Bubble solutions are of growing interest because of their various technological applications in surface cleaning, water treatment, and agriculture. However, their physicochemical properties, such as the stability and interfacial charge of bubbles, are not fully understood yet. In this study, the kinetics of radii in aqueous microbubble solutions are experimentally investigated, and the results are discussed in the context of Ostwald ripening. The obtained distributions of bubble radii scaled by mean radius and total number were found to be time-independent during the observation period. Image analysis of radii kinetics revealed that the average growth and shrinkage speed of each bubble is governed by diffusion-limited Ostwald ripening, and the kinetic coefficient calculated using the available physicochemical constants in the literature quantitatively agrees with the experimental data. Furthermore, the cube of mean radius and mean volume exhibit a linear time evolution in agreement with the Lifshitz–Slezov–Wagner (LSW) theory. The coefficients are slightly larger than those predicted using the LSW theory, which can be qualitatively explained by the effect of finite volume fraction. Finally, the slowdown and pinning of radius in the shrinkage dynamics of small microbubbles are discussed in detail.
REFERENCES
1.
M.
Alheshibri
, J.
Qian
, M.
Jehannin
, and V. S. J.
Craig
, “A history of nanobubbles
,” Langmuir
32
, 11086
–11100
(2016
).2.
F.
Eklund
and J.
Swenson
, “Stable air nanobubbles in water: The importance of organic contaminants
,” Langmuir
34
, 11003
–11009
(2018
).3.
L.
Zhou
, S.
Wang
, L.
Zhang
, and J.
Hu
, “Generation and stability of bulk nanobubbles: A review and perspective
,” Curr. Opin. Colloid Interface Sci.
53
, 101439
(2021
).4.
L.
Rayleigh
, “On the pressure developed in a liquid during the collapse of a spherical cavity
,” London, Edinburgh Dublin Philos. Mag. J. Sci.
34
, 94
–98
(1917
).5.
M. S.
Plesset
, “The dynamics of cavitation bubbles
,” J. Appl. Mech.
16
, 277
–282
(1949
).6.
P. S.
Epstein
and M. S.
Plesset
, “On the stability of gas bubbles in liquid-gas solutions
,” J. Chem. Phys.
18
, 1505
–1509
(1950
).7.
M. S.
Plesset
and S. S.
Sadhal
, “On the stability of gas bubbles in liquid-gas solutions
,” in Mechanics and Physics of Bubbles in Liquids
, edited by L.
van Wijngaarden
(Springer
, Dordrecht, The Netherlands
, 1982
), pp. 133
–141
.8.
P. B.
Duncan
and D.
Needham
, “Test of the Epstein–Plesset model for gas microparticle dissolution in aqueous media: Effect of surface tension and gas undersaturation in solution
,” Langmuir
20
, 2567
–2578
(2004
).9.
S.
Kentish
, J.
Lee
, M.
Davidson
, and M.
Ashokkumar
, “The dissolution of a stationary spherical bubble beneath a flat plate
,” Chem. Eng. Sci.
61
, 7697
–7705
(2006
).10.
J.-Y.
Kim
, M.-G.
Song
, and J.-D.
Kim
, “Zeta potential of nanobubbles generated by ultrasonication in aqueous alkyl polyglycoside solutions
,” J. Colloid Interface Sci.
223
, 285
–291
(2000
).11.
F. Y.
Ushikubo
, T.
Furukawa
, R.
Nakagawa
, M.
Enari
, Y.
Makino
, Y.
Kawagoe
, T.
Shiina
, and S.
Oshita
, “Evidence of the existence and the stability of nano-bubbles in water
,” Colloids Surf., A
361
, 31
–37
(2010
).12.
J.
Qiu
, Z.
Zou
, S.
Wang
, X.
Wang
, L.
Wang
, Y.
Dong
, H.
Zhao
, L.
Zhang
, and J.
Hu
, “Formation and stability of bulk nanobubbles generated by ethanol-water exchange
,” ChemPhysChem
18
, 1345
–1350
(2017
).13.
J.
Jin
, Z.
Feng
, F.
Yang
, and N.
Gu
, “Bulk nanobubbles fabricated by repeated compression of microbubbles
,” Langmuir
35
, 4238
–4245
(2019
).14.
W. A.
Ducker
, “Contact angle and stability of interfacial nanobubbles
,” Langmuir
25
, 8907
–8910
(2009
).15.
B. H.
Tan
, H.
An
, and C.-D.
Ohl
, “How bulk nanobubbles might survive
,” Phys. Rev. Lett.
124
, 134503
(2020
).16.
P. A.
Satpute
and J. C.
Earthman
, “Hydroxyl ion stabilization of bulk nanobubbles resulting from microbubble shrinkage
,” J. Colloid Interface Sci.
584
, 449
–455
(2021
).17.
B.
Dollet
and D.
Lohse
, “Pinning stabilizes neighboring surface nanobubbles against Ostwald ripening
,” Langmuir
32
, 11335
–11339
(2016
).18.
S.
Michelin
, E.
Guérin
, and E.
Lauga
, “Collective dissolution of microbubbles
,” Phys. Rev. Fluids
3
, 043601
(2018
).19.
X.
Zhu
, R.
Verzicco
, X.
Zhang
, and D.
Lohse
, “Diffusive interaction of multiple surface nanobubbles: Shrinkage, growth, and coarsening
,” Soft Matter
14
, 2006
–2014
(2018
).20.
W.
Ostwald
, “Studien über die bildung und umwandlung fester körper. 1. Abhandlung: Übersättigung und überkaltung
,” Z. Phys. Chem.
22U
, 289
–330
(1897
).21.
22.
R.
Shimizu
and H.
Tanaka
, “A novel coarsening mechanism of droplets in immiscible fluid mixtures
,” Nat. Commun.
6
, 7407
(2015
).23.
P. K.
Rastogi
and A. J.
Ardell
, “The coarsening behavior of the γ′ precipitate in nickel-silicon alloys
,” Acta Metall.
19
, 321
–330
(1971
).24.
D. H.
Jack
and R. W. K.
Honeycombe
, “Age hardening of an Fe-Ti-Si alloy
,” Acta Metall.
20
, 787
–796
(1972
).25.
T.
Hirata
and D. H.
Kirkwood
, “The prediction and measurement of precipitate number densities in a nickel-6.05 wt.% aluminium alloy
,” Acta Metall.
25
, 1425
–1434
(1977
).26.
Y.
Seno
, Y.
Tomokiyo
, K.
Oki
, and T.
Eguchi
, “Coarsening process of Co precipitates in Cu–Co alloys
,” Trans. Jpn. Inst. Met.
24
, 491
–498
(1983
).27.
N. C.
Lautze
, T. W.
Sisson
, M. T.
Mangan
, and T. L.
Grove
, “Segregating gas from melt: An experimental study of the Ostwald ripening of vapor bubbles in magmas
,” Contrib. Mineral. Petrol.
161
, 331
–347
(2011
).28.
A. S.
Kabalnov
, A. V.
Pertzov
, and E. D.
Shchukin
, “Ostwald ripening in emulsions: I. Direct observations of Ostwald ripening in emulsions
,” J. Colloid Interface Sci.
118
, 590
(1987
).29.
J.
Weiss
, N.
Herrmann
, and D. J.
McClements
, “Ostwald ripening of hydrocarbon emulsion droplets in surfactant solutions
,” Langmuir
15
, 6652
–6657
(1999
).30.
T.
Sakai
, K.
Kamogawa
, K.
Nishiyama
, H.
Sakai
, and M.
Abe
, “Molecular diffusion of oil/water emulsions in surfactant-free conditions
,” Langmuir
18
, 1985
–1990
(2002
).31.
P.
Taylor
, “Ostwald ripening in emulsions: Estimation of solution thermodynamics of the disperse phase
,” Adv. Colloid Interface Sci.
106
, 261
–285
(2003
).32.
S.
Mun
and D. J.
McClements
, “Influence of interfacial characteristics on Ostwald ripening in hydrocarbon oil-in-water emulsions
,” Langmuir
22
, 1551
–1554
(2006
).33.
S.
Ariyaprakai
and S. R.
Dungan
, “Influence of surfactant structure on the contribution of micelles to Ostwald ripening in oil-in-water emulsions
,” J. Colloid Interface Sci.
343
, 102
–108
(2010
).34.
I. M.
Lifshitz
and V. V.
Slyozov
, “Kinetics of diffusive decomposition of supersaturated solid solutions
,” J. Exp. Theor. Phys.
8
, 331
(1959
).35.
I. M.
Lifshitz
and V. V.
Slyozov
, “The kinetics of precipitation from supersaturated solid solutions
,” J. Phys. Chem. Solids
19
, 35
(1961
).36.
C.
Wagner
, “Theorie der alterung von niederschlägen durch umlösen (Ostwald-Reifung)
,” Z. Elektrochem., Ber. Bunsengesellschaft Phys. Chem.
65
, 581
–591
(1961
).37.
D. V.
Alexandrov
, “Kinetics of diffusive decomposition in the case of several mass transfer mechanisms
,” J. Cryst. Growth
457
, 11
–18
(2017
).38.
P. W.
Voorhees
, “The theory of Ostwald ripening
,” J. Stat. Phys.
38
, 231
–252
(1985
).39.
M.
Marder
, “Correlations and droplet growth
,” Phys. Rev. Lett.
55
, 2953
–2956
(1985
).40.
M.
Marder
, “Correlations and Ostwald ripening
,” Phys. Rev. A
36
, 858
–874
(1987
).41.
A.
Baldan
, “Review progress in Ostwald ripening theories and their applications to nickel-base superalloys Part I: Ostwald ripening theories
,” J. Mater. Sci.
37
, 2171
–2202
(2002
).42.
A. J.
Ardell
, “The effect of volume fraction on particle coarsening: Theoretical considerations
,” Acta Metall.
20
, 61
–71
(1972
).43.
A. D.
Brailsford
and P.
Wynblatt
, “The dependence of Ostwald ripening kinetics on particle volume fraction
,” Acta Metall.
27
, 489
–497
(1979
).44.
K.
Tsumuraya
and Y.
Miyata
, “Coarsening models incorporating both diffusion geometry and volume fraction of particles
,” Acta Metall.
31
, 437
–452
(1983
).45.
J. A.
Marqusee
and J.
Ross
, “Theory of Ostwald ripening: Competitive growth and its dependence on volume fraction
,” J. Chem. Phys.
80
, 536
(1984
).46.
Y.
Enomoto
, M.
Tokuyama
, and K.
Kawasaki
, “Finite volume fraction effects on Ostwald ripening
,” Acta Metall.
34
, 2119
–2128
(1986
).47.
J. H.
Yao
, K. R.
Elder
, H.
Guo
, and M.
Grant
, “Theory and simulation of Ostwald ripening
,” Phys. Rev. B
47
, 14110
–14125
(1993
).48.
J. H.
Yao
, K. R.
Elder
, H.
Guo
, and M.
Grant
, “Late stage droplet growth
,” Physica A
204
, 770
–788
(1994
).49.
J.
Schmelzer
and F.
Schweitzer
, “Ostwald ripening of bubbles in liquid-gas solutions
,” J. Non-Equilib. Thermodyn.
12
, 255
–270
(1987
).50.
V. V.
Slezov
, A. S.
Abyzov
, and Z. V.
Slezova
, “Kinetics of the phase separation of a low-viscosity liquid supersaturated with gas at the intermediate and later stages
,” Colloid J.
67
, 85
–96
(2005
).51.
H.
Watanabe
, M.
Suzuki
, H.
Inaoka
, and N.
Ito
, “Ostwald ripening in multiple-bubble nuclei
,” J. Chem. Phys.
141
, 234703
(2014
).52.
H.
Watanabe
, H.
Inaoka
, and N.
Ito
, “Ripening kinetics of bubbles: A molecular dynamics study
,” J. Chem. Phys.
145
, 124707
(2016
).53.
O. D.
Cima
, C.
Rocha
, A.
Teixeira
, and B.
Wienke
, “Ostwald ripening for air bubbles and decompression illness: Phenomenological aspects
,” arXiv 1806.05673v1 (2018
).54.
C. M. d.
Rocha
, “Evolution of air bubbles in glycerol/water mixtures by Ostwald ripening
,” Ph.D. thesis, Universidade Federal de Viçosa
, 2018
.55.
Y.
Uematsu
, D. J.
Bonthuis
, and R. R.
Netz
, “Nanomolar surface-active charged impurities account for the zeta potential of hydrophobic surfaces
,” Langmuir
36
, 3645
–3658
(2020
).56.
P.-G.
de Gennes
, F.
Brochard-Wyart
, and D.
Quéré
, Capillarity and Wetting Phenomena
(Springer
, New York
, 2004
).57.
Y.
Marcus
, Ions in Solution and Their Solvation
(John Wiley & Sons, Inc.
, 2015
).58.
R.
Battino
, T. R.
Rettich
, and T.
Tominaga
, “The solubility of nitrogen and air in liquids
,” J. Phys. Chem. Ref. Data
13
, 563
–600
(1984
).59.
B.
Giron
, B.
Meerson
, and P. V.
Sasorov
, “Weak selection and stability of localized distributions in Ostwald ripening
,” Phys. Rev. E
58
, 4213
–4216
(1998
).60.
B.
Meerson
, “Fluctuations provide strong selection in Ostwald ripening
,” Phys. Rev. E
60
, 3072
–3075
(1999
).61.
L.
Liebermann
, “Air bubbles in water
,” J. Appl. Phys.
28
, 205
–211
(1957
).62.
63.
R.
Sander
, “Compilation of Henry’s law constants (version 4.0) for water as solvent
,” Atmos. Chem. Phys.
15
, 4399
–4981
(2015
).64.
Y.
Uematsu
, D. J.
Bonthuis
, and R. R.
Netz
, “Charged surface-active impurities at nanomolar concentration induce Jones–Ray effect
,” J. Phys. Chem. Lett.
9
, 189
–193
(2017
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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