# From Bubbles to Nanobubbles

^{*}

## Abstract

**:**

## 1. Introduction

_{eq}is given by the following equation:

_{bubble}is the volume of the bubble, which also includes the bubble shell if the bubble is covered by a bubble shell.

## 2. Historical Definition of the Problem

_{c}just before the liquid raptures. At this point, the energy has a maximum value, ΔE

_{max}, which is formulated by Gibbs as:

_{c}is the pressure difference across the interface at the critical radius of the bubble.

_{∞}the gas concentration far away from the bubble and with c

_{s}the gas concentration at the bubble–liquid interface. In an undersaturated solution, c

_{∞}< c

_{s}, the NBs should dissolve away if the ambient pressure p

_{∞}is sufficiently high. In an oversaturated solution, c

_{∞}> c

_{s}, the NBs should grow, then rise and burst. In an even solution, c

_{∞}= c

_{s}, the system is unstable, and the slightest disturbance will cause the bubble to either expand or to dissolve. Nevertheless, experience defies this prediction.

_{o}at t = 0, and D is the mass diffusivity. Since a bubble in a liquid has only one surface, the Laplace equation reduces by a factor of 2:

_{H}is the Henry constant. By neglecting the second term on the left-hand side of Equation (5), Epstein and Plesset [4] found a solution that takes on the form:

_{s}/ρ = 0.02 and D = 2 × 10

^{−9}m

^{2}/s. Figure 2 shows the growth and shrinkage of an NB of R

_{o}= 100 nm, and Table 1 records the fate of different size bubbles according to this theory.

## 3. Explanations for NB Longevity

_{o}under a uniform side force F will cause a relative change of that area by the following calculation [32]:

^{−}will migrate to the surface of the bubble, whereas hydrophilic ones such as OH

^{−}will not.

_{r}is small, by increasing the pressure Δp across the gas–liquid interface, the radius of curvature decreases until r = R. Now, the bubble is unstable, and the slightest increase in Δp will cause the bubble to grow and the radius of curvature to increase. When the contact angle θ = θ

_{r}, the bubble will move up the side of the cavity until the buoyant force becomes greater than 2πRγ and burst. Figure 3 shows this course of events, where: r

_{1}> r

_{2}> r = R < r

_{3}< r

_{4}. If, on the other hand, θ

_{r}is large enough, when θ

_{r}= θ, the bubble will grow unpinned and eventually will move out of the cavity, rise, and burst. In both cases, a mass of gas may be left behind.

_{a}> (π + ω)/2, where c

_{a}is the advancing angle. Here, gas is creeping up the side of the cone until θ = θ

_{r}. The condition for equilibrium is now Δp = −2γ/R, where the negative sign indicates a concave curvature. Figure 4 illustrates this mechanism.

_{2}bubbles of >25 nm at a diatomite particle in situ with synchrotron-based scanning transmission soft X-ray microscopy (STXM). They strongly indicate that in situ studies provide useful information on material preparation, phase equilibrium, nucleation kinetics, and chemical composition in the confined space.

_{c}required for the formation of a surface bubble [48] of critical size is given by an equation similar to Equation (4), but with a factor Φ:

_{c}is the critical contact angle from the side of gas. Based on this geometry, Brenner and Lohse [17] have introduced a dynamic equilibrium mechanism for sNB stabilization, where the gas out-flux J

_{o}

_{ut}is compensated by gas in-flux J

_{in}at the contact line.

_{ο}e

^{−z}

^{/λ}is the short-ranged potential, which is attractive when ϕ

_{o}< 0 and repulsive when ϕ

_{o}> 0; λ = 1 nm is the interaction distance. Equation (12) predicts either a localized oversaturation next to a hydrophobic substrate or a localized undersaturation next to a hydrophilic solid.

_{w}= 1000 kg/m

^{3}is the water density. In the case of an air bubble of R = 100 nm and ρ = 20 kg/m

^{3}, γ = 67 mN/m. However, even this correction does not qualify Equation (13) as a solution to the problem. Nevertheless, the negative charge of bNB surfaces will prevent them from coalescing and, again, will form an electric double layer [53]. These electrokinetic properties of bNBs may help them to survive for a longer time. Moreover, the many bNBs presented in the solution may also help their stabilization because the large concentrations of bNBs can supply gas to the liquid, retarding their dissolution [54]. Figure 6 illustrates the electrical double layer for bNBs.

## 4. Discussion

_{b}due to buoyancy, balanced by the Rybczynski approximation, equals to [56]:

_{B}due to Brownian motion is given by Einstein’s formula:

^{2}> is the average particle displacement, R

_{G}is the gas constant, N

_{A}is Avogadro’s number, and T is the absolute temperature. Apparently, as t approaches 0, Equation (16) diverges and, therefore, does not represent the real velocity [57,58]. However, the smaller the bubble, the greater the velocity. Figure 7 compares the two given velocities for air/water bubbles of different radii.

_{∞}–c

_{s}= 0.01% will require 4 s for a 100 nm bubble to double its radius. At the same time, this doubled size bubble will be displaced ~6 μm away from its original position; that is, 60 times its original radius. Although the gas concentration in the bulk is taken to be spherically symmetric and the density in the bubble uniform, the motion of the bubble may put them in doubt.

_{+}and R

_{−}are the radii of the expanded and contracted bubbles, respectively. As a result, the average size of the bubble remains invariant. The displacements of the bubble in Figure 8a have a pattern shown in Figure 8b:

_{+}

^{2}> and <x

_{−}

^{2}> are the average displacements from over- to under-saturation. Hence, the generator of this pattern is made by two equal intervals of an angle of 90° alternating between the right and left of the teragon. This is a Peano curve with a fractal dimension H = 2 [65], thus connecting classical theory with the fractal character of Brownian motion [66,67].

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Boys, C.V. Soap Bubbles, Society for Promoting Christian Knowledge; Outlook Verlag: London, UK, 1916. [Google Scholar]
- Adamson, A.W.; Gast, A.P. Physical Chemistry of Surfaces, 6th ed.; John Wiley & Sons, Inc.: New York, NY, USA, 1997. [Google Scholar]
- Brennen, C.E. Cavitation and Bubble Dynamics; Oxford University Press: Oxford, UK, 1995. [Google Scholar]
- Epstein, P.S.; Plesset, M.S. On the stability of gas bubbles in liquid-gas solutions. J. Chem. Phys.
**1950**, 18, 1505–1509. [Google Scholar] [CrossRef] [Green Version] - Plesset, M.S.; Sadhal, S.S. On the stability of gas bubbles in liquid-gas solutions. Appl. Sci. Res.
**1982**, 38, 133–141. [Google Scholar] [CrossRef] [Green Version] - Mori, Y.; Hijikata, K.; Nagatani, T. Fundamental study of bubble dissolution in liquid. Int. J. Heat Mass Transf.
**1977**, 20, 41–50. [Google Scholar] [CrossRef] - Cha, Y.S. On the equilibfium of cavitation nuclei in liquid-gas solutions. J. Fluids Eng.
**1981**, 103, 425–430. [Google Scholar] [CrossRef] - Ball, P. Nanobubbles are not a superficial matter. ChemPhysChem
**2012**, 13, 2173–2177. [Google Scholar] [CrossRef] [PubMed] - ISO 20480-1:2017. Fine Bubble Technology-General Principles for Usage and Measurement of Fine Bubbles–Part 1: Terminology. Available online: https://www.iso.org/standard/68187.html (accessed on 10 September 2021).
- Fox, F.E.; Herzfeld, K.F. Gas bubbles with organic skin as cavitation nuclei. J. Acoust. Soc. Am.
**1954**, 26, 984–989. [Google Scholar] [CrossRef] - Harvey, E.N.; Barnes, D.K.; McElroy, W.D.; Whiteley, A.H.; Pease, D.C.; Cooper, K.W. Bubble formation in animals. I. Physical factors. J. Cell. Comp. Physiol.
**1944**, 24, 1–22. [Google Scholar] [CrossRef] - Crum, L.A. Nucleation and stabilization of microbubbles in liquids. Flow Turbul. Combust.
**1982**, 38, 101–115. [Google Scholar] [CrossRef] - Jones, S.; Evans, G.; Galvin, K. Bubble nucleation from gas cavities—A review. Adv. Colloid Interface Sci.
**1999**, 80, 27–50. [Google Scholar] [CrossRef] - Ohgaki, K.; Khanh, N.Q.; Joden, Y.; Tsuji, A.; Nakagawa, T. Physicochemical approach to nanobubble solutions. Chem. Eng. Sci.
**2010**, 65, 1296–1300. [Google Scholar] [CrossRef] - Nakashima, S.; Spiers, C.J.; Mercury, L.; Fenter, P.A.; Hochella, M.F., Jr. Physicochemistry of Water in Geological and Biological Systems—Structures and Properties of Thin Aqueous Films; Universal Academy Press Inc.: Tokyo, Japan, 2004; pp. 2–5. [Google Scholar]
- Takahashi, M. Potential of microbubbles in aqueous solutions: Electrical properties of the gas-water interface. J. Phys. Chem. B
**2005**, 109, 21858–21864. [Google Scholar] [CrossRef] - Brenner, M.P.; Lohse, D. Dynamic equilibrium mechanism for surface nanobubble stabilization. Phys. Rev. Lett.
**2008**, 101, 214505. [Google Scholar] [CrossRef] [Green Version] - Liu, Y.; Zhang, X. Nanobubble stability induced by contact line pinning. J. Chem. Phys.
**2013**, 138, 014706. [Google Scholar] [CrossRef] [PubMed] - Ducker, W.A. Contact Angle and Stability of Interfacial Nanobubbles. Langmuir
**2009**, 25, 8907–8910. [Google Scholar] [CrossRef] [PubMed] - Weijs, J.H.; Snoeijer, J.H.; Lohse, D. Formation of surface nanobubbles and the universality of their contact angles, A molecular dynamics approach. Phys. Rev. Lett.
**2012**, 108, 104501. [Google Scholar] [CrossRef] [Green Version] - Kyzas, G.Z.; Favvas, E.P.; Kostoglou, M.; Mitropoulos, A.C. Effect of agitation on batch adsorption process facilitated by using nanobubbles. Colloids Surf. A
**2020**, 607, 125440. [Google Scholar] [CrossRef] - Weijs, J.; Lohse, D. Why Surface Nanobubbles Live for Hours. Phys. Rev. Lett.
**2013**, 110, 054501. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zhang, X.; Chan, D.; Wang, D.; Maeda, N. Stability of Interfacial Nanobubbles. Langmuir
**2013**, 29, 1017–1023. [Google Scholar] [CrossRef] - Chan, C.U.; Arora, M.; Ohl, C.-D. Coalescence, Growth, and Stability of Surface-Attached Nanobubbles. Langmuir
**2015**, 31, 7041–7046. [Google Scholar] [CrossRef] - Eshibri, M.; Qian, J.; Jehannin, M.; Craig, V.S.J. A History of Nanobubbles. Langmuir
**2016**, 32, 11086–11100. [Google Scholar] [CrossRef] [PubMed] - Chen, C.; Li, J.; Zhang, X. The existence and stability of bulk nanobubbles: A long-standing dispute on the experimentally observed mesoscopic inhomogeneities in aqueous solutions. Commun. Theor. Phys.
**2020**, 72, 037601. [Google Scholar] [CrossRef] - Ayodele, A.T.; Valizadeh, A.; Adabi, M.; Esnaashari, S.S.; Madani, F.; Khosravani, M. Ultrasound nanobubbles and their applications as theranostic agents in cancer therapy: A review. Biointerface Res. Appl. Chem.
**2017**, 7, 2253–2262. [Google Scholar] - Michailidi, E.D.; Bomis, G.; Varoutoglou, A.; Kyzas, G.; Mitrikas, G.; Mitropoulos, A.C.; Efthimiadou, E.K.; Favvas, E.P. Bulk nanobubbles: Production and investigation of their formation/stability mechanism. J. Colloid Interface Sci.
**2019**, 564, 371–380. [Google Scholar] [CrossRef] [PubMed] - Maris, H.; Balibar, S. Negative Pressures and Cavitation Liquid Helium. Phys. Today
**2000**, 53, 29–34. [Google Scholar] [CrossRef] [Green Version] - Berthelot, M. Sur quelques phenomenes de dilation forcee de liquides. Ann. Chim. Phys.
**1850**, 30, 232–237. [Google Scholar] - Frenkel, J. Kinetic Theory of Liquids; The Clarendon Press: Oxford, UK, 1946. [Google Scholar]
- Garabedian, C.A.; Love, A.E.H. The mathematical theory of elasticity. Am. Math. Mon.
**1928**, 35, 196. [Google Scholar] [CrossRef] - Herzfeld, K.F. Proceedings of First Symposium on Naval Hydrodynamics; Sherman, F.S., Ed.; National Academy of Sciences: Washington, DC, USA, 1957; pp. 319–320. [Google Scholar]
- Strasberg, M. Onset of ultrasonic cavitation in tap watet. J. Acoust. Soc. Am.
**1959**, 31, 163–176. [Google Scholar] [CrossRef] - Akulichev, V.A. Hydration of ions and the cavitation resistance of water. Sov. Phys. Acoust.
**1966**, 12, 144–149. [Google Scholar] - Alty, T. The origin of the electrical charge on small particles in water. Proc. R. Soc. London. Ser. A Math. Phys. Sci.
**1926**, 112, 235–251. [Google Scholar] [CrossRef] - Sirotyuk, M.G. Stabflization of gas bubbles in water. Sov. Phys. Acoust.
**1970**, 16, 237–240. [Google Scholar] - Li, C.; Zhang, A.M.; Wang, S.; Cui, P. Formation and coalescence of nanobubbles under controlled gas concentration and species. AIP Adv.
**2018**, 8, 015104. [Google Scholar] [CrossRef] - Ishida, N.; Inoue, T.; Miyahara, M.; Higashitani, K. Nano bubbles on a hydrophobic surface in water observed by tapping-mode atomic force microscopy. Langmuir
**2000**, 16, 6377–6380. [Google Scholar] [CrossRef] - Lou, S.-T.; Ouyang, Z.-Q.; Zhang, Y.; Li, X.-J.; Hu, J.; Li, M.-Q.; Yang, F.-J. Nanobubbles on solid surface imaged by atomic force microscopy. J. Vac. Sci. Technol. B Microelectron. Nanometer Struct.
**2000**, 18, 2573. [Google Scholar] [CrossRef] - Zhang, X.H.; Khan, A.; Ducker, W.A. A nanoscale gas state. Phys. Rev. Lett.
**2007**, 98, 136101. [Google Scholar] [CrossRef] [Green Version] - Sugano, K.; Miyoshi, Y.; Inazato, S. Study of Ultrafine Bubble Stabilization by Organic Material Adhesion. Jpn. J. Multiph. FLOW
**2017**, 31, 299–306. [Google Scholar] [CrossRef] [Green Version] - Yasui, K.; Tuziuti, T.; Kanematsu, W. Mysteries of bulk nanobubbles (ultrafine bubbles); stability and radical formation. Ultrason. Sonochemistry
**2018**, 48, 259–266. [Google Scholar] [CrossRef] - Nirmalkar, N.; Pacek, A.W.; Barigou, M. On the existence and stability of bulk nanobubbles. Langmuir
**2018**, 34, 10964–10973. [Google Scholar] [CrossRef] [PubMed] - Tan, B.H.; An, H.; Ohl, C.-D. How Bulk Nanobubbles Might Survive. Phys. Rev. Lett.
**2020**, 124, 134503. [Google Scholar] [CrossRef] - Tan, B.H.; An, H.; Ohl, C.-D. Stability of surface and bulk nanobubbles. Curr. Opin. Colloid Interface Sci.
**2021**, 53, 101428. [Google Scholar] [CrossRef] - Pan, G.; He, G.; Zhang, M.; Zhou, Q.; Tyliszczak, T.; Tai, R.; Guo, J.; Bi, L.; Wang, L.; Zhang, H. Nanobubbles at hydrophilic particle−water interfaces. Langmuir
**2016**, 32, 11133–11137. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Fisher, J.C. The fracture of liquids. J. Appl. Phys.
**1948**, 19, 1062–1067. [Google Scholar] [CrossRef] - Loshe, D.; Zhang, X. Pinning and gas oversaturation imply stable single surface nanobubbles. Phys. Rev. E
**2015**, 91, 031003. [Google Scholar] - Qian, J.; Craig, V.S.J.; Jehannin, M. Long-term stability of surface nanobubbles in undersaturated aqueous solution. Langmuir
**2019**, 35, 718–728. [Google Scholar] [CrossRef] [PubMed] - Zhang, L.; Chen, H.; Li, Z.; Fang, H.; Hu, J. Long lifetime of nanobubbles due to high inner density. Sci. China Ser. G-Phys. Mech. Astron.
**2008**, 51, 219–224. [Google Scholar] [CrossRef] - Ulatowski, K.; Sobieszuk, P.; Mróz, A.; Ciach, T. Stability of nanobubbles generated in water using porous membrane system. Chem. Eng. Process. Process. Intensif.
**2018**, 136, 62–71. [Google Scholar] [CrossRef] - Jia, W.; Ren, S.; Hu, B. Effect of water chemistry on zeta potential of air bubbles. Int. J. Electrochem. Sci.
**2013**, 8, 5828–5837. [Google Scholar] - Weijs, J.H.; Seddon, J.R.T.; Lohse, D. Diffusive Shielding Stabilizes Bulk Nanobubble Clusters. ChemPhysChem
**2012**, 13, 2197–2204. [Google Scholar] [CrossRef] [Green Version] - Duncan, P.B.; Needham, D. Test of the Epstein−Plesset Model for Gas Microparticle Dissolution in Aqueous Media: Effect of Surface Tension and Gas Undersaturation in Solution. Langmuir
**2004**, 20, 2567–2578. [Google Scholar] [CrossRef] - Lamb, H. Hydrodynamics, 6th ed.; Cambridge University Press: London, UK, 1932. [Google Scholar]
- Li, T.; Raizen, M.G. Brownian motion at short time scales. Ann. Phys.
**2013**, 525, 281–295. [Google Scholar] [CrossRef] [Green Version] - Chicea, D. Coherent light scattering on nanofluids: Computer simulation results. Appl. Opt.
**2008**, 47, 1434–1442. [Google Scholar] [CrossRef] [PubMed] - Ultrafine Bubbles Recorded by NanoSight. 2019. Available online: www.acniti.com (accessed on 10 August 2021).
- Seddon, J.R.T.; Lohse, D.; Ducker, W.A.; Craig, V.S.J. A Deliberation on Nanobubbles at Surfaces and in Bulk. ChemPhysChem
**2012**, 13, 2179–2187. [Google Scholar] [CrossRef] - Seddon, J.R.T.; Zandvliet, H.J.; Lohse, D. Knudsen gas provides nanobubble stability. Phys. Rev. Lett.
**2011**, 107, 116101. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zhou, Y.; Han, Z.; He, C.; Feng, Q.; Wang, K.; Wang, Y.; Luo, N.; Dodbiba, G.; Wei, Y.; Otsuki, A.; et al. Long-Term Stability of Different Kinds of Gas Nanobubbles in Deionized and Salt Water. Materials
**2021**, 14, 1808. [Google Scholar] [CrossRef] [PubMed] - Nirmalkar, N.; Pacek, A.; Barigou, M. Interpreting the interfacial and colloidal stability of bulk nanobubbles. Soft Matter
**2018**, 14, 9643–9656. [Google Scholar] [CrossRef] [Green Version] - Oh, S.H.; Kim, J.-M. Generation and Stability of Bulk Nanobubbles. Langmuir
**2017**, 33, 3818–3823. [Google Scholar] [CrossRef] [PubMed] - Mandelbrot, B.B. The Fractal Geometry of Nature; Freeman Co.: New York, NY, USA, 1982. [Google Scholar]
- Vicsek, T.; Gould, H. Fractal Growth Phenomena. Comput. Phys.
**1989**, 3, 108. [Google Scholar] [CrossRef] - Saberi, A.A. Fractal structure of a three-dimensional Brownian motion on an attractive plane. Phys. Rev. E
**2011**, 84, 021113. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Mitropoulos, A.C.; Bomis, G. Device for Generating and Handling Nanobubbles. European Patent EP2995369A1, 2016. [Google Scholar]
- Favvas, E.P.; Kyzas, G.Z.; Efthimiadou, E.K.; Mitropoulos, A.K. Bulk nanobubbles, generation methods and potential applications. Curr. Opin. Colloid Interf. Sci.
**2021**, 54, 101455. [Google Scholar] [CrossRef] - Kyzas, G.Z.; Bomis, G.; Kosheleva, R.I.; Efthimiadou, E.K.; Favvas, E.P.; Kostoglou, M.; Mitropoulos, A.C. Nanobubbles effect on heavy metal ions adsorption by activated carbon. Chem. Eng. J.
**2019**, 356, 91–97. [Google Scholar] - Agarwal, A.; Ng, W.J.; Liu, Y. Principle and applications of microbubble and nanobubble technology for water treatment. Chemosphere
**2011**, 84, 1175–1180. [Google Scholar] [CrossRef] [PubMed] - Ebina, K.; Shi, K.; Hirao, M.; Hashimoto, J.; Kawato, Y.; Kaneshiro, S.; Morimoto, T.; Koizumi, K.; Yoshikawa, H. Oxygen and Air Nanobubble Water Solution Promote the Growth of Plants, Fishes, and Mice. PLoS ONE
**2013**, 8, e65339. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Liu, S.; Kawagoe, Y.; Makino, Y.; Oshita, S. Effects of nanobubbles on the physicochemical properties of water: The basis for peculiar properties of water containing nanobubbles. Chem. Eng. Sci.
**2013**, 93, 250–256. [Google Scholar] [CrossRef] - Fine Bubble Industries Association. Available online: fbia.or.jp (accessed on 9 August 2021).
- Koltsov, D.K. Fine Bubble Technology in the EU; BREC Solutions Ltd.: Glasgow, UK, 2016. [Google Scholar]

**Figure 1.**(

**a**) The spectrum of bubble sizes according to their stability. (

**b**) Bubble diameter classification according to ISO 20480-1-2017 [9].

**Figure 3.**A bubble impended in a crevice. The course of events Δp increases, where r is the radius of curvature, θr is the receding angle (small), and R is the pinning half distance between Points A and B. When r = R, the bubble is hemispherical.

**Figure 4.**A bubble impended in a cone crevice of a very small apical angle, ω, and θ, the equilibrium contact angle, with θ

_{a}as the advancing angle and θ

_{r}the receding angle. Notice that the meniscus is now concave.

**Figure 5.**(

**a**) Stabilization of an NB pinned on a surface. As the height and the contact angle decrease, the radius of the curvature increases and the pressure across the interface deflates. (

**b**) Free-standing sNBs. Notice the general case of non-homogeneous distribution of the dissolved gas. By dividing the bubble into slices of thickness (dz) and by ignoring the gas concentration in the liquid, the bottom slices show the largest contribution to gas exchange according to Equation (12).

**Figure 6.**The electrical double layer for bNBs; Ψ

_{δ}is the potential at the boundary between the compact and diffuse layers.

**Figure 7.**Buoyancy rise (cyan line) versus Brownian diffusion (purple line) for bubbles of different sizes. Cross-over point at R = 500 nm and υ = 1 μm/s.

**Figure 8.**(

**a**) A schematic representation of a bulk NB displacement, alternating from an oversaturated domain (blue) to an undersaturated domain (yellow) at equal times but with opposite perturbation conditions. Solid circles reflect the original size of the bubble, and broken circles indicate either expansion or contraction. Notice that the size of the average bubble is invariant. (

**b**) The bubble performs a Brownian walk of an alternating Peano curve of fractal dimension H = 2.

R_{o} | c_{∞} < c_{s} | Time to R = 0 | c_{∞} > c_{s} | Time to R = 10 R _{o} |
---|---|---|---|---|

10 μm | 0.75 c_{s} | 5 s | 1.25 c_{s} | 495 s |

1 μm | 100 ms | 5 s | ||

100 nm | 500 μs | 50 ms | ||

R_{o} | c_{∞} ≈ c_{s} | Timeto R = 0 | c_{∞} ≈ c_{s} | Timeto R = 10 R_{o} |

10 μm | 0.9999c_{s} | 3.5 h | 1.0001 | 14 days |

1 μm | 125 s | 3.4 h | ||

100 nm | 1.25 s | 124 s |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kyzas, G.Z.; Mitropoulos, A.C.
From Bubbles to Nanobubbles. *Nanomaterials* **2021**, *11*, 2592.
https://doi.org/10.3390/nano11102592

**AMA Style**

Kyzas GZ, Mitropoulos AC.
From Bubbles to Nanobubbles. *Nanomaterials*. 2021; 11(10):2592.
https://doi.org/10.3390/nano11102592

**Chicago/Turabian Style**

Kyzas, George Z., and Athanasios C. Mitropoulos.
2021. "From Bubbles to Nanobubbles" *Nanomaterials* 11, no. 10: 2592.
https://doi.org/10.3390/nano11102592