Aqueous Nitrogen-Nanobubble dispersion and supersaturation at elevated pressures up to 277 bara

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Aqueous Nitrogen-Nanobubble Dispersion and Supersaturation at Elevated 1
Pressures up to 277 Bara 2
Tesleem Lawal, Hao Wang, Ryosuke Okuno*, The University of Texas at Austin 3
*Corresponding author: Ryosuke Okuno, Ph.D. 4
Center for Subsurface Energy and the Environment, The University of Texas at Austin 5
200 E. Dean Keeton Street, Stop C0300, Austin, Texas 78712, U.S.A. 6
Phone: +1-512-471-3250; E-mail: okuno@utexas.edu 7
ABSTRACT 8
Aqueous nanobubble (NB) dispersion of gaseous species has been studied and applied for 9
various processes near atmospheric pressure, but its fundamental properties are not well 10
understood at elevated pressures. This paper presents an experimental program that measures the 11
gas content of aqueous NB dispersion of nitrogen (N2) at pressures up to 277 bara. The parameters 12
directly set in the experiments were temperature, external pressure, and total volume while the 13
overall composition of aqueous NB dispersion was obtained by constant mass expansion with 14
material balance. The experimental data were analyzed by using a thermodynamic model for 15
calculating an internally consistent set of properties at the experimental conditions. 16
Results show that the N2 content in aqueous NB dispersion increased significantly with 17
the system pressure. For example, the N2 content at 277 bara was 0.29 mol/L for aqueous NB 18
dispersion with deionized (DI) water, which was 2.9 times greater than the inherent solubility of 19
N2 in DI water at the same pressure. The effect of salinity was studied by using 0.88 M NaCl brine 20
in place of DI water, but the N2 contents were similar to those with DI water for the pressures 21
tested in this research. Application of a thermodynamic model using the GERG-2008 equation of 22
state to the experimental data indicates that NBs themselves were unlikely the main storage of N2, 23

but the existence of NBs enabled the supersaturation of the aqueous phase by N2 because of 24
capillary pressure. 25
26
Keywords: Nanobubble; Supersaturation; Nitrogen; Solubility; Capillary pressure; Phase 27
equilibrium 28
29
1. Introduction 30
Aqueous nanobubble (NB) dispersion has been studied to increase the amount of the water-31
immiscible gaseous species (e.g., nitrogen, oxygen, and carbon dioxide) in an aqueous fluid 32
beyond its inherent solubility. Two types of aqueous NB dispersions are surface nanobubbles and 33
bulk nanobubbles. While the former refers to gas-filled cavities attached to surfaces in the form of 34
spherical caps, the latter refers to gas-filled cavities freely suspended within a bulk liquid [1,2]. 35
This paper is concerned with bulk NBs in the context of aqueous nanobubble dispersions. 36
NBs are classified as having diameters smaller than 1 μm. Studies have shown that their 37
size depends on various parameters, such as gaseous species, pressure, pH, and other operating 38
conditions of their generation [3–5]. The unique properties of NBs, such as enhanced gas 39
concentration beyond the inherent solubility, kinetic stability, and enhanced interfacial area, have 40
made them the subject of research in various fields [6–10]. Most industrial applications are for 41
low-pressure open systems, such as agricultural applications [11], wastewater treatments [12–16], 42
surface cleaning, and separation of materials [17–20]. Comprehensive reviews of NB generation 43
techniques exist in the literature [3, 10, 21–24]. Commonly used techniques include cavitation 44
(acoustic and hydrodynamic) [25–27], water electrolysis [28–30], compression–decompression 45

[31–33], gas injection through porous (glass, ceramic, stainless steel) membranes [34–36], 46
repeated compression of microbubbles [37,38], and mixing of gas and water [39]. 47
The existence and long-term stability of NBs in low-pressure open systems have been 48
discussed in the literature; for example, Alheshibri et al. [1] introduced the concept of Laplace 49
Pressure Bubble Catastrophe (LBPC) regarding unstable nanobubbles. They suggested that, based 50
on classical theories like the Young-Laplace equation and Epstein-Plesset theory [40], the 51
significant pressure difference between the inside and outside of nanobubbles would cause them 52
to dissolve rapidly in milliseconds or less. As the bubble radius decreases, the Laplace pressure 53
increases exponentially, leading to accelerated dissolution. 54
Long-term stability of NBs has been observed even for low-pressure open systems for days 55
[7,41,42], weeks [25,43,44], and months [26,36,45]. Light scattering techniques (e.g., dynamic 56
light scattering or DLS and nanoparticle tracking analysis or NTA) [20,26,32,36,37,41], resonant 57
mass measurements [46,47], high-resolution imaging techniques (e.g., transmission electron 58
microscopy and scanning electron microscopy) [5,48,49], and spectral techniques have been used 59
to verify the existence of NBs [25,39]. These techniques, however, have been limited in 60
differentiating between nanobubbles and nanoparticles. They are also not easily adapted to 61
measurements of high-pressure aqueous NB samples because of the requirement of specially 62
designed experiment rigs. 63
Most discussions on NB stability were made for open systems near atmospheric pressure, 64
and many did not even specify the system for their analysis. Unlike those studied in the literature, 65
the current paper is focused on a high-pressure closed system of aqueous NB dispersion. As will 66
be shown in this paper, the enhanced gas content by aqueous NB dispersion tends to be more 67
significant at a higher pressure (therefore, a closed system); hence, this research was motivated by 68

potential applications of aqueous NB dispersion for subsurface processes, such as enhanced oil 69
recovery (EOR) and geological carbon sequestration (GCS). For example, carbonated water 70
injection has been studied for EOR [50–62] and also has attracted attention for CO2 in-situ 71
mineralization as GCS since the CarbFix project in Iceland [63–67]. An obvious limitation of 72
carbonated water is the CO2 concentration limited by the inherent solubility (e.g., 1 mol/L). 73
Although aqueous NB dispersion has the potential to enhance the gas content in aqueous 74
fluid as widely studied for open systems near atmospheric pressure, its fundamental properties are 75
not well understood especially at elevated pressures relevant to subsurface applications. This is at 76
least in part because it is not easy to directly measure properties of aqueous NB dispersion under 77
elevated pressure, such as gas content, bubble size, bubble number density, phase composition, 78
capillary pressure, and interfacial tension, which are expected to vary for different pressure, 79
temperature, gas species, salinity, and operation conditions of NB generation. Hence, there is a 80
critical need to generate fundamental experimental data on aqueous NB dispersion at elevated 81
pressures. To this end, we started by using nitrogen (N2), instead of CO2, as the gaseous species 82
in this research since CO2 dissolution in water gives additional complexities associated with a pH 83
change. 84
This paper presents an experimental program that measures the gas content of aqueous N2 85
NB dispersion at pressures up to 277 bara and analyzes the data using a thermodynamic model. 86
The parameters directly set in the experiments were temperature, external pressure, and total 87
volume, while the overall composition of aqueous NB dispersion was obtained by constant mass 88
expansion. The limited amount of data that were directly measured was supplemented by a 89
thermodynamic model, which generated a consistent set of properties, including those not directly 90
measurable, such as bubble size, number density, and capillary pressure. The depressurized 91

samples were subjected to measurement of bubble size distribution and bubble number density 92
using DLS and NTA. 93
To the best of our knowledge, this is the first experimental study of NB generation and gas 94
content measurement at high pressures, addressing a critical research gap in the literature. 95
Furthermore, the enhancement of gas content in water in the form of nanobubble dispersions holds 96
immense potential for accelerating storage security in GCS applications and enhancing oil 97
recovery. 98
99
2. Experimental methods 100
2.1. Materials 101
The aqueous samples used in the experiment were deionized (DI) water and sodium 102
chloride (NaCl) brine with a salinity of 50,000 ppm (equivalent to 0.88 M NaCl). The DI water 103
had a resistivity of 18.2 MΩ-cm. NaCl salt (Thermo Scientific Chemicals, purity of 99.0%) was 104
dissolved in DI water to formulate the brine solution. The aqueous solutions were checked for 105
impurities using a NanoSight NS500 instrument and no particles (impurities) were confirmed. 106
Nitrogen gas of research-grade (Linde Gas & Equipment, purity of 99.9999%) was used. 107
2.2. Gas content measurement 108
The N2 gas content measurement was performed in two stages. The first stage was the 109
generation and preparation of the NB sample while the second stage was the depressurization and 110
measurement of the N2 gas content. Several variables – pressure, salinity, volumetric co-injection 111
ratio, total injection flow rate, and membrane pore diameter – were tested for the gas content 112
measurements. Table 1 shows the variables investigated for the gas content measurements. All the 113
experiments were conducted at room temperature (295.15 K). The control experiments used DI 114

water, a co-injection ratio of 50% N2 + 50% DI water, a total injection flow rate of 100 mL/hr, a 115
membrane pore diameter of 5 μm, and pressures ranging from 35 to 277 bara. 116
117
Table 1. Experiment variables for the gas content measurement. 118
Variable Variations Other conditions
Salinity DI water, NaCl brine 35 – 277 bara; 5 μm
Co-injection ratio
50% N2; 50% DI water (or
NaCl brine) 35 – 277 bara; 5 μm
60% N2; 40% DI water 70, 139, 208 bara; 5 μm
Total injection flow rate 100 mL/hr 35 – 277 bara; 5 μm
500 mL/hr 70, 139, 208 bara; 5 μm
Membrane pore diameter 2 μm 70, 139, 208 bara
119
Stage 1: Generation and preparation of NB sample 120
Figure 1 shows a schematic of the experimental setup for generating the N2 NB. The setup 121
consists of five accumulators: two accumulators for N2 and DI water (or NaCl brine) and three 122
receiver accumulators; three stainless-steel porous membranes; one Hassler-type core holder with 123
a 70 Durometer Viton sleeve to house the membranes; spacers on either side of the membranes; a 124
hydraulic manual pump to maintain overburden pressure on the core holder; pressure gauges to 125
monitor experiment pressures; Teledyne ISCO syringe pumps to control pressure and flow rates; 126
and a sapphire visualization cell. 127
128

129
Figure 1. Schematic of the experimental setup used to generate the aqueous N2 NB fluid. 130
131
The stainless-steel porous membrane had a porosity of 37%, an average pore size of 5 μm 132
(with a maximum size of 10 μm), an outer diameter of 25.4 mm, and a length of 3 mm. The spacers 133
on either side of the membranes had fluid dispersion channels engraved on the cross-sectional 134
surface to allow for full distribution of fluid across the entire face of the membranes. A confining 135
pressure of 35 bara greater than the experiment pressure was applied to the core holder for each 136
experiment. The pressure gauges were zeroed before each experiment to ensure accurate and 137
consistent pressure readings across all experiments. The sapphire cell was used to visually monitor 138
the behavior of the NB sample and has a known volume (including all connection lines), Vcell, of 139
13.69 mL. It can withstand pressures up to 350 bara and temperatures up to 423.15 K. To prevent 140
gas trapping in any of its connections, the sapphire cell was configured to simulate a single-inlet 141
single-outlet cell by connecting valves to all its connection ports. Upon completion of each 142
experiment, the entire system was thoroughly cleaned with DI water and dried with air before 143
proceeding to the next experiment. 144

Before generating the NB, the entire system was evacuated for 1 hour. The system was 145
saturated with DI water (or NaCl brine) up to receiver accumulator #1 (2c in Figure 1) at the 146
experiment pressure. The sapphire cell and the top of receiver accumulators #2 and #3 (2d and 2e 147
in Figure 1) were filled with N2 at the experiment pressure. To generate the NB, N2 and DI water 148
(or NaCl brine) were co-injected (per the different configurations shown in Table 1) at a constant 149
flow rate through the porous membranes at the specified pressure, co-injection ratio, and total 150
injection flow rate. The co-injected fluids were received downstream of the porous membranes at 151
a constant refill flow rate (maintaining the system pressure) into receiver accumulator #1 until a 152
steady state was reached. After reaching a steady state (approximately 3 minutes for 500 mL/hr 153
and 15 minutes for 100 mL/hr), the co-injected fluids were then received by receiver accumulator 154
#2 at a constant refill flow rate. The duration of the co-injection was 60 minutes for 100 mL/hr and 155
12 minutes for 500 mL/hr. We posit that the formation of nanobubbles occurs in two main stages: 156
first, hydrodynamic mixing and gas snap-off across the membrane leads to the creation of 157
dispersed N2 bubbles in the aqueous phase that is supersaturated by N2, and secondly, the bulk 158
microbubbles are compressed to form bulk nanobubbles under elevated pressure conditions. 159
After the co-injection period, receiver accumulator #2 contained excess bulk N2 as well as 160
the N2 NB. The contents of receiver #2 were then injected through the sapphire cell into receiver 161
#3 at a constant flow rate. First, the N2 gas initially in the sapphire cell was displaced by the excess 162
bulk N2 from receiver #2. Then, the bulk N2 was further displaced by the N2 NB. We ensured the 163
cell contained only N2 NB with no trapped gas by injecting at least twice the cell volume of N2 164
NB into the cell. After filling the cell with the N2 NB, the top and bottom valves of the cell were 165
closed to isolate the cell from the other parts of the system. The sapphire cell then contained the 166
aqueous NB fluid sample at pressure, P1. 167

Stage 2: Depressurization and gas content measurement 168
Figure 2 shows a schematic of the experimental setup for measuring the gas content in the 169
generated N2 NB. The setup consists of a sapphire cell containing the NB sample, a piston 170
accumulator with a pressure gauge, and a glass beaker. 171
172
173
Figure 2. Schematic of the experimental setup to measure the gas content in the aqueous N2 NB 174
fluid. 175
176
The sapphire cell was connected to the accumulator via a stainless-steel tubing. The piston 177
of the accumulator was set at the top of the accumulator. The dead volumes of the tubing and the 178
accumulator were known. Before depressurizing the N2 NB sample, the tubing and dead volume 179
of the accumulator were evacuated for 15 minutes. Then, the N2 NB sample was gradually 180
depressurized. First, the top valve of the sapphire cell was slowly opened to fill the tubing with 181
depressurized N2 escaping the NB sample. Then, the top valve of the accumulator was slowly 182
opened to allow further escape of N2 from the NB sample into the accumulator. Finally, the bottom 183
valve of the accumulator was opened to gauge the displacement of the piston as the aqueous NB 184

fluid sample was depressurized or expanded. The water collected corresponded to the volume of 185
depressurized N2 in the aqueous NB fluid. The mass of the water collected is denoted as mw2, and 186
the pressure at the top side of the accumulator after depressurization is P2. Finally, the remaining 187
water (or brine) in the cell was collected and its mass mw3 was measured. The atmospheric 188
pressure, P3, during the experiment was 1.0135 bara. 189
The N2 gas content was calculated on the following basis: 190
1. There was a negligible amount of N2 in the remaining water phase in the sapphire cell because 191
the solubility of N2 in water at atmospheric pressure is small and because the presence of any 192
bubbles has a negligible impact on the gas content as shown later for NTA data. 193
2. The amount of water was corrected for the transfer of water to the expanded gas phase as mist. 194
The gas content, represented in units of mole per liter (mole of N2 in a volume of aqueous NB 195
fluid), was then calculated as shown below: 196
𝑥(𝑚𝑜𝑙/𝐿)=mole of 𝑁 (mol)
volume of NB sample (L) (1) 197
mole of N2(mol) =𝜌𝑉
𝑀𝑊=󰇧 𝜌
𝑀𝑊󰇨𝑃𝑉𝑍
𝑃𝑍(2) 198
where ρ1 is the density of N2 at the experimental pressure, V1 is the volume of N2 in the aqueous 199
NB fluid at experimental pressure, MW is the molecular weight of N2, P1 is the experimental 200
pressure, P2 is the depressurized pressure, V2 is the total volume of N2 at atmospheric pressure, Z1 201
is the compressibility factor of N2 at the experimental pressure, and Z2 is the compressibility factor 202
of N2 at atmospheric pressure. 203
The gas content data was compared to the thermodynamic solubility of N2 in water at 204
298.15 K [68] and N2 in NaCl brine at 303.15 K [69,70] to determine the solubility enhancement 205
factor of aqueous NB fluids. Studies showed that N2 solubility in NaCl brine at low molarities 206

(e.g., 1 M) is insensitive to temperature [69–71]. For each configuration shown in Table 1, the 207
procedure remained the same. The repeatability of the experiment was tested by repeating the 208
experiments three times at 104 bara for DI water. The standard deviation from these experiments 209
was applied to the remaining experiments as error bars. 210
2.3. Bubble size measurement for depressurized samples 211
The size distribution, number density, mean, and mode of the N2 NB were measured for 212
depressurized samples at atmospheric pressure using two light scattering techniques: dynamic light 213
scattering (DLS) and nanoparticle tracking analysis (NTA). The samples for the bubble size 214
measurement were generated using the same procedure described in Section 2.2. Upon isolating 215
the sapphire cell, however, the sample in the cell was depressurized to atmospheric pressure 216
similarly to the method of compression–decompression [31–33] for low-pressure bulk nanobubble 217
generation. The depressurized sample containing N2 NBs at atmospheric pressure was transferred 218
into glass vials and stored at room temperature. Bubble size measurements were performed 1, 2, 219
7, and 10 days after the NB formation. On day 1, the measurements were performed 1 hour after 220
depressurization, and on the subsequent days, the measurements were performed 26, 147, and 217 221
hours after depressurization. Before measuring the size distribution of the samples, DLS and NTA 222
measurements of the DI water sample were performed three times, and no particles were detected. 223
The DLS measurements used a ZEN3500 Zetasizer Nano ZS particle size analyzer 224
(Malvern Panalytical Ltd.). DLS is a non-invasive scattering technique that measures particle sizes 225
by capturing the random change in intensity of light scattered by particles undergoing Brownian 226
motion within an aqueous medium. The fluctuations in scattered light intensity are then translated 227
into particle sizes using the Stokes-Einstein equation: 228
𝑑=𝑘𝑇
3πη𝐷 (3) 229

where dh is the hydrodynamic diameter, kB is the Boltzmann constant, T is the temperature, η is 230
the dynamic viscosity of the aqueous phase, and D is the diffusion coefficient of particles in the 231
aqueous phase. 232
The Zetasizer Nano ZS can determine a particle size distribution within the range from 4 233
nm to 3 μm. The experiments were performed at 295.15 K to maintain consistent conditions and 234
with a refractive index of 1.33 for water and 1.0 for N2. The particle intensity distribution is 235
determined directly from the measurements and is then mathematically transformed into a number 236
distribution. The measurements were taken at a fixed scattering angle of 173 degrees and repeated 237
twice for each sample. 238
The NTA measurements used a NanoSight NS500 (Malvern Panalytical Ltd.). The NTA 239
technique, built upon dark-field microscopy (DFM), tracks individual particle trajectories to 240
compute sizes based on the Stokes-Einstein equation. The measurements were performed at room 241
temperature and the settings for screen gain, focus, camera level, and detection threshold were 242
optimized to ensure accurate detection of particles while minimizing noise. Each sample was 243
recorded three times and the duration of each capture was 30 seconds. One advantage of NTA over 244
DLS is its capability to determine the number density of particles in an aqueous medium. 245
The DLS and NTA measurements in this research were only for depressurized samples of 246
aqueous NB dispersion, and their application to high-pressure samples is currently not available. 247
Although the measurement conditions are different from the envisioned applications to high-248
pressure processes, the DLS and NTA data are useful to validate the samples of aqueous NB 249
dispersion and to observe the transient behavior of depressurized samples in an open system. Also, 250
low-pressure data serve as a reference for high-pressure data with a correlative capability of a 251
thermodynamic model in this research. 252

253
3. Results and discussion 254
3.1. Effect of pressure and salinity 255
Tables 2 and 3 show the measured gas content data in the experiments for aqueous N2 NB 256
fluid in DI water and 50,000 ppm NaCl brine, respectively. Figure 3 presents the gas content data 257
in mol/L for DI water and NaCl brine at a constant co-injection ratio of 50% N2 + 50% DI water 258
(or NaCl brine), a total injection flow rate of 100 mL/hr, and a 5 μm membrane. The red squares 259
and blue triangles in Figure 3 represent the inherent solubility of N2 in water and NaCl brine, 260
respectively. The error bars in Figure 3 represent an estimate of the variability in the experimental 261
measurements. Note that xN2 in Tables 2 and 3 and Figure 3 represents the overall N2 concentration 262
including the dispersion of N2 bubbles and the dispersion of N2 molecules in the external aqueous 263
phase. 264
Table 2. Measured gas content data for aqueous N2 NB in DI water at 295.15 K. 265
P1
(bara)
P2
(bara)
mw2
(g)
mw3
(g)
Vcell
(mL)
xN2
(mol/L)
Inherent
solubility (mol/L)
Solubility
enhancement
34.59
1.22
4.54
10.765 ± 3
13.69
0.0515
0.0112
4.59
68.93
1.29
11.4
10.930 ± 3
13.69
0.0801
0.0226
3.54
104.2
1.15
23.58
11.405 ± 3
13.69
0.1118
0.0432
2.59
103.3
1.29
19.49
11.310 ± 3
13.69
0.1098
0.0425
2.58
103.4
1.29
21.22
11.295 ± 3
13.69
0.1165
0.0425
2.74
138.2
1.22
32.01
11.040 ± 3
13.69
0.1505
0.0526
2.86
207.8
1.22
57.41
11.834 ± 3
13.69
0.2401
0.0796
3.02
277.1
1.22
71.92
12.040 ± 3
13.69
0.2922
0.1000
2.92
266
Table 3. Measured gas content data for aqueous N2 NB in 50,000 ppm NaCl brine at 295.15 K. 267
P1
(bara)
P2
(bara)
mw2
(g)
mb3
(g)
Vcell
(mL)
xN2
(mol/L)
Inherent
solubility (mol/L)
Solubility
enhancement
47.07
1.22
3.53
11.155 ± 3
13.69
0.0463
0.0167
2.77
69.82
1.22
9.01
11.850 ± 3
13.69
0.0637
0.0258
2.47
103.0
1.22
19.98
10.800 ± 3
13.69
0.1075
0.0255
4.22
138.5
1.29
27.62
11.530 ± 3
13.69
0.1402
0.0349
4.02
207.8
1.29
43.66
11.800 ± 3
13.69
0.2008
0.0509
3.94
274.0
1.36
66.55
11.980 ± 3
13.69
0.3037
0.0648
4.69
268

The results show that as pressure increased from 35 to 277 bara, the gas content increased 269
significantly for both DI water and NaCl brine. Note that this figure shows the N2 concentration 270
on a logarithmic scale. The gas content in aqueous NB dispersion with NaCl brine was close to 271
that with DI water across all the pressures tested. Thus, the 0.88 M NaCl brine had no significant 272
impact on the N2 gas content in the aqueous NB sample. The N2 concentration in the N2 NB 273
dispersion with NaCl brine was 2.5 times greater than the inherent solubility at 69.8 bara, and the 274
enhancement factor was as large as 4.7 at 274.0 bara as shown in Table 3. An extrapolation of the 275
gas content data to atmospheric pressure for DI water gives an N2 gas content of 0.0121 mol/L (or 276
4.7 × 10-4 mole fraction of N2). 277
278
279
Figure 3. N2 gas content in DI water and 50,000 ppm NaCl brine. The red squares represent the 280
thermodynamic solubility of N2 in water [68]. The blue triangles represent the thermodynamic 281
solubility of N2 in NaCl brine [69,70]. 282

283
3.2. Effect of coinjection ratio, total injection rate, and membrane pore diameter 284
Figure 4 shows the effects of co-injection ratio, total injection flow rate, and membrane 285
pore diameter at different pressures on the gas content of N2 in the aqueous NB sample (DI water). 286
Overall, the results show negligible impacts of co-injection ratio, total injection flow rate, and 287
membrane pore diameter on the N2 gas content compared to the baseline experiments. These 288
results are in contradiction to the results reported for low-pressure experiments [4,35,45] about the 289
effect of changing the co-injection ratios or pore membrane diameters on gas content data. This is 290
likely because these effects were significant and noticeable at low pressures and then became less 291
significant at high pressures; that is, increasing the pressure had the most significant impact on the 292
N2 gas content in DI water and NaCl brine among the experimental parameters tested in this 293
research. 294
295

296
Figure 4. N2 gas content in DI water at different operating conditions (co-injection ratio, total 297
injection flow rate, and membrane pore diameter) and different pressures. The baseline case used 298
a co-injection rate of 50% N2 + 50% DI water through a 5 μm membrane at a total injection flow 299
rate of 100 mL/hr. 300
301
3.3. Bubble size measurement using DLS and NTA 302
Figure 5 shows the size distributions of depressurized samples for aqueous NB dispersion 303
of N2 in DI water based on DLS. Table 4 shows the mean and mode bubble sizes, polydispersity 304
indices (PDI), and diffusion coefficients from the DLS measurements on days 1, 2, 7, and 10. 305
Before the measurements, the DI water used to generate the NB was checked for the presence of 306
nanosized impurities and none were detected. 307
308

Table 4. Mean, mode, PDI, and diffusion coefficients of the aqueous N2 NB sample using DLS. 309
Day Bubble size,
mean (nm)
Bubble size,
mode (nm)
PDI Diffusion
coefficient (m
2
/s)
1
235.1 ±
7.4
3
158.6
±
5.45
0.354 ±
0.05
(
1.93
±
0.0
6
)
×
10
-12
2 169.6 ± 5.09 132.4 ± 14.9 0.112 ± 0.16
(
2.67
±
0.08
)
×
10
-12
7
212.3 ±
6.08
134.0
±
20.9
0.359 ±
0.01
(
2.13
±
0.06
)
×
10
-12
10 156.7 ± 10.9 107.7 ± 7.28 0.243 ± 0.26
(
2.90
±
0.
20
)
×
10
-12
310
311
Figure 5. Size distribution of the aqueous N2 NB sample using DLS. 312
313
The DLS data show notable trends in bubble size over time. On day 1, the mean bubble 314
size was 235.1 nm, which decreased to 169.6 nm on day 2, followed by an increase to 212.3 nm 315
on day 7, and a subsequent decrease to 156.7 nm on day 10. The mode of the bubble size was 316
158.6, 132.4, 134.0, and 107.7 nm for days 1, 2, 7, and 10, respectively. The difference in behavior 317
between the mean and mode bubble sizes comes from the transient distribution of bubble sizes as 318
given in Figure 5. The PDI data also reflect the transient size distribution using DLS. On day 1, 319
the PDI was 0.354, correlating to a mean size significantly larger than the mode size. This suggests 320

the presence of a substantial number of larger bubbles contributing to the scattered light signal. 321
However, on day 2, the PDI dropped to 0.112, indicating the absence of significantly larger 322
bubbles. On day 7, the PDI increased to 0.359, possibly indicating the coalescence of smaller 323
bubbles into larger bubbles, causing the mean size to become greater than the mode size. Finally, 324
on day 10, the PDI decreased again to 0.243, further confirming the reduction in the number of 325
larger particles, and thus a reduction in the mean bubble size. The PDI behavior gives credence to 326
the presence of gas-filled nanobubbles which tend to coalesce into larger bubbles and eventually 327
dissipate either through bursting or rising to the surface. 328
Figure 6 shows the laser-illuminated N2 nanobubbles using NTA at atmospheric pressure 329
on days 1, 2, 7, and 10. The detected nanobubbles are shown as white dots on a black background. 330
One advantage of NTA over DLS is its capability to determine a bubble number density in the 331
sample. Figure 7 shows the size distribution of the N2 NB in DI water. Table 5 gives the mean and 332
mode bubble sizes, bubble number densities, and diffusion coefficients from the NTA 333
measurements. The transient behavior of NB size distribution is also shown in Figure 8. Like the 334
DLS measurements, the DI water used to generate the NB for the NTA measurements was checked 335
for the presence of nanosized impurities and no impurities were detected. 336
Figures 7 and 8 show that the overall behavior of aqueous NB dispersion became more 337
stabilized over time, suggesting that the numerical results given in Tables 4 and 5 should be 338
carefully understood together with the overall trends shown in Figures 5, 7, and 8. 339
Table 5. Mean, mode, bubble number density, and diffusion coefficients of the aqueous N2 NB 340
sample using NTA. 341
Day Bubble size,
mean (nm)
Bubble size,
mode (nm)
Bubble number density
(bubbles/mL)
Diffusion
coefficient (m
2
/s)
1
101.8 ± 11.9
97.9
0
± 14.6
(9.25 ± 0.63)
×
10
7
(
4.74
± 0.
92
)
×
10
-12
2 116.5 ± 20.4 103.2 ± 11.0
(2.56 ± 1.39)
×
10
8
(
4.20
±
1.12
)
×
10
-12
7
103.2 ± 6.30
84.7
0
± 12.5
(5.85 ± 2.18)
×
10
7
(
4.45
±
0.47
)
×
10
-12
10 128.0 ± 17.8 102.1 ± 8.60
(1.72 ± 0.69)
×
10
7
(3.67 ± 0.78)
×
10
-12

342
(a)
Day 1
(b)
Day 2
(c)
Day 7
(d)
Day 10
Figure 6. Laser-illuminated N2 NB in DI water using NTA. 343
344

345
Figure 7. Size distribution of the aqueous N2 NB sample using NTA. 346
347

348
Figure 8. NB number density of the aqueous N2 NB samples using NTA. 349
350
On day 1, the mean bubble size was 101.8 nm, and the mode bubble size was 97.9 nm with 351
a bubble concentration of 9.25 × 107 bubbles/mL. There was a close agreement between the mean 352
and mode bubble sizes. On day 2, both the mean and mode bubble sizes increased to 116.5 nm and 353
103.2 nm, respectively, with a notably higher number density of 2.56 × 108 bubbles/mL. The 354
results from days 1 and 2 show a significant level of transient behavior of aqueous NB dispersion 355
with the possibilities of bubble coalescence, growth, and nucleation over time. On day 7, the mean 356
bubble size slightly decreased to 103.2 nm, and the mode bubble size decreased to 84.7 nm. The 357
number density was 5.85 × 107 bubbles/mL. Finally, on day 10, the mean bubble size increased to 358
128.0 nm, while the mode bubble size also increased to 102.1 nm with a number density of 1.72 × 359
107 bubbles/mL. 360

Figure 9 compares DLS and NTA measurements at atmospheric pressure in terms of mean 361
and mode bubble sizes. NTA measurements show a closer agreement between the mean and mode 362
sizes than DLS measurements. This is because of the inherent difference in the measurement 363
principles of both measurement techniques. That is, NTA measures the rate of Brownian motion 364
of the bubbles while DLS measures the fluctuations in the scattered light intensity of the bubbles 365
undergoing Brownian motion. This fundamental difference leads to NTA being less susceptible to 366
polydispersity, thus, showing a closer agreement between the mean and mode bubble sizes. 367
368
369
Figure 9. Mean and mode of the aqueous N2 NB sample using DLS and NTA. 370
371
3.4. Thermodynamic analysis of aqueous NB dispersion of N2 372
The most important benefit of using thermodynamics to analyze the experimental data in 373
this research is that a thermodynamic model can give an internally consistent set of properties for 374

the entire experimental conditions, which enables understanding the overall behavior of aqueous 375
NB dispersion. Also, such properties include unmeasurable ones in high-pressure experiments, 376
such as phase composition and capillary pressure. As described previously, the experimental 377
procedure directly specifies the temperature, total volume, and pressure of a closed system of 378
aqueous nanobubble dispersion of N2. Then, the constant mass expansion of the system gives the 379
mole numbers of water and N2. With these experimentally measurable variables, the most 380
convenient approach to analyzing the experimental data is to minimize the Helmholtz free energy 381
using a thermodynamic model [72]. Then, a solution for the minimization problem gives 382
thermodynamic properties for the dispersion of N2-rich nanobubbles in the aqueous phase that is 383
supersaturated by N2 at the experimental conditions. 384
The traditional two-phase system with a planar interface requires NC + 2 variables to be 385
set, where NC is the number of components; however, the current problem requires setting NC + 3 386
variables. The additional variable comes from the generalization to allow for different pressures 387
for the two phases (i.e., capillary pressure). In this research, the NC + 3 variables are temperature, 388
total volume, aqueous-phase pressure, and mole numbers of the components (water and N2). With 389
these specifications, this section describes properties of the aqueous NB dispersions generated in 390
the experiments using a single thermodynamic model, which gives internal consistency of the 391
calculated properties. We recognize limitations of the modeling; for example, the binary system 392
(water and N2) requires a uniform size of bubbles, and the mole numbers of water and N2 (from 393
the constant mass expansion) contain uncertainty. Therefore, thermodynamic properties given for 394
aqueous NB dispersions in this section must be understood as apparent values satisfying 395
experimentally specified conditions and material balance. 396

The modeling approach largely follows Achour and Okuno [72] and Achour et al. [73], but 397
we have extended it to cover all experimental conditions in this research. The GERG-2008 398
equation of state (EOS, [74]) was used because the EOS used in this research should be reliable in 399
constructing the Helmholtz free energy surface in metastable regions [75,76]; i.e., the aqueous 400
phase supersaturated by N2. The EOS was first calibrated using experimental data for water-N2 at 401
298.15, 308.15, 318.15, and 323.15 K from 80 to 1015 bara [77]. Then, it was calibrated for NaCl 402
brine-N2 using Smith et al. [69] and O’Sullivan and Smith [70], in which 1 M NaCl brine was used 403
at 303.15, 324.65, 375.65, and 398.15 K from 12 to 608 bara. Although the experimental 404
temperature in this research, 295.15 K, is not contained in the data of Smith et al. [69] and 405
O’Sullivan and Smith [70], the N2 solubility in NaCl brine at small molarities (e.g., 1 M) is 406
insensitive to temperature. Also, the NaCl concentration in this research, 0.88 M, is close to the 407
NaCl concentration, 1 M, for the data. Figure 10 compares the calculated results using the GERG-408
2008 EOS with the experimental data in the literature for water-N2 and NaCl brine-N2. Results 409
show good agreement between the EOS results and the data; therefore, the GERG-2008 EOS was 410
successfully calibrated. Supplementary Material gives a detailed description of the GERG-2008 411
EOS model and parameters for the water-N2 and NaCl brine-N2 mixtures. 412
413

414
Figure 10. Calibrated GERG-2008 EOS model for the N2/water [77,78] and N2/NaCl brine 415
[69,70] solubility data at different pressures and temperatures. 416
417
The experimental data given in Tables 2 and 3 were then used to solve the calibrated EOS 418
for properties of aqueous NB dispersion of N2 for the given temperature, total volume, mole 419
numbers for water/brine and N2, and external-phase pressure. Among these input variables, the 420
water mole numbers based on mw3 (Table 2) and mb3 (Table 3) were quite influential to the 421
resulting diameter of bubbles. Tables 2 and 3 show that the uncertainty of mw3 (and mb3) was ±3 422
g. Even a minor variation (e.g., 0.1 g) in mw3 (or mb3) significantly influenced the calculated 423
apparent bubble diameter by one order of magnitude; therefore, it was not possible to quantitatively 424
determine an apparent bubble diameter for these data with an order-of-magnitude accuracy using 425
thermodynamic calculations only. Therefore, we allowed for adjustment in mole numbers of the 426
two components within the uncertainty range such that the Helmholtz free energy was minimized 427
while satisfying the specified temperature, total volume, and external pressure. We confirmed that 428
such adjustments resulted in overall compositions within the uncertainty range stated above. 429

Figures 11 and 12 show the results from the GERG-2008 EOS, such as bubble diameter, 430
bubble number density, supersaturation of aqueous phase by N2, the fraction of N2 as bubble 431
dispersion, and capillary pressure, for the N2 NB fluid in DI water and NaCl brine, respectively. 432
The error bars were determined as half the difference between the smallest and largest values at 433
104 bara (for DI water) since the experiment was repeated three times at this pressure. For the 434
aqueous supersaturation levels (Figures 11c and 12c), the N2 concentration in the aqueous phase 435
was compared with the inherent solubility of N2 based on the GERG-2008 EOS. For Figures 11d 436
and 12d, the mole number of N2 as bubbles was divided by the total mole number of N2 for each 437
sample. 438
Figures 11ab and 12ab show that the calculated diameter decreased, and the number density 439
of bubbles increased with increasing external pressure. For the DI water case, the extrapolation to 440
atmospheric pressure using the two lowest pressure data yields a bubble diameter of 158 nm. This 441
extrapolated diameter lies within the range of measured bubble diameters, 50-400 nm, at 442
atmospheric pressure in the literature [1,21]. Also see Figures 5, 7, and 9 for the data measured in 443
this research. Figures 11cd and 12cd show that a large fraction of the N2 in the system is 444
molecularly dissolved in the external aqueous phase. That is, the existence of bubbles increases 445
the N2 content in the system by increasing the molecule dispersion (supersaturation) in the aqueous 446
phase much more than by containing N2 as bubbles. The presence of bubbles in aqueous NB fluid 447
tends to increase the level of supersaturation in the external aqueous phase with capillary pressure 448
(Figures 11e and 12e). The results indicate that this supersaturation is the main contribution to the 449
amount of N2 in the aqueous NB fluid, which has fundamental impacts on the research and 450
development of NB technologies. 451

Figure 3 shows that the N2 content did not substantially change between DI water and NaCl 452
brine. However, comparison of Figures 11 and 12 indicates that the NaCl salinity may have 453
reduced the amount of N2 that was molecularly dissolved, which required increasing the amount 454
of N2 as bubbles to satisfy the material balance in the closed system of the experiments in this 455
research. 456

457
Figure 11. Bubble diameter, bubble number density, N2 mole fraction, fraction of N2 contained in 458
bubbles, and capillary pressure of aqueous NB fluid in DI water at 295.15 K for pressures up to 459
277 bara. 460
461

462
Figure 12. Bubble diameter, bubble number density, N2 mole fraction, fraction of N2 contained in 463
bubbles, and capillary pressure of aqueous NB fluid in NaCl brine at 295.15 K for pressures up 464
to 274 bara. 465
466
467

4. Conclusions 468
This paper presented a new set of experimental data for aqueous NB dispersions of N2 at elevated 469
pressures of up to 277 bara using N2 and DI water or 0.88 M NaCl brine with specially designed 470
stainless-steel porous membranes. The N2 content in the generated NB sample was investigated 471
for different parameters, such as pressure, salinity, co-injection ratio, total injection flow rate, and 472
membrane pore diameter. The experimental results were supplemented with the GERG-2008 EOS 473
model to give a qualitative overview of the characteristics of the aqueous NB fluid. The main 474
conclusions are as follows: 475
1. The N2 content in aqueous NB dispersion increased significantly with pressure. At 277 bara, 476
for example, the inherent solubility of N2 in DI water is 0.10 mol/L, but the N2 content was 477
enhanced to 0.29 mol/L by aqueous NB dispersion with DI water. With 0.88 M NaCl brine, 478
the inherent solubility of N2 is 0.065 mol/L at 274 bara, but the N2 content was enhanced to 479
0.30 mol/L by aqueous NB dispersion. The impact of NaCl salinity on the N2 content in 480
aqueous NB dispersion was not observed for high-pressure experiments in this research. 481
2. The N2 content in aqueous NB dispersion was insensitive to injection parameters, such as the 482
total injection rate and the co-injection ratio, in this research. In particular, using a 2 μm 483
membrane resulted in a similar gas content as using a 5 μm membrane. 484
3. Analysis of the experimental data using the GERG-2008 EOS showed that the apparent 485
diameter of N2 NBs ranged from 14 to 120 nm for DI water and 5 to 115 nm for 0.88 M NaCl 486
brine under the experimental conditions. Additionally, the analysis indicated that NBs were 487
not the main storage of N2, but they enabled the supersaturation of the aqueous phase by N2 488
enhancing the N2 content in the system. 489
4. The DLS and NTA data measured for depressurized samples of aqueous NB dispersion of N2 490
in this research showed transient behavior over 10 days. Number densities and size 491

distributions of NBs were consistent with the reported data in the literature. 492
493
Declaration of Competing Interest 494
The authors declare that they have no known competing financial interests or personal 495
relationships that could have appeared to influence the work reported in this paper. 496
497
Acknowledgements 498
We gratefully acknowledge the members of the Energi Simulation Industrial Affiliate Program on 499
Carbon Utilization and Storage (ES Carbon UT) at the Center for Subsurface Energy and the 500
Environment at the University of Texas at Austin for their support. Ryosuke Okuno holds the 501
Pioneer Corporation Faculty Fellowship in Petroleum Engineering at the University of Texas at 502
Austin. 503
504
Nomenclature 505
Abbreviations 506
CO2 carbon dioxide 507
DFM dark-field microscopy 508
DI deionized 509
DLS dynamic light scattering 510
EOR enhanced oil recovery 511
EOS equation of state 512
GCS geological carbon sequestration 513
LPBC Laplace Pressure Bubble Catastrophe 514
N2 nitrogen 515
NaCl sodium chloride 516
NB nanobubble 517
NC number of components 518
NTA nanoparticle tracking analysis 519
PDI polydispersity index 520
521

Symbols 522
D diffusion coefficient 523
dh hydrodynamic diameter 524
kB Boltzmann constant 525
m mass 526
MW molecular weight 527
P pressure 528
T temperature 529
V volume 530
x gas content 531
Z compressibility factor 532
ρ density 533
η dynamic viscosity 534
535
Subscripts 536
b brine 537
cell sapphire cell 538
w water 539
540
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