always an optical section (i.e., circumference of a bubble) at which part of the particle network seemed to be attached to the bubble surface. Figure 15 gives an example of this. Thus, it appears likely that the adsorbed particle layers on all the bubbles were contiguous with the silica particle network in the bulk aqueous phase. In Table 2 we have summarized the results of the bubble stability characteristics with different particle types and conditions. The particles are clearly not very efficient at forming foams, or alternatively, they are too hydrophobic to provide adequate stability to coalescence. One limitation of our interpretation is the lack of knowledge of the contact angle of these very small particles. Unfortunately, there does not appear to be a reliable method of measuring the contact angle on 20-nm particles. However, it is extremely unlikely that any stable air bubbles would be formed at all if the contact angle on the 20% SiOR and 33% SiOR particles was >90°, at least in the absence of salt. Binks et al.5a-e have clearly shown for oil-water systems that there is an extremely strong tendency for emulsion

8524

Langmuir, Vol. 20, No. 20, 2004

Dickinson et al.

Figure 15. CLSM images of two bubbles stabilized by 1 wt % dispersion of 33% SiOR particles in 3 mol dm-3 NaCl. (a) The bubbles still appear to be surrounded by a thin layer of silica particles but are separate from the surrounding silica particle network. Size bar ) 80 µm. However, part (b) shows the same two bubbles at an optical section 38 µm below image (a). (b) The outline of the bubbles is no longer in focus and the bubbles appear as dark circles, but they appear connected to the surrounding network of silica particles. Size bar ) 80 µm. Table 2. Summary of Bubble Stability Characteristics with Different Particle Types and Conditionsa

Figure 14. Examples of CLSM pictures obtained in a system of 1 wt % of 33% SiOR particles in 3 mol dm-3 NaCl (previously sonicated for 1 h). (a) A particle stabilized bubble with at least one large particle aggregate attached to its surface. The bubble has a bright outline, presumably due to a thin layer of adsorbed particles, against the darker background of the aqueous solution. Size bar ) 40 µm. (b) The same bubble as in part (a), but at a higher magnification. Size bar ) 16 µm. (c) Appearance of a network of silica particles in the aqueous phase. Size bar ) 40 µm.

bubble stability

ease of bubble formation

particle type, % SiOR

particle concentration, wt %

with