Long-Term Stability of Different Kinds of Gas Nanobubbles in Deionized and Salt Water

Nanobubbles have many potential applications depending on their types. The long-term stability of different gas nanobubbles is necessary to be studied considering their applications. In the present study, five kinds of nanobubbles (N2, O2, Ar + 8%H2, air and CO2) in deionized water and a salt aqueous solution were prepared by the hydrodynamic cavitation method. The mean size and zeta potential of the nanobubbles were measured by a light scattering system, while the pH and Eh of the nanobubble suspensions were measured as a function of time. The nanobubble stability was predicted and discussed by the total potential energies between two bubbles by the extended Derjaguin–Landau–Verwey–Overbeek (DLVO) theory. The nanobubbles, except CO2, in deionized water showed a long-term stability for 60 days, while they were not stable in the 1 mM (milli mol/L) salt aqueous solution. During the 60 days, the bubble size gradually increased and decreased in deionized water. This size change was discussed by the Ostwald ripening effect coupled with the bubble interaction evaluated by the extended DLVO theory. On the other hand, CO2 nanobubbles in deionized water were not stable and disappeared after 5 days, while the CO2 nanobubbles in 1 mM of NaCl and CaCl2 aqueous solution became stable for 2 weeks. The floating and disappearing phenomena of nanobubbles were estimated and discussed by calculating the relationship between the terminal velocity of the floating bubble and bubble size.


Generation of Different Kinds of Nanobubbles
Nanobubble water was produced by a ultra-micro bubble generator (XZCP-K-1.1) (100 nm to 10 µm) provided by Xiazhichun Co. Ltd. (Kunming, China). When the generator was turned on, gas from a gas cylinder was pumped into the machine in a negative pressure, and inlet and outlet pipes were immersed in deionized water/electrolyte solutions in the 10 L glass container where there was a circulation between the inlet and outlet, as shown in Figure 1A. The machine mixed the gas and liquid, and then high-density, uniform and "milky" nanobubble water ( Figure 1B) was produced through a nozzle by the hydrodynamic cavitation method. The cloudy and milky nanobubble water gradually became clear through the process of the microbubbles rising and collapsing at the air-water interface ( Figure 1C). This process took 2 to 3 min ( Figure 1D). The machine worked for 15 min to generate high number density nanobubble water of more than 10 8 bubbles/mL (obtained from NanoSight, NS300, Malvern (Worcestershire, UK) outsourcing).
Materials 2021, 14, x FOR PEER REVIEW 3 of 21 store the nanobubble water temporarily and 50 mL plastic centrifuge tubes were used to store the nanobubble water after they were rinsed well with deionized water.

Generation of Different Kinds of Nanobubbles
Nanobubble water was produced by a ultra-micro bubble generator (XZCP-K-1.1) (100 nm to 10 μm) provided by Xiazhichun Co. Ltd. (Kunming, China). When the generator was turned on, gas from a gas cylinder was pumped into the machine in a negative pressure, and inlet and outlet pipes were immersed in deionized water/electrolyte solutions in the 10 L glass container where there was a circulation between the inlet and outlet, as shown in Figure 1A. The machine mixed the gas and liquid, and then high-density, uniform and "milky" nanobubble water ( Figure 1B) was produced through a nozzle by the hydrodynamic cavitation method. The cloudy and milky nanobubble water gradually became clear through the process of the microbubbles rising and collapsing at the airwater interface ( Figure 1C). This process took 2 to 3 min ( Figure 1D). The machine worked for 15 min to generate high number density nanobubble water of more than 10 8 bubbles/mL (obtained from NanoSight, NS300, Malvern (Worcestershire, UK) outsourcing). After the above-mentioned preparation steps, the nanobubble water had a temperature of about 313 K. It was then left to cool down to room temperature. Next, from the prepared nanobubble water, the large sizes of the bubbles, from 1 to 10 μm, were removed by centrifugal treatment in the following manner. The nanobubble water was stored in a 50 mL centrifuge tube; then, centrifugal treatment was performed in 6000 rpm, i.e., 31.4 m/s peripheral velocity, for 6 min to remove possible impurities and large bubbles. After centrifugation, the size distribution, zeta potential, Eh and pH were measured from one centrifuge tube to record the first day's data while other sealed centrifuge tubes with nanobubble water were kept at room temperature (298 K) for continuous measurements.

Characterization of Bulk Nanobubble Suspensions
The nanobubble size was measured by the dynamic light scattering method (DLS, NanoBrook Omni, Brookhaven Instruments, Holtsville, NY, USA). The machine's measurement range is between 1 nm and 10 μm. Since nanobubbles experience Brownian motion, the scattered light fluctuates as a function of time due to the particles' random movements, and the diffusion coefficient can be obtained from a computer digital correlator. The particle hydrodynamic diameter can be calculated by the Stokes-Einstein equation [35] as described below: After the above-mentioned preparation steps, the nanobubble water had a temperature of about 313 K. It was then left to cool down to room temperature. Next, from the prepared nanobubble water, the large sizes of the bubbles, from 1 to 10 µm, were removed by centrifugal treatment in the following manner. The nanobubble water was stored in a 50 mL centrifuge tube; then, centrifugal treatment was performed in 6000 rpm, i.e., 31.4 m/s peripheral velocity, for 6 min to remove possible impurities and large bubbles. After centrifugation, the size distribution, zeta potential, Eh and pH were measured from one centrifuge tube to record the first day's data while other sealed centrifuge tubes with nanobubble water were kept at room temperature (298 K) for continuous measurements.

Characterization of Bulk Nanobubble Suspensions
The nanobubble size was measured by the dynamic light scattering method (DLS, NanoBrook Omni, Brookhaven Instruments, Holtsville, NY, USA). The machine's measurement range is between 1 nm and 10 µm. Since nanobubbles experience Brownian motion, the scattered light fluctuates as a function of time due to the particles' random movements, and the diffusion coefficient can be obtained from a computer digital correlator. The particle hydrodynamic diameter can be calculated by the Stokes-Einstein equation [35] as described below: where D T , k, T, η, d h is the diffusion coefficient, Boltzmann constant, liquid absolute temperature, viscosity, and hydrodynamic diameter, respectively. One measurement duration time was 3 min, and the instrument performed the size measurement 3 times. After size measurements, the zeta potential was measured by the same instrument that performed the 3 measurements, consisting of 20 runs/measurement. Every experiment was performed in duplicate and then the average size and measurement error were calculated and plotted.
The zeta potential value was obtained through the micro-electrophoresis method by the phase analysis light scattering method (NanoBrook Omni, Brookhaven Instruments). The zeta potential of the bubbles in the aqueous solution with salt was calculated by using the Smoluckowski model f (κa) = 1 in Equation (2) for a >> 1/κ (κa >> 1); however, the zeta potential of the bubbles in deionized water was calculated by using the Hückel model f (κa) = 2/3 in Equation (2) individually for a << 1/κ (κa << 1) [34] because of the small bubble size. The electrophoretic mobility µ in the Henry equation is shown as follows: where ε r , ε 0 are relative permittivity and permittivity of free space, respectively, ζ is the zeta potential, η is fluid viscosity, κ is the Debye length, a is bubble radius and f (κa) is the Henry function [36]. The viscosity, refractive index and relative dielectric constant of water at 293 K are 1.002 × 10 −2 poise, 1.332, and 80.2, respectively [37]. Nanobubble water pH and Eh values were measured by pH meter (Inlab Expert Pro, Mettler Toledo, Greifensee, Switzerland) and Eh meter (by oxidation-reduction potential meter, Inlab Redox, Mettler Toledo), respectively.

Zeta Potential of Different Kinds of Nanobubbles
The zeta potentials of prepared different kinds of nanobubbles (N 2 , O 2 , Ar + 8%H 2 , air and CO 2 ) depending on pH were measured and are plotted in Figure 2. The pH was adjusted from the natural pH by adding NaOH or HCl to achieve the desired pH. The natural pH of nanobubbles in deionized water was between a pH of 6 to 7, except for CO 2 nanobubble suspensions. The zeta potential of N 2 , O 2 , Ar + 8%H 2 nanobubbles were negative at about −15 to −30 mV at a natural pH of 6 to 7, while the zeta potential of CO 2 nanobubbles in deionized water was positive at about +10 mV at a natural pH of 4 to 4.5. The solubility of gas, dielectric constant of gas [37] and the isoelectric point (IEP) of nanobubbles determined in this study are listed in Table 1. Since the solubility of CO 2 is high (7.07 × 10 −4 , Table 1), the HCO 3 − adsorption on the CO 2 bubble surface can cause a positive zeta potential in the deionized water due to the concentration of counter ions. The CO 2 solubility phenomena can be explained in the following Equations (3)-(8) [38] assuming that CO 2 gas is dissolved in water.
, pK a 1 = 6.35 (6) , pK a 2 = 10.33 (8) Figure 2. Zeta potential of N2, O2, Ar + 8%H2 and CO2 nanobubbles in deionized water as a function of pH. Table 1. Solubility of gas, dielectric constant [37] and isoelectric point of nanobubbles determined from the results shown in Figure 1. The natural pH of CO2 nanobubbles in the deionized water was around 4.2. The IEPs of nanobubbles in the deionized water containing air, Ar + 8%H2, O2, N2, and CO2 had a pH of 4.2, 4.6, 4.7, 5.2 and 5.7, respectively (Table 1). They were determined from the two pH values of zeta potential, assuming a linear relationship. Among all the gases studied, the IEP of CO2 was the highest (i.e., 5.7). This can be explained by the dissolution of the bubble surface, as discussed above, and because the IEP increased with the dielectric constant of gas increase, as listed in Table 1.

Time Effect of Mean Size and Zeta Potential of Different Gas Nanobubbles and pH and Eh of Nanobubble Suspensions
The effect of time after the preparation of the nanobubble water on the nanobubble mean diameter of N2, O2, Ar + 8%H2, air and CO2 gas in deionized water (A), 1 mM NaCl aqueous solution (B), 1 mM CaCl2 aqueous solution (C) and 1 mM AlCl3 aqueous solution (D) are shown in Figure 3. The zeta potential of the nanobubbles and the pH and Eh as a function of time are shown in Figures 4 and 5, respectively. In this section, we introduce and discuss the results in the absence of salt followed by the results in the presence of salt. The Eh value change can be correlated to the H2 nanobubble concentration change, O2 nanobubble existence and CO2 nanobubble dissolution in water.   [37] and isoelectric point of nanobubbles determined from the results shown in Figure 1.

Gas
Solubility of Gas in 298. 15  The natural pH of CO 2 nanobubbles in the deionized water was around 4.2. The IEPs of nanobubbles in the deionized water containing air, Ar + 8%H 2 , O 2, N 2 , and CO 2 had a pH of 4.2, 4.6, 4.7, 5.2 and 5.7, respectively (Table 1). They were determined from the two pH values of zeta potential, assuming a linear relationship. Among all the gases studied, the IEP of CO 2 was the highest (i.e., 5.7). This can be explained by the dissolution of the bubble surface, as discussed above, and because the IEP increased with the dielectric constant of gas increase, as listed in Table 1.

Time Effect of Mean Size and Zeta Potential of Different Gas Nanobubbles and pH and Eh of Nanobubble Suspensions
The effect of time after the preparation of the nanobubble water on the nanobubble mean diameter of N 2 , O 2 , Ar + 8%H 2 , air and CO 2 gas in deionized water (A), 1 mM NaCl aqueous solution (B), 1 mM CaCl 2 aqueous solution (C) and 1 mM AlCl 3 aqueous solution (D) are shown in Figure 3. The zeta potential of the nanobubbles and the pH and Eh as a function of time are shown in Figures 4 and 5, respectively. In this section, we introduce and discuss the results in the absence of salt followed by the results in the presence of salt. The Eh value change can be correlated to the H 2 nanobubble concentration change, O 2 nanobubble existence and CO 2 nanobubble dissolution in water.

Nanobubble Characteristics Change as a Function of Time in Deionized Water
In the absence of salt, the initial mean diameters of the N2, O2, Ar + 8%H2 and air nanobubbles were around 200 nm and gradually increased to 400-530 nm in 30 days. After 30 days, the mean diameter slightly decreased and was stable at 330-480 nm in 60 days ( Figure 3A). The zeta potentials of those gases were between −12 and −32 mV for 60 days ( Figure 4A). Variation trends of nanobubbles are similar to previous reports. Ulatowski et al. (2019) reported the O2 nanobubbles size produced by porous tube type was 200 nm on the initial day and unchanged after 10 days, while the N2 nanobubble mean size was 300 nm at −11 mV of zeta potential on the initial day and 400 nm at about −12 mV after 35 days [3]. Meegoda et al. (2019) reported the O2 nanobubble mean size produced by the cavitation method was 180 nm at −20 mV of zeta potential on the initial day and the O2 bubble mean size increased to 285 nm at −16 mV after 7 days [9]. Michailidi et al. (2020) reported that with the nanobubbles prepared by the high shear cavitation method, initially the O2 nanobubble mean size was 350 nm and the air nanobubble mean size was 430 nm, while the O2 and air nanobubble sizes increased to 560 and 500 nm, respectively, after two weeks; both bubbles existed at 640 nm size after 2 and 3 months [4]. Although the nanobubble size depends on the preparation methods, the N2 and O2 nanobubbles' size increase with time was similar to our results that the prepared nanobubble sizes of various gases were about 200 nm initially and the nanobubble size increased to 300 to 500 nm with 2 to 4 weeks.  reported that the number density of air nanobubbles prepared by the acoustic cavitation method gradually decreased; however, about 90 nm of nanobubbles existed for almost one year [6].
On the other hand, the CO2 nanobubble size gradually increased with time and the size changed from 180 nm initially to 350 nm in 5 days ( Figure 3A). After 5 days, the CO2 nanobubbles were not stable and could not be detected by DLS because the CO2 dissolved in the water and the electric double layer was compressed; therefore, the bubbles were coagulated due to the Van der Waals interaction (and the hydrophobic interaction) as discussed in the following Section 3.3.1. Ushikubo et al. (2010) reported that with the nanobubbles prepared by the pressurized type, the zeta potential of CO2 nanobubbles was negative at pH 4, initially; however, the bubbles disappeared at pH 6.1 due to the dissociation of CO2 [39]. In our experiment, the zeta potential of CO2 nanobubbles was +9 mV at pH 4.2 on the first day and it gradually increased with time to +17 mV at pH 4.6 after 5 days ( Figure 4A). As shown in Figure 5A, the Eh of Ar + 8%H2 nanobubble suspension in-

Nanobubble Characteristics Change as a Function of Time in Deionized Water
In the absence of salt, the initial mean diameters of the N 2 , O 2 , Ar + 8%H 2 and air nanobubbles were around 200 nm and gradually increased to 400-530 nm in 30 days. After 30 days, the mean diameter slightly decreased and was stable at 330-480 nm in 60 days ( Figure 3A). The zeta potentials of those gases were between −12 and −32 mV for 60 days ( Figure 4A). Variation trends of nanobubbles are similar to previous reports. Ulatowski et al.
(2019) reported the O 2 nanobubbles size produced by porous tube type was 200 nm on the initial day and unchanged after 10 days, while the N 2 nanobubble mean size was 300 nm at −11 mV of zeta potential on the initial day and 400 nm at about −12 mV after 35 days [3]. Meegoda et al. (2019) reported the O 2 nanobubble mean size produced by the cavitation method was 180 nm at −20 mV of zeta potential on the initial day and the O 2 bubble mean size increased to 285 nm at −16 mV after 7 days [9]. Michailidi et al. (2020) reported that with the nanobubbles prepared by the high shear cavitation method, initially the O 2 nanobubble mean size was 350 nm and the air nanobubble mean size was 430 nm, while the O 2 and air nanobubble sizes increased to 560 and 500 nm, respectively, after two weeks; both bubbles existed at 640 nm size after 2 and 3 months [4]. Although the nanobubble size depends on the preparation methods, the N 2 and O 2 nanobubbles' size increase with time was similar to our results that the prepared nanobubble sizes of various gases were about 200 nm initially and the nanobubble size increased to 300 to 500 nm with 2 to 4 weeks.  reported that the number density of air nanobubbles prepared by the acoustic cavitation method gradually decreased; however, about 90 nm of nanobubbles existed for almost one year [6].
On the other hand, the CO 2 nanobubble size gradually increased with time and the size changed from 180 nm initially to 350 nm in 5 days ( Figure 3A). After 5 days, the CO 2 nanobubbles were not stable and could not be detected by DLS because the CO 2 dissolved in the water and the electric double layer was compressed; therefore, the bubbles were coagulated due to the Van der Waals interaction (and the hydrophobic interaction) as discussed in the following Section 3.3.1. Ushikubo et al. (2010) reported that with the nanobubbles prepared by the pressurized type, the zeta potential of CO 2 nanobubbles was negative at pH 4, initially; however, the bubbles disappeared at pH 6.1 due to the dissociation of CO 2 [39]. In our experiment, the zeta potential of CO 2 nanobubbles was +9 mV at pH 4.2 on the first day and it gradually increased with time to +17 mV at pH 4.6 after 5 days ( Figure 4A). As shown in Figure 5A, the Eh of Ar + 8%H 2 nanobubble suspension increased from 250 to 400 mV in one day and also the Eh of N 2 nanobubble Materials 2021, 14, 1808 9 of 20 suspension increased from 330 to 420 mV in one day. The Eh of O 2 and air nanobubble suspensions were between 400 and 450 mV initially, then to 60 days. The Eh of the CO 2 bubble suspension increased as the pH increased with time ( Figure 5A').

Nanobubble Characteristics Change as a Function of Time in Salt Aqueous Solutions
In the presence of salt, the nanobubbles were prepared in 1 mM NaCl, CaCl 2 or AlCl 3 aqueous solution. In 1 mM NaCl aqueous solution, N 2 and air nanobubble sizes were initially 200 nm and gradually increased; they were not observed after 7 days. Meanwhile, O 2 , Ar + 8%H 2 , and CO 2 bubble sizes were initially 200 to 300 nm, gradually increased and they were not detected after 14 days ( Figure 3B). The existence period of CO 2 bubbles became longer in the 1 mM NaCl aqueous solution than in the absence of salt (i.e., 5 days in deionized water) ( Figure 3A). The zeta potentials of N 2 , O 2 , Ar + 8%H 2 and air nanobubbles were small, within ±5 mV at initial days to 14 days ( Figure 4B), while the zeta potential of CO 2 nanobubbles was higher than +12 mV initially and was kept +10 mV for 14 days ( Figure 4B). Ke et al. (2019) reported that with the nanobubbles produced by the pressurized type, the initial N 2 nanobubble average size was about 200 nm in the 0.1 mM NaCl aqueous solution [2] and the size was similar to our result in the 1 mM NaCl condition ( Figure 3B). In 1 mM NaCl aqueous solution, Leroy et al. (2012) measured that the zeta potential of H 2 gas was −20 mV at pH 6 [40] and Yang et al. (2001) reported the initial zeta potential of H 2 nanobubbles was −30 mV [41]. In our measurement of Ar + 8%H 2 nanobubble, the zeta potential was much smaller at −5 mV at pH 6 in 1 mM NaCl ( Figure 3B). Meegoda et al. (2019) reported that the O 2 nanobubble mean size prepared by the high shear cavitation type was 214 nm at −22 mV of zeta potential initially and the O 2 bubble mean size was almost the same at 219 nm at −14 mV in 7 days [9]. In our experiment, the O 2 bubble mean size was about 300 nm for 14 days ( Figure 3B), similar to the above-mentioned previous result; however, the zeta potential was +6 mV ( Figure 4B). The Eh value increased from 220 to 360 mV with the Ar + 8%H 2 nanobubble suspension in one day, which was the same as nanobubbles in the deionized water suspension. The Eh of the N 2 nanobubble suspension was 360 mV and the Eh of other nanobubble suspensions was a little high at about 450 mV in 7 days ( Figure 5B). The pH of CO 2 was from 4.3 to 4.4 and the Eh, pH, zeta potential and mean size of the CO 2 suspension were almost constant in the 1 mM NaCl aqueous solution compared with its suspension in deionized water.
In 1 mM CaCl 2 salt aqueous solution, O 2 was not stable after 7 days, while N 2 , Ar + 8%H 2 and air bubbles could be observed until 14 days, but no more were detected after 14 days ( Figure 3C). The CO 2 nanobubbles existed until about 20 days in 1 mM CaCl 2 . The absolute value of the zeta potential of N 2 , O 2 , Ar + 8%H 2 and air nanobubbles was low, at less than 10 mV, while the zeta potential of CO 2 was higher than +10 mV ( Figure 4C). Cho et al. (2005) reported that the air nanobubble size prepared by the sonicating method was 850 nm at −8 mV zeta potential [42], and their reported results were similar to our results after one day ( Figures 3C and 4C). The size of the air, N 2 and O 2 nanobubbles in 1 mM CaCl 2 salt aqueous solution increased extremely with time. Yang et al. (2001) reported that the zeta potential of the H 2 nanobubble was −5.5 mV [8], and their result was similar to our result of Ar + 8%H 2 nanobubble after one day ( Figure 4C). For the Eh value ( Figure 5C), the Eh of the 8%H 2 +Ar nanobubble suspension increased from 190 to 370 mV in one day, same as the nanobubbles in the other water suspensions. The Eh of N 2 , O 2 , air and CO 2 nanobubble suspensions were between 400 and 450 mV and the pH of N 2 , O 2, Ar + 8%H 2 and air nanobubble suspensions were between 5.5 and 6. The pH of CO 2 solution increased from 4.4, initially, to 5.3 after 7 days ( Figure 5C).
In 1 mM AlCl 3 salt aqueous solution, N 2 and O 2 were not stable after 7 days, while air, CO 2 and Ar + 8%H 2 nanobubbles could be observed until 14 days; however, they were not detected after 14 days. The size of the Ar + 8%H 2 nanobubble was more stable, at between 200 and 300 nm for 14 days, compared with other bubbles ( Figure 3D). The zeta potentials of all prepared bubbles were positive ( Figure 4D) possibly due to the presence of high valence ions (Al 3+ ) adsorbing on the bubble surfaces. Yang et al. (2001) reported that the zeta potential of H 2 nanobubble was +12 mV [41], and their result was similar to our result of +15 mV of Ar + 8%H 2 nanobubbles at the initial day ( Figure 4D). Han et al. (2006) reported that the zeta potential of O 2 nanobubbles prepared by electrolysis was +20 mV at pH 6 in 10 mM NaCl + 1 mM AlCl 3 aqueous solution [43]. The trivalent ion Al 3+ ion caused the positive charge in all our prepared nanobubbles ( Figure 4D). For the Eh value ( Figure 5D), the Eh of the Ar + 8%H 2 nanobubble suspension increased from 190 to 410 mV in one day, same as the gas nanobubbles in the other water suspensions. The Eh of N 2 , O 2 , air and CO 2 nanobubble suspensions were between 450 and 500 mV, and were higher than the Eh of the Ar + 8%H 2 suspension. The pH of N 2 , O 2, Ar + 8%H 2 and air were from 4.15 to 4.35, which were lower than the pH of other suspensions. The pH of CO 2 slightly increased from 4.0 to 4.3 in 5 days ( Figure 5A') and its increase was limited compared with other suspensions in the salt aqueous solution and deionized water ( Figure 5B).
The stable days of N 2 , O 2 , 8% H 2 +Ar, air and CO 2 nanobubbles produced in different solutions are listed in Table 2. The N 2 , O 2 , Ar + 8%H 2 and air nanobubbles in 1 mM of the three salts with different valences (+1, +2 and +3) decreased the existence period for 1 to 2 weeks compared with deionized water in the absence of salt (>60 days). On the other hand, CO 2 bubbles existed only 5 days in deionized water in the absence of salt; however, CO 2 bubbles existed 14 days in the 1 mM salt aqueous solution. The stability differences will be further discussed in the following section.

Nanobubble Stabilization Estimation by Using the Extended DLVO Theory
The thickness of the electric double layer (Debye length = 1/κ) of the nanobubble is calculated in the next formula: where κ is the Debye-Hückel parameter, n is the concentration of anion or cation in the solution and is equal to 1000 N A C (N A is the Avogadro number and C is concentration mol/L), z is the valence of ion, e is the electron charge, ε r is the relative dielectric constant and ε 0 is the permittivity of vacuum. The calculated Debye lengths of the nanobubbles studied in our experiment are listed in Table 3 in order to discuss differences in the nanobubble stability and to have some idea of how to keep the nanobubble stable for a longer duration. The Debye length is 300 nm at pH 6 around N 2 , O 2 and Ar + 8%H 2 nanobubbles in deionized water, and 140 nm at pH 4.2 and 70 nm at pH 4.7 around CO 2 nanobubbles. Since the characteristics of CO 2 nanobubbles are different from others (Figures 3-5), the Debye length (1/κ) around CO 2 bubbles and HCO 3 − , OH − , CO 3 2− ion concentration in the presence of CO 2 nanobubbles in deionized water as a function of pH were also calculated and shown in Figure 6 in order to discuss their relationship. The concentration of various ions was calculated from using Equations (3)-(8).   A thick electric double layer (300 nm, Table 3) is present around the N2, O2 and Ar + 8%H2 nanobubbles in deionized water and can stabilize those nanobubbles with high enough zeta potential (i.e., −16 to −32 mV, Figure 4A). On the other hand, the Debye length of CO2 nanobubbles (70 nm at pH 4.7 in DI water, Table 3) and other nanobubbles in salt aqueous solution (3-10 nm, Table 3) are thin and thus, the influence of the Van der Waals and hydrophobic attraction can be more dominant in coagulating and coalescing the nanobubbles. In order to quantify the influence of the electrical double layer potential, the Van der Waals potential and the hydrophobic interaction potential, their potential energies were calculated by using the extended DLVO theory as described in the following sections. Tchaliovska et al. investigated the thickness of thin flat foam films formed in aqueous dodecyl ammonium chloride solution [44]. Angarska et al. showed that the value of the critical thickness of the foam film was sensitive to the magnitude of the attractive surface forces acting on the film using sodium dodecyl sulfate and the total disjoining pressure operative on the films, which was expressed as a sum of the Van der Waals and hydrophobic contributions [45]. Figure 7 shows the two nanobubble positions and geometries considered in our potential calculation. The total potential energy VT between two nanobubbles can be given by the potential energy due to the Van der Waals interaction (VA), hydrophobic interaction (Vh) and the electrostatic interaction (VR) as follows [46][47][48][49][50]; VA + Vh is shown in the follow equation: A thick electric double layer (300 nm, Table 3) is present around the N 2 , O 2 and Ar + 8%H 2 nanobubbles in deionized water and can stabilize those nanobubbles with high enough zeta potential (i.e., −16 to −32 mV, Figure 4A). On the other hand, the Debye length of CO 2 nanobubbles (70 nm at pH 4.7 in DI water, Table 3) and other nanobubbles in salt aqueous solution (3-10 nm, Table 3) are thin and thus, the influence of the Van der Waals and hydrophobic attraction can be more dominant in coagulating and coalescing the nanobubbles. In order to quantify the influence of the electrical double layer potential, the Van der Waals potential and the hydrophobic interaction potential, their potential energies were calculated by using the extended DLVO theory as described in the following sections. Tchaliovska et al. investigated the thickness of thin flat foam films formed in aqueous dodecyl ammonium chloride solution [44]. Angarska et al. showed that the value of the critical thickness of the foam film was sensitive to the magnitude of the attractive surface forces acting on the film using sodium dodecyl sulfate and the total disjoining pressure operative on the films, which was expressed as a sum of the Van der Waals and hydrophobic contributions [45]. Figure 7 shows the two nanobubble positions and geometries considered in our potential calculation. The total potential energy V T between two nanobubbles can be given by the potential energy due to the Van der Waals interaction (V A ), hydrophobic interaction (V h ) and the electrostatic interaction (V R ) as follows [46][47][48][49][50]; V A + V h is shown in the follow equation: where the Hamaker constant A for air in water whose value of air-water-air of 3.7 × 10 −20 J [46] was used to investigate our system in nanobubble-water-nanobubble. The K is a hydrophobic constant for air in water. Yoon and Aksoy calculated the K using the extended DLVO theory [49] while Wang and Yoon measured the K as a function of the SDS concentration at different kinds of NaCl concentrations and showed that K was estimated at 10 −17 J in the absence of salt and 10 −19 J in the 1 mM NaCl aqueous solution [50]. In our calculation, 10 −19 J of K was used in 1 mM CaCl 2 and AlCl 3 aqueous solutions and 10 −18 J of K was used in deionized water containing CO 2 nanobubbles by considering the reference values [50].
where the Hamaker constant A for air in water whose value of air-water-air of 3.7 × 10 −20 J [46] was used to investigate our system in nanobubble-water-nanobubble. The K is a hydrophobic constant for air in water. Yoon and Aksoy calculated the K using the extended DLVO theory [49] while Wang and Yoon measured the K as a function of the SDS concentration at different kinds of NaCl concentrations and showed that K was estimated at 10 −17 J in the absence of salt and 10 −19 J in the 1 mM NaCl aqueous solution [50]. In our calculation, 10 −19 J of K was used in 1 mM CaCl2 and AlCl3 aqueous solutions and 10 −18 J of K was used in deionized water containing CO2 nanobubbles by considering the reference values [50]. The radius of nanobubbles is a1 and a2 and their distance R = a1 + a2 + h is defined as shown in Figure 7, and h is the surface-to-surface distance between two nanobubbles. The potential energy of VR is expressed as follows, where are surface potentials of the nanobubbles of radii a1 and a2, respectively.

Stability Calculation of Nanobubbles in Deionized Water
The mean diameters of the prepared nanobubbles of N2, O2, Ar + 8%H2 and air in deionized water were between 170 and 230 nm, as shown in Figure 3. With time, these diameters gradually increased, and they were between 390 and 530 nm after 30 days. Then, they slightly decreased to between 330 and 480 nm and were stable after 60 days. As the mean bubble diameter was measured in our experiment, the increase in bubble size indicates that the small size nanobubbles coalesce with other bubbles, and those small bubbles disappear.
The above-mentioned phenomenon is well known as the Ostwald ripening effect [51], which explains the deposition of a smaller object on a larger object due to the latter being more energetically stable than the former. By using Lemlich's theory [52], it can be explained by using next equation [53]: where a is the bubble radius, t is time, K' is a constant and p is instantaneous bubble mean radius. This equation tells us that the bubbles with a radius larger than a grow, and those The radius of nanobubbles is a 1 and a 2 and their distance R = a 1 + a 2 + h is defined as shown in Figure 7, and h is the surface-to-surface distance between two nanobubbles. The potential energy of V R is expressed as follows, where ψ 1 and ψ 2 are surface potentials of the nanobubbles of radii a 1 and a 2 , respectively.

Stability Calculation of Nanobubbles in Deionized Water
The mean diameters of the prepared nanobubbles of N 2 , O 2 , Ar + 8%H 2 and air in deionized water were between 170 and 230 nm, as shown in Figure 3. With time, these diameters gradually increased, and they were between 390 and 530 nm after 30 days. Then, they slightly decreased to between 330 and 480 nm and were stable after 60 days. As the mean bubble diameter was measured in our experiment, the increase in bubble size indicates that the small size nanobubbles coalesce with other bubbles, and those small bubbles disappear.
The above-mentioned phenomenon is well known as the Ostwald ripening effect [51], which explains the deposition of a smaller object on a larger object due to the latter being more energetically stable than the former. By using Lemlich's theory [52], it can be explained by using next equation [53]: where a is the bubble radius, t is time, K is a constant and p is instantaneous bubble mean radius. This equation tells us that the bubbles with a radius larger than a grow, and those with a radius smaller than p shrink. By using the results shown in Figure 2 (zeta potential) and Figure 3 (bubble size), the bubble stability is further discussed by calculating the total potential energy between two nanobubbles. Figure 8 shows the potential energies between two nanobubbles in deionized water. Figure 8A shows the potential energies between two same-size gas bubbles of 200 nm of Ar + 8%H 2 on the initial day. The total potential energy V T is 20 kT at 300 nm (the Debye length) and the maximum potential is 30 kT. The other bubbles of air, N 2 and O 2 bubble show almost same potential curves. It indicates that the two bubbles have enough of a potential barrier to disperse each other. Figure 8B shows the potential energies between 450 nm of two same-size bubbles of Ar + 8%H 2 after 30 days. The maximum total potential energy V T is 15 kT, i.e., the threshold total potential energy to determine coagulation or dispersion [54], and it indicates that Ar + 8%H 2 nanobubbles would be stable, although the absolute value of zeta potential is smallest in Ar + 8%H 2 nanobubbles (−13 mV, Figure 4A) compared with the ones of other O 2 , N 2 and air nanobubbles bubbles, shown in Figure 4. with a radius smaller than p shrink. By using the results shown in Figures 2 (zeta potential) and 3 (bubble size), the bubble stability is further discussed by calculating the total potential energy between two nanobubbles. Figure 8 shows the potential energies between two nanobubbles in deionized water. Figure 8A shows the potential energies between two same-size gas bubbles of 200 nm of Ar + 8%H2 on the initial day. The total potential energy VT is 20 kT at 300 nm (the Debye length) and the maximum potential is 30 kT. The other bubbles of air, N2 and O2 bubble show almost same potential curves. It indicates that the two bubbles have enough of a potential barrier to disperse each other. Figure 8B shows the potential energies between 450 nm of two samesize bubbles of Ar + 8%H2 after 30 days. The maximum total potential energy VT is 15 kT, i.e., the threshold total potential energy to determine coagulation or dispersion [54], and it indicates that Ar + 8%H2 nanobubbles would be stable, although the absolute value of zeta potential is smallest in Ar + 8%H2 nanobubbles (−13 mV, Figure 4A) compared with the ones of other O2, N2 and air nanobubbles bubbles, shown in Figure 4.  When the CO2 nanobubbles were prepared, their mean size was 160 nm and zeta potential was low, i.e., +9 mV. Figure 9A shows the potential energies between two 160 nm bubbles. The total potential barrier was not appeared at 140 nm the Debye length. Figure 9B shows the potential energies between two 350 nm bubbles after 5 days. As the total potential barrier was also not appeared, these larger bubbles would also coagulate, coalesce and increase the size and, thus, CO2 bubbles could not be observed after 5 days. When the CO 2 nanobubbles were prepared, their mean size was 160 nm and zeta potential was low, i.e., +9 mV. Figure 9A shows the potential energies between two 160 nm bubbles. The total potential barrier was not appeared at 140 nm the Debye length. Figure 9B shows the potential energies between two 350 nm bubbles after 5 days. As the total potential barrier was also not appeared, these larger bubbles would also coagulate, coalesce and increase the size and, thus, CO 2 bubbles could not be observed after 5 days.  . Total potential energy VT as a function of the distance between two nanobubbles at +9 mV zeta potential on the prepared day for CO2 (A) and +5 mV after 5 days for CO2 nanobubble (B) in deionized water. (A) Two 160 nm bubbles on the prepared day, (B) two 350 nm bubbles after 5 days.

Stability Calculation of Nanobubbles in Salt Aqueous Solutions
In the 1 mM NaCl aqueous solution, the absolute values of the zeta potential of O2, N2, Ar + 8%H2 and air nanobubbles were less than 10 mV; the total potential energy barrier could not appear. Figure 10A shows the potential energies between two 160 nm N2 nanobubbles. The total potential energy VT is negative at any distance and does not show the potential barrier; therefore, the nanobubbles are not stable and can coagulate. Figure 10B shows the potential energies between two 200 nm CO2 nanobubbles. Although the abso- Figure 9. Total potential energy V T as a function of the distance between two nanobubbles at +9 mV zeta potential on the prepared day for CO 2 (A) and +5 mV after 5 days for CO 2 nanobubble (B) in deionized water. (A) Two 160 nm bubbles on the prepared day, (B) two 350 nm bubbles after 5 days.

Stability Calculation of Nanobubbles in Salt Aqueous Solutions
In the 1 mM NaCl aqueous solution, the absolute values of the zeta potential of O 2 , N 2 , Ar + 8%H 2 and air nanobubbles were less than 10 mV; the total potential energy barrier could not appear. Figure 10A shows the potential energies between two 160 nm N 2 nanobubbles. The total potential energy V T is negative at any distance and does not show the potential barrier; therefore, the nanobubbles are not stable and can coagulate. Figure 10B shows the potential energies between two 200 nm CO 2 nanobubbles. Although the absolute zeta potential was slightly larger than the sN 2 nanobubbles at the Debye length 10 nm, there is no potential barrier indicating the attraction between the two bubbles. The CO 2 nanobubble size existed between 200 and 400 nm for 14 days, as shown in Figure 3B; however, after 14 days, the CO 2 bubble was disappeared.
(A) Two 160 nm CO2 gas bubbles on the prepared day (B) Two 350 nm CO2 gas bubbles after 5 days Figure 9. Total potential energy VT as a function of the distance between two nanobubbles at +9 mV zeta potential on the prepared day for CO2 (A) and +5 mV after 5 days for CO2 nanobubble (B) in deionized water. (A) Two 160 nm bubbles on the prepared day, (B) two 350 nm bubbles after 5 days.

Stability Calculation of Nanobubbles in Salt Aqueous Solutions
In the 1 mM NaCl aqueous solution, the absolute values of the zeta potential of O2, N2, Ar + 8%H2 and air nanobubbles were less than 10 mV; the total potential energy barrier could not appear. Figure 10A shows the potential energies between two 160 nm N2 nanobubbles. The total potential energy VT is negative at any distance and does not show the potential barrier; therefore, the nanobubbles are not stable and can coagulate. Figure 10B shows the potential energies between two 200 nm CO2 nanobubbles. Although the absolute zeta potential was slightly larger than the sN2 nanobubbles at the Debye length 10 nm, there is no potential barrier indicating the attraction between the two bubbles. The CO2 nanobubble size existed between 200 and 400 nm for 14 days, as shown in Figure 3B; however, after 14 days, the CO2 bubble was disappeared.
(A) Two 160 nm N2 gas bubbles on the prepared day (B) Two 200 nm CO2 gas bubbles on the prepared day In the 1 mM CaCl2 aqueous solution, as the absolute values of the zeta potential of O2, N2, Ar + 8%H2 and air nanobubbles were less than 10 mV ( Figure 4C), like the one in 1 the mM NaCl aqueous solution ( Figure 4B), the total potential energy barrier did not ap- Figure 10. Total potential energy V T as a function of the distance between two nanobubbles at −5 mV zeta potential on the prepared day for N 2 (A) and +12 mV on the prepared day for CO 2 nanobubble (B) in 1 mM NaCl aqueous solution. (A) Two 160 nm N 2 bubbles on the prepared day, (B) two 200 nm CO 2 bubbles on the prepared day.
In the 1 mM CaCl 2 aqueous solution, as the absolute values of the zeta potential of O 2 , N 2 , Ar + 8%H 2 and air nanobubbles were less than 10 mV ( Figure 4C), like the one in 1 the mM NaCl aqueous solution ( Figure 4B), the total potential energy barrier did not appear. Figure 11A shows the potential energies between 230 nm of two same-size N 2 nanobubbles on the prepared day. The total potential energy V T was negative at any distance and did not show the potential barrier, and thus it indicates that the nanobubbles were not stable due to their coagulation. The zeta potential of CO 2 was more than +10 mV, as shown in Figure 4C; however, the potential barrier still did not appear because the Debye length around the CO 2 bubbles decreased in the presence of 1 mM CaCl 2 salt (i.e., 5 nm vs. 40 nm (pH 4.2) in deionized water, Table 2, while the CO 2 nanobubble mean size 1 mM CaCl 2 was stable at about 300 nm until 14 days ( Figure 3C), same as the one in the 1 mM of NaCl aqueous solution ( Figure 3B). Figure 11C shows the potential energies between two 750 nm N 2 nanobubbles after 3 days in a 1 mM CaCl 2 aqueous solution. With the smaller zeta potential −7 mV, the potential barrier is not appeared, and it corresponds to the further coagulation/coalescence of the bubbles ( Figure 3C).
In the 1 mM AlCl 3 aqueous solution, Figure 11B shows the potential energy between two 170 nm Ar + 8%H 2 nanobubbles on the prepared day. Although the absolute value of the zeta potential was higher (+16 mV, Figure 4D) than the one of Ar + 8%H 2 nanobubbles prepared in a CaCl 2 aqueous solution (−2 mV, Figure 4C), there was no potential barrier due to the small electrostatic interaction potential (<15 kT) and the bubbles may be unstable. In Figure 11D, with the N 2 nanobubble size of 300 nm and the higher zeta potential (+25 mV, Figure 4D), the potential barrier was not also appeared. two 170 nm Ar + 8%H2 nanobubbles on the prepared day. Although the absolute value of the zeta potential was higher (+16 mV, Figure 4D) than the one of Ar + 8%H2 nanobubbles prepared in a CaCl2 aqueous solution (−2 mV, Figure 4C), there was no potential barrier due to the small electrostatic interaction potential (<15 kT) and the bubbles may be unstable. In Figure 11D, with the N2 nanobubble size of 300 nm and the higher zeta potential (+25 mV, Figure 4D), the potential barrier was not also appeared.  In the case of N 2 , O 2 , Ar + 8%H 2 and air in 1 mM salt concentration, the presence of Ca 2+ ion from CaCl 2 salt decreased the absolute value of the zeta potential by its adsorption on the bubble surface and a stronger coagulation could happen by thinning the electric double layer at the natural pH (without pH adjustment). Here, the overall bubble stability phenomena are summarized. Except for the 1 mM Ca 2+ ion aqueous solution, the stability phenomena nearly followed the Shultz-Hardy rule. Comparing bubble size and existence time, the stability order of the N 2 , O 2 , Ar + 8%H 2 and air nanobubbles identified from our study was: no salt addition > 1 mM NaCl > 1 mM AlCl 3 > 1 mM CaCl 2 in deionized water. On the other hand, the stability order of CO 2 nanobubbles was: 1 mM NaCl > 1 mM CaCl 2 > 1 mM AlCl 3 > no salt addition, due to the effect of CO 2 dissolution in deionized water, as discussed in Section 3.3.

Nanobubble Movement in Salt Aqueous Solution
The nanobubbles move by Brownian motion. The Brownian diffusion can be described in the following Equations (14) and (15) where the bubble movement distance is ∆x 2 and Equation (1) is incorporated to define D T .
If the bubble size d h is small, the movement distance becomes longer since they have inverse correlation, as described in Equations (14) and (15).
On the other hand, a large, coalesced bubble floats, following the terminal velocity u defined by the Stokes equation of laminar flow: where ρ is the density of water and g is the gravitational acceleration.
Bubbles experiencing diffusion change their movement direction frequently in a short time. On the other hand, the bubble displacement due to the buoyancy force is always pointing upwards against the gravitational force. The terminal velocity depends on the bubble diameter, as shown in Figure 12, based on our calculation using Equation (16). A bubble smaller than 1 µm can experience very low terminal velocity (<1 × 10 −6 m/s) which prevents bubbles from floating against the buoyancy force. Our results partially agree with the previous literature.  reported that the number density of about a 100 nm mean size of nanobubbles gradually decreased over one year, and still existed at about 100 nm after one year [8].
The nanobubbles move by Brownian motion. The Brownian diffusion can be described in the following Equations (14) and (15) where the bubble movement distance is ∆ and Equation (1) is incorporated to define DT.
If the bubble size dh is small, the movement distance becomes longer since they have inverse correlation, as described in Equations (14) and (15).
On the other hand, a large, coalesced bubble floats, following the terminal velocity u defined by the Stokes equation of laminar flow: where ρ is the density of water and g is the gravitational acceleration.
Bubbles experiencing diffusion change their movement direction frequently in a short time. On the other hand, the bubble displacement due to the buoyancy force is always pointing upwards against the gravitational force. The terminal velocity depends on the bubble diameter, as shown in Figure 12, based on our calculation using Equation (16). A bubble smaller than 1 μm can experience very low terminal velocity (<1 × 10 −6 m/s) which prevents bubbles from floating against the buoyancy force. Our results partially agree with the previous literature.  reported that the number density of about a 100 nm mean size of nanobubbles gradually decreased over one year, and still existed at about 100 nm after one year [8].   Figure 13 shows the schematic diagrams of nanobubble stability in deionized water ( Figure 13A) and the nanobubble size change in a salt aqueous solution ( Figure 13B). The nanobubbles in deionized water stably exist for two months by the Brownian motion. On the other hand, in the nanobubbles in a 1 mM salt aqueous solution, the nanobubbles coalesced with each other and increased the size, and the large-size bubbles gradually floated and disappeared after one or two weeks.
The surface charge on the front direction of a floating larger bubble can decrease, while the tail direction of the bubble retains more ions; thus, the electric double layer charge distribution can be distorted [55]. The bubbles in the direction of a floating large bubble can interact with that large bubble. If there is a small nanobubble in the front direction of a moving bubble, it can coagulate and coalesce with large bubbles and the coalesced large bubbles can be disappeared. This phenomenon occurred for the larger size of the bubbles in a salt aqueous solution with time, as observed in this study.
The surface charge on the front direction of a floating larger bubble can decrease, while the tail direction of the bubble retains more ions; thus, the electric double layer charge distribution can be distorted [55]. The bubbles in the direction of a floating large bubble can interact with that large bubble. If there is a small nanobubble in the front direction of a moving bubble, it can coagulate and coalesce with large bubbles and the coalesced large bubbles can be disappeared. This phenomenon occurred for the larger size of the bubbles in a salt aqueous solution with time, as observed in this study.

Conclusions
This research investigated five kinds of gas nanobubbles (N2, O2, Ar + 8%H2, air and CO2) for their long-term stability, to consider the application of the nanobubbles containing aqueous solutions. Each gas in a cylinder was injected into deionized water or a 1 mM of salt aqueous solution, and nanobubbles were prepared by the hydrodynamic cavitation method. The mean diameter, zeta potential of bubbles, pH and Eh of nanobubble suspensions were measured and these characteristics changed, as the function of time was also studied.

•
The IEPs of different gas nanobubbles in deionized water varied, and the CO2 nanobubbles showed the highest value of pH at 5.7.

•
The N2, O2, Ar + 8%H2 and air nanobubbles in deionized water showed the long-term stability for 60 days. During the 60 days, the bubble size gradually increased and decreased. Thus, this size change, explained by the Ostwald ripening effect, was also coupled with a bubble stability discussion using the total potential energy between two nanobubbles under different conditions calculated by the extended DLVO theory.

•
The CO2 nanobubbles produced in deionized water were not stable and disappeared after five days. The CO2 nanobubbles in water dissolved the HCO3 -ion, which could

Conclusions
This research investigated five kinds of gas nanobubbles (N 2 , O 2 , Ar + 8%H 2 , air and CO 2 ) for their long-term stability, to consider the application of the nanobubbles containing aqueous solutions. Each gas in a cylinder was injected into deionized water or a 1 mM of salt aqueous solution, and nanobubbles were prepared by the hydrodynamic cavitation method. The mean diameter, zeta potential of bubbles, pH and Eh of nanobubble suspensions were measured and these characteristics changed, as the function of time was also studied.

•
The IEPs of different gas nanobubbles in deionized water varied, and the CO 2 nanobubbles showed the highest value of pH at 5.7.

•
The N 2 , O 2 , Ar + 8%H 2 and air nanobubbles in deionized water showed the long-term stability for 60 days. During the 60 days, the bubble size gradually increased and decreased. Thus, this size change, explained by the Ostwald ripening effect, was also coupled with a bubble stability discussion using the total potential energy between two nanobubbles under different conditions calculated by the extended DLVO theory.

•
The CO 2 nanobubbles produced in deionized water were not stable and disappeared after five days. The CO 2 nanobubbles in water dissolved the HCO 3 − ion, which could decrease the total potential energy between CO 2 bubbles, and thus the CO 2 nanobubbles became unstable.

•
The N 2 , O 2 , Ar + 8%H 2 and air nanobubbles produced in the 1 mM salt aqueous solution were not stable. The potential barrier between the nanobubbles disappeared, and the bubble size gradually increased with their coalescence, followed by floating and disappearing after 14 days for O 2 , Ar + 8%H 2 and air nanobubbles, and 7 days for N 2 nanobubbles. On the other hand, the CO 2 nanobubbles in the 1 mM of NaCl and CaCl 2 aqueous solution became more stable than the CO 2 nanobubbles in deionized water, and a 200 to 300 nm mean bubble size was kept for two weeks. • A bubble smaller than 1 µm can experience very low terminal velocity (<1 × 10 −6 m/s) which prevents bubbles from floating against the buoyancy force.