Long-term stability of surface nanobubbles in under-saturated

Subscriber access provided by YORK UNIV

Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers

Long-term stability of surface nanobubbles in under-saturated aqueous solution Jing Qian, Vincent S. J. Craig, and Marie Jehannin Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b03487 • Publication Date (Web): 18 Dec 2018 Downloaded from http://pubs.acs.org on December 22, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Long-term stability of surface nanobubbles in under-saturated aqueous solution Jing Qian1, Vincent S. J. Craig1¶, Marie Jehannin1. 1Department

of Applied Mathematics, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 2601, Australia ¶ Corresponding author: [email protected]

Abstract Surface nanobubbles should not be stable for more than a few milliseconds, however they have been shown to persist for days. Pinning of the three-phase contact line of surface nanobubbles has been proposed to explain the discrepancy between the theoretical and experimental results. According to this model, two factors stabilize surface nanobubbles, namely solution over-saturation and surface pinning. Hereby, we investigate experimentally the impact of the solution saturation on the stability of nanobubbles. For this purpose, surface nanobubbles have been nucleated on hydrophobic surfaces, by two methods, and then characterized by Atomic Force Microscopy (AFM). Thereafter, the surrounding liquid has been exchanged multiple times with partially degassed water. Two degassing techniques are presented. Both sets of experiments lead to the conclusion that surface nanobubbles are stable in under-saturated conditions for hours. We compare the measured lifetime of nanobubbles to calculations for pinned nanobubbles in under-saturated conditions. The stability of surface nanobubbles in undersaturated solutions observed here is incommensurate with the pinning mechanism as the origin of the long-term stability of surface nanobubbles.

ACS Paragon Plus Environment

1

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 32

Introduction Surface nanobubbles are gas filled, nano-sized (base radius 10 mins before the DMSO was exchanged with fresh ultra-pure water. The system was left to equilibrate for at least 15 minutes before beginning the AFM measurements in water. AFM imaging and measurement of interaction forces AFM measurements were conducted using a Multimode 8 Nanoscope (Bruker, United States) employing a glass liquid cell sealed with a 10 mm inner diameter silicon O-ring that had been stored in a fresh aliquot of ethanol before and between experiments. Storing the O-ring in ethanol minimizes the opportunity for contamination from the O-ring. To avoid any contamination26, the liquid inside the cell was exchanged using a freshly cleaned 10 mL glass syringe connected to the liquid cell with Teflon tubing. Silicon probes (CSG10, NTMDT, Russia), with a gold coating on the back were used for imaging and performing force measurements (k~ 0.25 N/m, f0 ~ 7 KHz in water). Shortly before being mounted in the liquid cell, the cantilever was plasma cleaned, in the presence of water vapor, for 30s at 30W. All the images were recorded in Tapping Mode (TM-AFM). In tapping mode an important parameter5, 27

𝐴

is the set point ratio 𝑟 = 𝐴0, where A is the imaging amplitude and 𝐴0 is the free amplitude of

the cantilever. The set point ratio, r, was set to 0.86±0.03 and 0.83±0.02 for the first and second set of experiments respectively. The exact values of the amplitude set-point ratios can be found in the Supplementary Material (Tables S2 and S3). The force-distance curves measured on both the solid surface and nanobubbles were obtained using force volume mode scanning. The deflection versus piezo z-position at each location was measured over an area of 2×2 µm using a square grid with points separated by 31 nm and a zramp size of 400 nm.


8

Page 9 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Hydrophobic substrate characterisation The average advancing and receding contact angles of water on three surfaces were determined using a CAM 200 contact angle goniometer (KSV, Germany). Atomic Force Microscopy images were obtained in air using ScanAsyst mode over an area of 10×10 µm in order to determine the root mean square (RMS) roughness using the NanoScope Analysis 1.5 software. Properties of Surface Nanobubbles Nanobubble profiles were obtained using the “section” tool in the NanoScope Analysis 1.5 software. The sections were chosen parallel to the fast-scanning direction of the AFM image across the apex of the nanobubble. An in-house Matlab program was then used to fit the profiles with a circle, from which the nanobubble radius of curvature, R and the contact angle θ, (measured through the denser phase28) were determined. The error-bars on R and θ were determined by choosing 5 different baselines for the profile fitting. As a result, these error-bars do not take into account other uncertainties such as the interaction between the AFM tip and the bubble29.

Results and Discussion A hydrophobised surface was used as the substrate for surface nanobubble formation. The surface exhibits advancing and receding contact angles with water of θa=92.8±1.3° and θr=83.8±2.2° respectively. An AFM image of the surface in air after silanization is shown in the supporting information (figure S1). The RMS surface roughness of the treated wafer is similar to the underlying surface at 0.26±0.1 nm.

Nanobubbles produced by the CWHS method


9

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 32

An AFM image of the surface nanobubbles nucleated in water oversaturated with air, by the CWHS method23, is shown in figure 2 (Sol. 0). The surrounding media was then exchanged for degassed water with successive saturation ratios of 0.83 (Figure 2, Sol. 1), 0.66 (Figure 2, Sol. 2), 0.48 (Figure 2, Sol.3), 0.22 (Figure 2, Sol. 4) and 0.94 (Figure 2, Sol.5). The details of the solutions are shown in Table 1. The second column indicates the time from the first nanobubble image at which the AFM images were recorded in each solution. The dissolved oxygen concentration was measured using an oxygen meter whereas the corresponding dissolved nitrogen concentration was calculated assuming a constant ratio of nitrogen to oxygen in solution. The dissolved gas concentration after bubble nucleation (Sol. 0), is not known as it cannot be measured in the liquid cell. However, the liquid was assumed to be oversaturated, as this is regarded as a necessary condition for the nucleation of nanobubbles. Table 1: Saturation ratio and gas composition of solutions in which nanobubbles produced by the CWHS method were imaged. Time (min) [O2] (mg/L) [N2] (mg/L) fa Sol. 0 0 over-sat. over-sat. >1 (min) Sol. 1 80 6.9 12.0 0.83 Sol. 2 140 5.5 9.5 0.66 Sol. 3 200 4.0 6.9 0.48 Sol. 4 280 1.8 3.1 0.22 b Sol. 5 360 7.9 13.6 0.94 aThe solution saturation ratio, f, is calculated with reference to the saturation values at 25°C 30; [O ] (mg/L)=8.3 and [N ] (mg/L)=14.6 2 2 bSolution

5 is purified water as received


10

Page 11 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 2: AFM height images of nanobubbles on a silanized silicon surface at different saturation ratios, f. The nanobubbles were nucleated using the cold water/hot surface (CWHS) method. First water at 4°C was introduced into the liquid cell and left to equilibrate at room temperature before imaging (Sol. 0). The water was then exchanged with partially degassed water prepared using the vacuum technique and the surface re-imaged (Sol. 1). The exchange was repeated several times, each time with a solution with a decreasing content of dissolved gas (Sol. 2, 3 & 4). Finally, a nearly saturated solution was introduced and the nanobubbles imaged (Sol. 5.) The circles and letters A, B and C mark the bubbles from which the profiles presented in figure 3 were obtained. Scale bar: 1 µm.

As shown in the AFM height images obtained in partially degassed water (see Figure 2, Sol. 1-4), the nanobubbles remained for hours after the over-saturated water was displaced with partially degassed water. In this set of experiments, the gas concentration was stepwise lowered to 22% saturation (Figure 2, Sol. 4). Ultra-pure water was used for the final exchange of solvent leading to an increase of the dissolved gas concentration in the surrounding liquid (Figure 2, Sol. 5).

Profiles of nanobubbles A, B and C in the different solutions can be found in figure 3, with the corresponding radius of curvature, R, and contact angle, θ, determined from the fitted circular profile. Initially the radius of curvature is around 100 nm and the contact angles are ~150° and


11

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 32

these values are consistent across the solutions with decreasing gas content. This trend is not impacted by the increase in the dissolved gas content during the last solvent exchange. The evolution of the profiles is very similar for the three bubbles investigated, which were chosen randomly. Visually, from the bubble profiles, the height, h, and radius of contact area, a, of the bubbles appears to increase between exchanges, however the shape of the profile can be influenced by small changes in the imaging conditions. This will influence each nanobubble in the same manner and therefore we attribute the similarity in the changes in the profiles to variations in the imaging conditions. There is no evidence that the size or shape of the nanobubbles imaged is controlled by the gas saturation.


12

Page 13 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 3: Top left: Radius of curvature (continuous lines) and contact angle (dashed line) determined from section profiles of bubbles A (dark), B (blue) and C (red) (from figure 2) in water with different gas saturations. The error bars correspond to the uncertainty in selecting the position of the base of the nanobubble (ie the location of the substrate). Bottom left: Symbol legend for the nanobubble profiles and the corresponding saturation ratio, f, in brackets. Right: Profiles of nanobubbles A, B and C (as indicated in figure 2) in solutions of varying f. The symbols are the experimental data points whereas the continuous lines are the corresponding spherical cap fits.

Nanobubbles produced by the DWE method Nanobubbles were also produced on the silanized silicon substrates by DMSO/water exchange (DWE). Typical AFM images of the silicon wafer in DMSO and in H2O, after the DMSO has been exchanged with water, are shown in figure 4. We found this method to be more reliable for producing nanobubbles than the widely used ethanol/water exchange process23, or the CWHS method23 presented above.

Figure 4: Top row: AFM height image of hydrophobized silica surfaces in DMSO (Panel a) and the same surface after DMSO has been exchanged for water (panel b). Surface nanobubbles are evident after DMSO/water exchange. Scale bars are 200 nm. The cross sectional profiles, fitted with sections of a circle for nanobubbles numbered 1 and 2, are also shown. The deviation from a circle is


13

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 32

attributed to an imaging artefact associated with deformation of the nanobubble and imperfect feedback which causes overshoot at the apex– the fast scan direction is from left to right.

Contamination is known to be an issue when studying surface nanobubbles. Previously, droplets of PMDS contaminant have been mistaken for nanobubbles22,

26, 31-33.

To check

whether the nucleated objects observed here are nanobubbles, force curve measurements were performed as per the method proposed by An et al.34 to distinguish surface nanobubbles from PDMS contaminants. The vertical deflection of the cantilever, as it approaches and retracts from the sample, is shown in figure 5 for measurements performed directly on the substrate (top row) and on a nucleated object (bottom row). On the substrate, no deflection is measured until the cantilever is in contact with the surface (Z-piezo displacement=30 nm). On the nanobubble, an attractive force is measured when the tip comes into contact with the object (Zpiezo displacement=42 nm), the following linear repulsion of the cantilever, as a function of the piezo Z-displacement, during the cantilever approach and retraction is typical for nanobubbles34. When the cantilever makes contact with the substrate (Z-piezo displacement=27 nm) the cantilever and surface move in concert, this is known as the compliance region. Thus, from this result, it can be concluded that the object is indeed a nanobubble. The nanobubble height is the distance between the first tip-object contact and the intercept between the compliance region and the baseline, which in this case corresponds to ~22 nm.


14

Page 15 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 5: Force measurements performed at different locations on the substrate. The red lines are the cantilever deflection measured during surface approach and the black lines correspond to the retraction of the cantilever from the surface. Top row: Deflection measured on the silica surface as a function of the Z-piezo displacement. Bottom row: Deflection measured on a nanobubble. The linear evolution of the retraction and extension curves, between 26 and 50 nm of piezo displacement, is typical of nanobubbles (See 34).

Once the nanobubbles had been nucleated and the force curves recorded, we studied the stability of the nanobubbles in under-saturated conditions. Several liters of water were degassed using the membrane contactor (Sol. Z). Its oxygen and nitrogen content was measured. Solutions X and Y were prepared by mixing Solution Z with ultra-pure water to obtain solutions with a higher concentration of dissolved gas than solution Z. The oxygen concentration in each solution was measured immediately before use. The dissolved nitrogen concentrations in solutions X and Y were calculated using mass conservation and are presented in the supporting information (Table S1). The solution in the AFM fluid cell was exchanged by slowly passing 5 mls of the relevant solution through the fluid cell, which has a volume of 0.2 mls. The surface


15

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 32

was imaged by AFM after each exchange (Figure 6). The time interval between the exchange of the solvent and imaging is reported in figure 6.

Figure 6: AFM images of surface nanobubbles in saturated water immediately after nanobubble nucleation (panel a), in partially degassed water with a saturation ratio of 0.63 (panel b), saturation ratio of 0.40 (panel c) and saturation ratio of 0.19 (panel d). The stability was investigated by leaving the nanobubble in degassed water (f=0.19) for 16 hours (panel e). Scale Bar: 200 nm. The graph indicates the evolution of the saturation ratio in the liquid cell over time. The red diamonds correspond to the time at which the AFM images presented in the different panels have been recorded.

The AFM height images reveal that nanobubbles are stable in under-saturated conditions, even after immersion for many hours in 19% degassed water (Figure 6e). Unfortunately, the imaging position varied between AFM images due to displacements during fluid exchange. The sample position was unchanged between samples f=0.63 and f=0.40, in these images the position of a specific nanobubble is indicated by a blue square (Figure 6b and 6c). For each solution, the radius of curvature and contact angles measured from the AFM image are shown in figure 7.


16

Page 17 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 7: The average radius of curvature (blue solid line) and contact angle (orange dashed line) of nanobubbles in the different degassed solutions obtained from the nanoubbles shown in Figures 6a-6e. The x-axis indicates the AFM images used for the measurement. The height and contact angle were obtained by fitting a circle to the cross-section of each and every nanobubble in each frame. The cross-sections were taken parallel to the fast scanning direction of the AFM image.

The initial radius of curvature and contact angle of the nanobubbles produced using DWE are around 50 nm and 145° respectively. The radius of curvatures are smaller than those obtained in the first set of experiments and usually found in the literature23, 35, 36. The values of the radius of curvature and contact angle are stable and independent of the gas saturation level.

The formation of nanobubbles using the CWHS method has been confirmed from the deflection versus separation curves as per An et al.23. However, the success rate of nanobubble nucleation using this method was low on the silanized silicon wafer and attempts to nucleate them on HOPG were unsuccessful. The low success rate in our experiments may be attributed to the use of a liquid cell. The liquid cell has the advantage of limiting exposure of the solution to air and therefore reducing the possible influence of contamination and ease of fluid exchange, however the flow conditions differ from the open dish used in the experiments of An et al. where the


17

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 32

liquid was directly deposited onto the hot surface and this may impact on the success rate for nanobubble production. Another possible reason for the low success rate here is that the fluid cell only allows a very small region of the surface to be accessible for imaging (typically less than 500 m x 500 m) where the use of an open dish allows a large surface area to be searched for presence of nanobubbles. We have presented a new method to produce surface nanobubbles by DMSO/water exchange (DWE). This is a modification of the well-known solvent exchange method, in which water is used to displace ethanol. Here DMSO is used in place of ethanol. Although the solubility of nitrogen is around 4 times lower in DMSO than in ethanol37, 38, this technique was found to nucleate nanobubbles with a higher success rate than the ethanol/water exchange procedure. The successful nucleation of nanobubbles by the DMSO/water exchange method can be explained by considering the molecular interactions in DMSO/water mixtures. Symons39 investigated the solubility of hydrogen gas as a function of the mixing entropy of DMSO/water mixtures. He showed the gas solubility was a minimum at 25°C for a DMSO molar ratio of 30 mol%. This minimum corresponds to the region for which the solution entropy is maximal. The stronger intermolecular bonds at 25-35 mol% DMSO suggests that the average bond length has decreased, leaving less room for gas molecules, and a decrease in the gas solubility. It is supposed that the solubility of oxygen and nitrogen in DMSO/water mixtures follows the same trend. For water/ethanol mixtures, the non-linearity of the gas solubility as a function of the water content has previously been proposed as the origin of nanobubble nucleation by ethanol/water exchange10. For gas solubility in DMSO/water mixtures, not only is the solubility curve non-linear, but a minimum exists39, which likely contributes to the higher success rate obtained for the nucleation of nanobubbles with DMSO/water exchange compared to ethanol/water exchange. An additional effect could be the large negative mixing enthalpy of DMSO with water40,

41,


which induces an increase in

18

Page 19 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

temperature of the mixture during the exchange, an effect known to favor the formation of nanobubbles23. The nanobubbles nucleated by DWE have a size which is toward the lower range of nanobubbles nucleated by ethanol/water exchange reported in the literature1, 13. This could be due to the lower minimal (negative) mixing enthalpy of DMSO/water mixtures (-3.0 kJ/mol40) compared to ethanol/water mixtures (-0.8 kJ/mol42). This may lead to a greater areal density of nanobubbles with smaller sizes as would be expected from classical nucleation theory. Sample contamination has been a significant issue in nanobubble science43, 44. In the CWHS experiments presented here, only water is used to induce nanobubble nucleation this limits the risk of contamination. However, in the DWE experiments both water and DMSO are used. Recently, An and al.34 proposed to use AFM force spectroscopy to distinguished surface nanobubbles from contaminants. Application of this approach in the DWE experiments confirmed that the nucleated object are nanobubbles. During the approach of the AFM tip toward a nanobubble, the tip first undergoes a strong attraction force as the tip is partially engulfed in the bubble. This is characterized by a jump-in on the deflection piezo-displacement curve13, 34. In figure 5 (bottom row), such a jump-in can be observed in the approach curve at a piezo displacement (Z) of 42 nm. The further penetration of the bubble by the tip, is characterized by a linear slope in the deflection vs displacement graph, until the tip makes contact with the solid surface34 as seen here between Z=27 and 42 nm. These results are supported by publications from other groups5,

10, 45.

An et al.34 compared the force curves

obtained on nanobubbles with those performed on PDMS droplets, a contaminant commonly encountered in nanobubble science. In the case of PDMS, the tip-droplet interaction is not linear but instead a sharp jump-to-contact is observed as the tip penetrates the nanodroplet. Such jump-to-contact is absent from the force measurements obtained here (Figure 5 bottom row), which indicates that the nucleated objects are not PDMS contaminants. Previously,


19

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 32

similar measurements have also been performed using bare tips on non-polar oil droplets of lower viscosity, such as decane46 and others hydrocarbons47.

In these cases, as in the

nanobubble cases, a linear repulsion is recorded by the AFM as the tip penetrates the object, which make these two classes of force curves difficult to distinguish. However, in a few cases, a short-range attraction has been measured as the tip approaches the substrate through a nanobubble10, 45. This has not been reported for an approach to an oil nanodroplet. A shortrange attraction has been measured in the force measurements presented here (Figure 5 bottom row), which indicates that the nucleated objects are nanobubbles. This attraction is likely a Van der Waals attraction, which can be recorded through a nanobubble due to the higher Hamaker constant of the silica-air-silica system (approx. 6.5 x 10-20 J48) compared to the silica-apolar oil-silica system (0.07 x 10-20 J for dodecane48). The nanobubble dimensions obtained from AFM images are distorted13, due to the influence of tip shape and hydrophobicity29, as well as imaging artifacts that are dependent upon the imaging parameters employed such as the amplitude set-point ratio27. The result is that the nanobubble heights determined from the profiles are underestimated and the contact angles are slightly overestimated. This is clear in the DWE experiments, where the bubble height in oversaturated water, determined from the force-curve measurement (22 nm) is significantly larger than the height in the image (≈ 10 nm). This leads to an overestimation of the radius of curvature (considering no error on the lateral diameter). However, it can be assumed that the imaging artifacts between images within the same experiment are similar, as the set-point ratio only varied marginally between experiments (see Supporting Information table S2 and S3). Moreover, the tip convolution and hydrophobicity remain identical within an experiment, as the solvent viscosity and density are unchanged. This enables the height, lateral radius and radius of curvature of nanobubbles between two degassed solutions to be compared qualitatively, notwithstanding the errors in the absolute values.


20

Page 21 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Comparison of observed and theoretical lifetimes of nanobubbles When considering the dissolution of nanobubbles two distinct cases need to be considered. One in which the nanobubbles are free standing surface nanobubbles, in which case the contact angle is maintained as the bubble shrinks; and the case in which the three-phase line is pinned during dissolution. Free standing (i.e not pinned) Nanobubbles Taking into account the effect of the Laplace pressure, Epstein and Plesset expressed the evolution of the radius of curvature, 𝑅, as a function of time, 𝑡 of a dissolving bubble in a liquid at pressure 𝑝 and temperature 𝑇, as49: 𝜏

𝑑𝑅 = ― 𝜅 × 𝑑 ×

1 ― 𝑓 + 𝑅 × 𝜌(∞) 1+

2×𝜏 3 × 𝑅 × 𝜌(∞)

1

× (𝑅 +

1

) 𝑑𝑡

𝜋×𝜅×𝑡

(1)

Where, for a pure nitrogen bubble, 𝑑 = 0.014, which is the ratio of saturated gas concentration to the gas density, 𝜅 = 2.01 × 10 ―9 𝑚2𝑠 ―1 is the diffusion coefficient of the gas in the liquid50, 𝑓 is the ratio of dissolved gas over the saturation concentration, 𝜌(∞) is the gas density at pressure 𝑝 and temperature T. The coefficient 𝜏 =

2𝑀𝛾 𝐵𝑇

where, M is the gas molar mass, 𝛾 is the

liquid/gas surface tension and 𝐵 is the ideal gas constant. This demonstrates that the bubble lifetime predicted using the Epstein-Plesset theory is inconsistent with the long lifetime of experimentally observed surface nanobubbles (see Supporting Information figure S2 and S3). Pinned Nanobubbles The pinning mechanism has been proposed to account for the long-term stability of surface nanobubbles in over-saturated conditions17, 18, 51. In the case of a bubble with a pinned threephase contact line, its radius of curvature decreases and contact angle increases during bubble


21

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 32

dissolution resulting in an equilibrium being established with the oversaturated solution which would explain the long-term stability. This mechanism, named the pinning mechanism, can be valid only in oversaturated conditions, as to be stable in under-saturated conditions, the pressure inside the bubble would need to be lower than the external pressure, which is incompatible with the Laplace equation for a concave object as it infers a negative Laplace pressure. Below the Epstein-Plesset theory has been adapted to calculate the lifetime of a pinned bubble in under-saturated conditions. Under the hypothesis that the dissolution of gas molecules from the bubble is not impacted by the presence of a solid substrate and is constant everywhere on the water/bubble interface, the evolution over time of the radius of curvature for a pinned surface bubble is given by:

𝜅𝑑(1 ― 𝑓 +

𝑑𝑅 2(ℎ ― 𝑅) =― × 𝑑𝑡 ℎ 1+

(

𝜏 ) 𝑅𝜌(∞)

)

2𝜏 𝑎2(2𝑅 ― ℎ) 1+ 3𝑅𝜌(∞) 2ℎ𝑅2

×

{

}

1 1 + 𝑅 𝜋×𝜅×𝑡

(2)

The steps leading to equation (2), which is an adaptation of the Epstein-Plesset calculation for a spherical cap, can be found in the Supporting Material along with a sketch of the relevant geometrical parameters and their notations (Figure S5). Furthermore, as the three-phase line is pinned, the radius of the three-phase contact line between the bubble and the solid, a, is considered to be constant. The derivative of the spherical cap height is found using the Pythagorean relation 𝑅2 = 𝑎2 + (ℎ ― 𝑅)2 which yields to the relation between the change of the bubble height, dh, and radius of curvature, dR:


22

Page 23 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

𝑑𝑅 =

ℎ―𝑅 ℎ

(3)

𝑑ℎ

The time evolution of the height for a pinned bubble is obtained by combining equations (2) and (3):

𝑑ℎ =― 𝑑𝑡

2𝜅𝑑(1 ― 𝑓 + ― 1+

(

𝜏 ) 𝑅𝜌(∞)

)

2𝜏 𝑎2(2𝑅 ― ℎ) 1+ 3𝑅𝜌(∞) 2ℎ𝑅2

×

{

}

1 1 + 𝑅 𝜋×𝜅×𝑡

(4)

Figures 8a and 8b show the calculated radius of curvature and height versus time for a free standing bubble in solution with dissolved gas concentrations close to or equal to that surrounding a 100 nm bubble with the surface tension of water at equilibrium and in a saturated solution. The initial lateral radius of the bubble (a) is 75 nm. As predicted by the EpsteinPlesset theory, the 100 nm bubble is stable in a solution for which the gas solubility exactly matches its solubility (f=15.409). However, the nanobubble size increases or decreases dramatically as soon as the dissolved gas ratio deviates slightly from the equilibrium value (f=15.405 and f=15.504). The time evolution of a pinned bubble under the same conditions was obtained from Equations 2 and 4 (Figures 8c and 8d). For a pinned bubble, as the dissolved gas concentration slightly decreases (f=15.405) or increases (f=15.504) from the equilibrium value, the nanobubble height is stable for seconds. In over-saturated conditions, the pinned mechanism, as expressed by Equation 4, can indeed explain the longer lifespan of pinned nanobubbles compared to the free standing case (Figure 8). However, this stabilization mechanism holds only in over-saturated conditions. The pinned surface nanobubbles are still short-lived at saturation, i.e., for a solution in equilibrium with the atmosphere (f=1), as seen in figures 8c and 8d.


23

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 32

Figure 8: Calculated radius of curvature (left) and height (right) as a function of time for a free standing (top raw) and a pinned (bottom raw) bubble with an initial radius of curvature of 100 nm and lateral radius of 75 nm in saturated and over-saturated solutions. For the pinned case the x-axis is displayed using a log scale. For the free standing nanobubble the evolution of the radius of curvature was obtained from Equation 1. Equations 2 and 4 were used to calculate the evolution of the radius of curvature and the height of a pinned bubble. In both cases, the red curve (f=15.4) corresponds to a dissolved gas content in equilibrium with a 100 nm bubble. Light blue (f=15.5) and green (f=15.3) curves are small fluctuations from the equilibrium value. Note in panel c that the lines for f=15.3 and f=15.5 are indistinguishable from f= 15.4 The slight differences seen in the height of these bubbles in panel d reflects their initial change in shape that leads to a change in radius of curvature which brings the bubble into equilibrium with the surroundings. The infinity sign represents the long-term stability of the nanobubbles in equilibrium with their surroundings. The light dark curve (f=1) corresponds to a bubble in a solution for which the dissolved gas content is in equilibrium with a gas phase at 1 atm. This bubble shrinks and disappears rapidly. Bubbles at lower saturation levels will disappear even more rapidly.

Figure 9 exhibits the calculated evolution of the radius of curvature, R, and height, h, for a pinned nanobubble with an initial contact angle of θ=150°, with initial radius of curvatures of R0=100nm, 1000 nm and 2000 nm. The gas saturation levels (f) were chosen to match those used in the CWHS experiments. As expected, when the nanobubble is pinned, the radius of curvature, R, increases as the bubbles dissolve. However, the bubble height rapidly drops to zero in less than one second. Thus the calculated lifetime of a pinned nanobubble in undersaturated solution is orders of magnitude lower than the lifetime observed experimentally (Figures 2 and 6).


24

Page 25 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 9: Calculated evolution of the radius of curvature (left) and height (right) of pinned bubbles for an initial contact angle θ=150° and initial radius of curvature, R0 of 2000 nm (top), 1000 nm (middle) and 100 nm (bottom) for solutions with dissolved gas ratios, f, corresponding to the CWHS experiments (0.83 (dark blue), 0.66 (green), 0.48 (red), 0.22 (light blue) and 0.94 (purple)). In this calculation, it is considered that the bubbles consist of pure nitrogen. The initial parameters used are csat=14.6 mg/L, M=28 g/L, d=0.014 and κ=2.01×10-9 m2.s-1. The type of gas is expressed via the diffusivity coefficient which is ~10% larger for oxygen,52 therefore air or oxygen filled nanobubbles are expected to dissolve more rapidly than nitrogen filled nanobubbles (at the same saturation level).

The model proposed here for the evolution of nanobubbles during dissolution is simple and several limitations need to be considered. One of the limitations is that only a single species of gas is considered, being nitrogen, whereas the bubbles consists of a mixture of oxygen and nitrogen in an unknown ratio. However, simulations indicate that the dissolution of an oxygen bubble is slightly faster than a nitrogen bubble, because of the greater diffusivity of oxygen52. Hence with regard to the gas type, the dissolution times presented in Figure 9 are overestimated.


25

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 32

The influence of gas type on bubble lifetime is shown in the Supplementary Material (Figure S4). The hypothesis under which the rate of gas dissolution is constant along the bubble area is also a rough approximation. In the similar case of liquid evaporating from a sessile drop with a low contact angle, it is well known that the evaporation rate is faster close to the contact line53. This effect can be explained by geometrical considerations, as a larger relative volume of the continuous phase is accessible for the molecule at the edge of the drop than for the one in the center of the drop (when the contact angle measured through the phase into which the molecules are diffusing is greater than 90°). This hypothesis leads to an under-estimation of the bubble dissolution rate. We need also to consider that imaging nanobubbles with AFM leads to errors in the measurement of nanobubble height, nanobubble base radius, contact angle and radius of curvature. The bubble height determined from the bubble profile is usually underestimated5, which corresponds to an over-estimation of the radius of curvature. These effects cannot explain the discrepancy between the lifetimes of nanobubbles in our experimental observations and the pinned bubble model. Whilst pinning extends the lifetime of nanobubbles, comparison between the experimental and simulated results show that the pinning mechanism alone is not sufficient to account for the long-term stability of nanobubbles in under-saturated conditions. Some AFM images indicate that nanobubbles are pinned, as suggested by the evolution of bubble profiles, in these cases pinning could be part of the stabilization process, but it has to be accompanied by another effect to explain the observed stability. Experimental measurements have been realized to quantify the pinning forces54. This study has shown that surface nanobubbles that are mechanically moved and therefore depinned remain stable. These results are consistent with the necessity of


26

Page 27 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

another stabilizing effect to fully explain the long-term stability of nanobubbles. Recently, Tan et al.55 proposed that in under-saturated solution, the nanobubbles would be stabilised by both pinning and attractive hydrophobic forces. According to their model, surface nanobubbles are stable in under-saturated solution only on hydrophobic substrates, which is in good agreement with experimental observation. Moreover, surface nanobubbles could also be present on hydrophilic surfaces in over-saturated solutions. Surface nanobubbles are observed as swarms of bubbles, rather than in isolation. This suggests that the presence of many nanobubbles is important to their stability56, 57. Ostwald ripening has been observed between proximal surface nanobubbles suggesting that they are interacting by diffusive transport of gases. Further, the nanobubbles themselves may act as a source of gas that maintains supersaturation of the solution near the surface. In these experiments the nanobubbles remain on the surface during exchange of the solution with the fluid cell. Whilst the volume of fluid passed through the cell is many times the volume of the cell (~ 25 times), the fluid near the surface may not be exchanged during this process and thereby immediately after exchange the concentration of dissolved gas may differ between the surface region and the bulk of the liquid in the fluid cell. Therefore for nanobubbles in an initially saturated (or supersaturated) solution, even after the solution is exchanged with undersaturared water, it is possible that the surface region initially remains saturated (or supersaturated). In this case the timescale for this region to equilibrate with the bulk solution could be the important parameter for surface nanobubble dissolution. We think that this does not explain the results observed here, where the bubbles are exposed to the undersaturated solution for hours, hence as a result the surface layer should equilibrate with the bulk solution on a much shorter timescale. Further we considered the effect dissolving nanobubbles might have on the dissolved gas concentration within the fluid cell. Our calculations show that if a surface was 20% covered with nanobubbles


27

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 32

and all those nanobubbles dissolved, the effect would be to increase the saturation level of dissolved gas in the fluid cell by ~ 0.0001%. Therefore this effect can be ignored. From the experimental results presented here, once formed, air nanobubbles are only slightly sensitive to the dissolved gas concentration. This suggests that a kinetic barrier is preventing rapid transfer of gas across the interface of the nanobubble, hindering rapid dissolution. This might be attributable to significant quantities of surface contaminants but experiments suggest that this is not the case13. Further evidence for this is the observation that adjacent surface nanobubbles are not in equilibrium (as evidenced by their different radii of curvature) whilst there is evidence of gas exchange through Ostwald ripening10. We note that a recently published manuscript reports that surface nanobubbles produced by decompression were stable in undersaturated water, which is consistent with our observations reported here58.

Conclusions We have introduced a new method to produce surface nanobubbles, namely DMSO/water exchange (DWE). We found the nucleation of surface nanobubbles to be more reproducible using this method than using ethanol/water exchange or cold water on a hot substrate23. Two independent sets of experiments were carried out to investigate the stability of surface nanobubbles in undersaturated conditions. Both lead to the conclusion that nanobubbles were stable for long periods of time (hours) in undersaturated solutions, even after several consecutive solvent exchanges with partially degassed water. The results were compared to the calculated time for dissolution using a modified version of the Epstein-Plesset theory for pinned bubbles. The discrepancy between experimental and simulated results demonstrates that the pinning mechanism alone cannot explain the long-term stability of surface nanobubbles.


28

Page 29 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Acknowledgments The authors would like to acknowledge Timothy Sawkins and Ron Cruikshank, from the Australian National University, for technical support. VSJC gratefully acknowledges the financial support of the Australian Research Council through the Linkage program (LP140100594) and Tennant Company for the gift of a metering pump used with the membrane contactor.

Supporting Information AFM image of a silanized surface, saturation ratio and composition of solutions, evolution of the radius of curvature of free standing bubble, evolution of the radius of curvature and height of pinned bubbles, amplitude set-point ratios used in imaging, schematic of the evolution of a free standing and pinned nanobubble, derivation of the evolution equation for a pinned surface nanobubble

59

References 1. Lou, S.-T.; Ouyang, Z.-Q.; Zhang, Y.; Li, X.-J.; Hu, J.; Li, M.-Q.; Yang, F.-J., Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena 2000, 18, (5), 2573-2575. 2. Ishida, N.; Inoue, T.; Miyahara, M.; Higashitani, K., Langmuir 2000, 16, (16), 6377-6380. 3. Karpitschka, S.; Dietrich, E.; Seddon, J. R. T.; Zandvliet, H. J. W.; Lohse, D.; Riegler, H., Physical Review Letters 2012, 109, (6), 066102. 4. Seo, D.; German, S. R.; Mega, T. L.; Ducker, W. A., The Journal of Physical Chemistry C 2015, 119, (25), 14262-14266. 5. Zhang, X. H.; Maeda, N.; Craig, V. S., Langmuir 2006, 22, (11), 5025-5035. 6. Epstein, P. S.; Plesset, M. S., The Journal of Chemical Physics 1950, 18, (11), 1505-1509. 7. Alheshibri, M.; Qian, J.; Jehannin, M.; Craig, V. S., Langmuir 2016, 32, (43), 11086-11100. 8. Ljunggren, S.; Eriksson, J. C., Colloids and Surfaces A: Physicochemical and Engineering Aspects 1997, 129, 151-155. 9. Ducker, W. A., Langmuir 2009, 25, (16), 8907-8910. 10. An, H. J.; Liu, G. M.; Atkin, R.; Craig, V. S. J., Acs Nano 2015, 9, (7), 7596-7607. 11. Brenner, M. P.; Lohse, D., Physical Review Letters 2008, 101, (21), 214505.


29

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 32

12. Zhang, X.; Uddin, M. H.; Yang, H.; Toikka, G.; Ducker, W.; Maeda, N., Langmuir 2012, 28, (28), 10471-10477. 13. Zhang, X. H.; Maeda, N.; Craig, V. S. J., Langmuir 2006, 22, (11), 5025-5035. 14. Seddon, J. R. T.; Lohse, D.; Ducker, W. A.; Craig, V. S. J., ChemPhysChem 2012, 13, (8), 21792187. 15. Lohse, D.; Zhang, X., Reviews of Modern Physics 2015, 87, (3), 981-1035. 16. Sun, Y.; Xie, G.; Peng, Y.; Xia, W.; Sha, J., Colloids and Surfaces A: Physicochemical and Engineering Aspects 2016, 495, 176-186. 17. Lohse, D.; Zhang, X., Physical Review E 2015, 91, (3), 031003. 18. Weijs, J. H.; Lohse, D., Physical Review Letters 2013, 110, (5), 054501. 19. Svetovoy, V. B.; Dević, I.; Snoeijer, J. H.; Lohse, D., Langmuir 2016, 32, (43), 11188-11196. 20. Maheshwari, S.; van der Hoef, M.; Zhang, X.; Lohse, D., Langmuir 2016, 32, (43), 1111611122. 21. Liu, Y.; Wang, J.; Zhang, X.; Wang, W., The Journal of Chemical Physics 2014, 140, (5), 054705. 22. Berkelaar, R. P.; Dietrich, E.; Kip, G. A. M.; Kooij, E. S.; Zandvliet, H. J. W.; Lohse, D., Soft Matter 2014, 10, (27), 4947-4955. 23. An, H.; Tan, B. H.; Zeng, Q.; Ohl, C.-D., Langmuir 2016, 32, (43), 11212-11220. 24. Francis, M.; Pashley, R.; Rzechowicz, M., Desalination and Water Treatment 2011, 25, (1-3), 150-158. 25. Guan, M.; Guo, W.; Gao, L. H.; Tang, Y. Z.; Hu, J.; Dong, Y. M., Chemphyschem 2012, 13, (8), 2115-2118. 26. An, H.; Liu, G.; Craig, V. S., Advances in colloid and interface science 2015, 222, 9-17. 27. Walczyk, W.; Schönherr, H., Langmuir 2013, 29, (2), 620-632. 28. Craig, V. S. J., Soft Matter 2011, 7, (1), 40-48. 29. Walczyk, W.; Schönherr, H., Langmuir 2014, 30, (24), 7112-7126. 30. Benson, B. B.; Krause, D., Limnology and Oceanography 1984, 29, (3), 620-632. 31. Seddon, J. R. T.; Bliznyuk, O.; Kooij, E. S.; Poelsema, B.; Zandvliet, H. J. W.; Lohse, D., Langmuir 2010, 26, (12), 9640-9644. 32. Zhang, X. H.; Zhang, X.; Sun, J.; Zhang, Z.; Li, G.; Fang, H.; Xiao, X.; Zeng, X.; Hu, J., Langmuir 2007, 23, (4), 1778-1783. 33. Zhang, X.; Maeda, N., The Journal of Physical Chemistry C 2011, 115, (3), 736-743. 34. An, H.; Tan, B. H.; Ohl, C.-D., Langmuir 2016, 32, (48), 12710-12715. 35. Zhang, X. H.; Quinn, A.; Ducker, W. A., Langmuir 2008, 24, (9), 4756-4764. 36. Borkent, B. M.; de Beer, S.; Mugele, F.; Lohse, D., Langmuir 2010, 26, (1), 260-268. 37. Dymond, J. H., The Journal of Physical Chemistry 1967, 71, (6), 1829-1831. 38. Battino, R.; Rettich, T. R.; Tominaga, T., Journal of Physical and Chemical Reference Data 1984, 13, (2), 563-600. 39. Symons, E. A., Canadian Journal of Chemistry 1971, 49, (24), 3940-3947. 40. Clever, H. L.; Pigott, S. P., The Journal of Chemical Thermodynamics 1971, 3, (2), 221-225. 41. Catalán, J.; Díaz, C.; García-Blanco, F., The Journal of Organic Chemistry 2001, 66, (17), 58465852. 42. Boyne, J. A.; Williamson, A. G., Journal of Chemical & Engineering Data 1967, 12, (3), 318318. 43. An, H.; Liu, G.; Craig, V. S. J., Advances in Colloid and Interface Science 2015, 222, 9-17. 44. James, R. T. S.; Detlef, L., Journal of Physics: Condensed Matter 2011, 23, (13), 133001. 45. Wang, Y.; Wang, H.; Bi, S.; Guo, B., Scientific reports 2016, 6, 30021. 46. Zhang, X. H.; Ducker, W., Langmuir 2008, 24, (1), 110-115. 47. Connell, S. D. A.; Allen, S.; Roberts, C. J.; Davies, J.; Davies, M. C.; Tendler, S. J. B.; Williams, P. M., Langmuir 2002, 18, (5), 1719-1728. 48. Israelachvili, J. N., Elsevier: 2011.


30

Page 31 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

49. Epstein, P. S.; Plesset, M. S., J. Chem. Phys. 1950, 18, (11), 1505-1509. 50. Ferrell, R. T.; Himmelblau, D. M., Journal of chemical and engineering data 1967, 12, (1), 111-115. 51. Zhang, X. H.; Chan, D. Y. C.; Wang, D. Y.; Maeda, N., Langmuir 2013, 29, (4), 1017-1023. 52. Ferrell, R. T.; Himmelblau, D. M., Journal of Chemical and Engineering Data 1967, 12, (1), 111-+. 53. Hu, H.; Larson, R. G., The Journal of Physical Chemistry B 2002, 106, (6), 1334-1344. 54. Tan, B. H.; An, H.; Ohl, C.-D., Physical Review Letters 2017, 118, (5), 054501. 55. Tan, B. H.; An, H.; Ohl, C.-D., Physical Review Letters 2018, 120, (16), 164502. 56. Zhu, X. J.; Verzicco, R.; Zhang, X. H.; Lohse, D., Soft Matter 2018, 14, (11), 2006-2014. 57. Alheshibri, M.; Qian, J.; Jehannin, M.; Craig, V. S. J., Langmuir 2016, 32, (43), 11086-11100. 58. Fang, Z.; Wang, L.; Wang, X. Y.; Zhou, L. M.; Wang, S.; Zou, Z. L.; Tai, R. Z.; Zhang, L. J.; Hu, J., Journal of Physical Chemistry C 2018, 122, (39), 22418-22423. 59. Tan, B. H.; An, H. J.; Ohl, C. D., Physical Review Letters 2018, 120, (16).


31

Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 32

TOC graphic


32

Long-term stability of surface nanobubbles in under-saturated

Recommend Documents