The quasi-static growth of CO2 bubbles

doi:10.1017/JFM.2013.667

Home
/
Papers
/
The quasi-static growth of CO2 bubbles

Journal Article•DOI•

The quasi-static growth of CO2 bubbles

Oscar R. Enríquez¹, Chao Sun¹, Detlef Lohse¹, Andrea Prosperetti², Devaraj van der Meer¹ - Show less +1 more•Institutions (2)

University of Twente¹, Johns Hopkins University²

01 Feb 2014-Journal of Fluid Mechanics (Cambridge University Press)-Vol. 741

TL;DR: In this article, the authors studied the growth of an isolated gas bubble in a slightly supersaturated water-CO2 solution at 6 atm pressure and found that the time evolution of the bubble radius differs noticeably from existing theoretical solutions.

read less

Abstract: We study experimentally the growth of an isolated gas bubble in a slightly supersaturated water–CO2 solution at 6 atm pressure. In contrast to what was found in previous experiments at higher supersaturation, the time evolution of the bubble radius differs noticeably from existing theoretical solutions. We trace the differences back to several combined effects of the concentration boundary layer around the bubble, which we disentangle in this work. In the early phase, the interaction with the surface on which the bubble grows slows down the process. In contrast, in the final phase, before bubble detachment, the growth rate is enhanced by the onset of density-driven convection. We also show that the bubble growth is affected by prior growth and detachment events, though they are up to 15 min apart.

...read moreread less

Citations

PDF

Open Access

More filters

Journal Article•DOI•

Surface nanobubbles and nanodroplets

[...]

Detlef Lohse, Xuehua Zhang

31 Aug 2015-Reviews of Modern Physics

TL;DR: A review on surface nanobubbles and nanodroplets can be found in this article, where the authors discuss the nucleation, growth, and dissolution dynamics of surfaces.

...read moreread less

Abstract: Surface nanobubbles are nanoscopic gaseous domains on immersed substrates which can survive for days. They were first speculated to exist about 20 years ago, based on stepwise features in force curves between two hydrophobic surfaces, eventually leading to the first atomic force microscopy (AFM) image in 2000. While in the early years it was suspected that they may be an artifact caused by AFM, meanwhile their existence has been confirmed with various other methods, including through direct optical observation. Their existence seems to be paradoxical, as a simple classical estimate suggests that they should dissolve in microseconds, due to the large Laplace pressure inside these nanoscopic spherical-cap-shaped objects. Moreover, their contact angle (on the gas side) is much smaller than one would expect from macroscopic counterparts. This review will not only give an overview on surface nanobubbles, but also on surface nanodroplets, which are nanoscopic droplets (e.g., of oil) on (hydrophobic) substrates immersed in water, as they show similar properties and can easily be confused with surface nanobubbles and as they are produced in a similar way, namely, by a solvent exchange process, leading to local oversaturation of the water with gas or oil, respectively, and thus to nucleation. The review starts with how surface nanobubbles and nanodroplets can be made, how they can be observed (both individually and collectively), and what their properties are. Molecular dynamic simulations and theories to account for the long lifetime of the surface nanobubbles are then reported on. The crucial element contributing to the long lifetime of surface nanobubbles and nanodroplets is pinning of the three-phase contact line at chemical or geometric surface heterogeneities. The dynamical evolution of the surface nanobubbles then follows from the diffusion equation, Laplace’s equation, and Henry’s law. In particular, one obtains stable surface nanobubbles when the gas influx from the gas-oversaturated water and the outflux due to Laplace pressure balance. This is only possible for small enough surface bubbles. It is therefore the gas or oil oversaturation ζ that determines the contact angle of the surface nanobubble or nanodroplet and not the Young equation. The review also covers the potential technological relevance of surface nanobubbles and nanodroplets, namely, in flotation, in (photo)catalysis and electrolysis, in nanomaterial engineering, for transport in and out of nanofluidic devices, and for plasmonic bubbles, vapor nanobubbles, and energy conversion. Also given is a discussion on surface nanobubbles and nanodroplets in a nutshell, including theoretical predictions resulting from it and future directions. Studying the nucleation, growth, and dissolution dynamics of surface nanobubbles and nanodroplets will shed new light on the problems of contact line pinning and contact angle hysteresis on the submicron scale.

...read moreread less

616 citations

Cites background from "The quasi-static growth of CO2 bubb..."

...In a classical paper, Epstein and Plesset (1950) calculated the lifetime of a spherical isolated bubble of initial radius R0 and at rest in an infinitely extended liquid-gas solution in which the gas concentration far away from the bubble is c∞, whereas the gas solubility is cs....
[...]
...More values for the dissolution times for various bubble sizes and undersaturations ζ < 0 are given in Epstein and Plesset (1950) and Ljunggren and Eriksson (1997)....
[...]
...In a classical paper, Epstein and Plesset (1950) calculated the lifetime of a spherical isolated bubble of initial radius R0 and at rest in an infinitely extended liquid-gas solution in which the gas concentration far away from the bubble is c∞, whereas the gas solubility is cs. Although Epstein and Plesset (1950) had the growth (shrinkage) of macroscopic bubbles in oversaturated (undersatured) gas solutions in mind, their calculation is also applicable for microscopic and nanoscopic bubbles, as the effect of surface tension is explicitly taken into consideration and as the employed hydrodynamical equations hold down to the nanoscale (Bocquet and Charlaix, 2010)....
[...]
...More values for the dissolution times for various bubble sizes and undersaturations ζ < 0 are given in Epstein and Plesset (1950) and Ljunggren and Eriksson (1997). What directly follows from Eq....
[...]
...More values for the dissolution times for various bubble sizes and undersaturations ζ < 0 are given in Epstein and Plesset (1950) and Ljunggren and Eriksson (1997). What directly follows from Eq. (20) is that small bubbles [with R0 ≪ σ=P0 and at the same time R0 ≪ 2σ=ðP0c∞=csÞ] cannot stably exist in the bulk, even not for oversaturation c∞ > cs: The surface tension squeezes them out and they dissolve in time τlife ≈ R(2)0ρg=3Dcs. Therefore, according to Epstein and Plesset (1950) there are no stable bulk nanobubbles....
[...]

Journal Article•DOI•

Influence of Bubbles on the Energy Conversion Efficiency of Electrochemical Reactors

[...]

Andrea Angulo¹, Peter van der Linde², Han J. G. E. Gardeniers², Miguel A. Modestino¹, David Fernandez Rivas² - Show less +1 more•Institutions (2)

New York University¹, University of Twente²

18 Mar 2020-Joule

TL;DR: In this paper, a review of the current knowledge on the effects of bubbles on electrochemical systems with the aim to identify opportunities and motivate future research in this area is presented. But, we lack a detailed understanding on the intricate dependencies between bubble evolution processes and electrochemical phenomena.

...read moreread less

212 citations

Cites background from "The quasi-static growth of CO2 bubb..."

..., pressure driven and electrolysis experiments), the bubble detachment occurs at comparable radii, suggesting that the source of dissolved gasses does not have strong effects in bubble detachment.(89)...
[...]

Journal Article•DOI•

Pinning and gas oversaturation imply stable single surface nanobubbles

[...]

Detlef Lohse¹, Xuehua Zhang¹, Xuehua Zhang²•Institutions (2)

University of Twente¹, RMIT University²

27 Mar 2015-Physical Review E

TL;DR: The theory predicts how the contact angle of the pinned bubble depends on ζ and the surface nanobubble's footprint lateral extension L, and predicts an upper lateral extension threshold for stable surface Nanobubbles to exist.

...read moreread less

Abstract: Surface nanobubbles are experimentally known to survive for days at hydrophobic surfaces immersed in gas-oversaturated water This is different from bulk nanobubbles, which are pressed out by the Laplace pressure against any gas oversaturation and dissolve in submilliseconds, as derived by Epstein and Plesset [J Chem Phys 18, 1505 (1950)] Pinning of the contact line has been speculated to be the reason for the stability of the surface nanobubbles Building on an exact result by Popov [Phys Rev E 71, 036313 (2005)] on coffee stain evaporation, here we confirm this speculation by an exact calculation for single surface nanobubbles It is based only on (i) the diffusion equation, (ii) Laplace pressure, and (iii) Henry's equation, ie, fluid dynamical equations which are all known to be valid down to the nanometer scale The crucial parameter is the gas oversaturation ζ of the liquid At the stable equilibrium, the gas overpressures due to this oversaturation and the Laplace pressure balance The theory predicts how the contact angle of the pinned bubble depends on ζ and the surface nanobubble's footprint lateral extension L It also predicts an upper lateral extension threshold for stable surface nanobubbles to exist

...read moreread less

176 citations

Journal Article•DOI•

Influence of Bubbles on the Energy Conversion Efficiency of Electrochemical Reactors

[...]

Andrea Angulo¹, Peter van der Linde², Han J. G. E. Gardeniers², Miguel A. Modestino¹, David Fernandez Rivas² - Show less +1 more•Institutions (2)

New York University¹, University of Twente²

12 Feb 2020-arXiv: Soft Condensed Matter

TL;DR: In this article, a review of the current knowledge on the effects of bubbles on electrochemical systems with the aim to identify opportunities and motivate future research in this area is presented. But, we lack a detailed understanding on the intricate dependencies between bubble evolution processes and electrochemical phenomena.

...read moreread less

Abstract: Bubbles are known to influence energy and mass transfer in gas evolving electrodes. However, we lack a detailed understanding on the intricate dependencies between bubble evolution processes and electrochemical phenomena. This review discusses our current knowledge on the effects of bubbles on electrochemical systems with the aim to identify opportunities and motivate future research in this area. We first provide a base background on the physics of bubble evolution as it relates to electrochemical processes. Then we outline how bubbles affect energy efficiency of electrode processes, detailing the bubble-induced impacts on activation, ohmic and concentration overpotentials. Lastly, we describe different strategies to mitigate losses and how to exploit bubbles to enhance electrochemical reactions.

...read moreread less

161 citations

Journal Article•DOI•

Gas Bubbles in Electrochemical Gas Evolution Reactions

[...]

Xu Zhao¹, Hang Ren², Long Luo¹•Institutions (2)

Wayne State University¹, Miami University²

19 Mar 2019-Langmuir

TL;DR: The classical theories as well as recent advancements in this field are summarized and an outlook on future research topics are provided.

...read moreread less

Abstract: Electrochemical gas evolution reactions are of vital importance in numerous electrochemical processes including water splitting, chloralkaline process, and fuel cells. During gas evolution reactions, gas bubbles are vigorously and constantly forming and influencing these processes. In the past few decades, extensive studies have been performed to understand the evolution of gas bubbles, elucidate the mechanisms of how gas bubbles impact gas evolution reactions, and exploit new bubble-based strategies to improve the efficiency of gas evolution reactions. In this feature article, we summarize the classical theories as well as recent advancements in this field and provide an outlook on future research topics.

...read moreread less

147 citations

1
2
3
4
…
5
6
7
8
9
10
11
12
13
14
15
16

Collapse

References

PDF

Open Access

More filters

Journal Article•DOI•

On the stability of gas bubbles in liquid-gas solutions

[...]

Paul S. Epstein¹, M. S. Plesset¹•Institutions (1)

California Institute of Technology¹

01 Nov 1950-Journal of Chemical Physics

TL;DR: In this article, approximate solutions for the rate of solution by diffusion of a gas bubble in an undersaturated liquid-gas solution are presented, with the neglect of the translational motion of the bubble.

...read moreread less

Abstract: With the neglect of the translational motion of the bubble, approximate solutions may be found for the rate of solution by diffusion of a gas bubble in an undersaturated liquid‐gas solution; approximate solutions are also presented for the rate of growth of a bubble in an oversaturated liquid‐gas solution. The effect of surface tension on the diffusion process is also considered.

...read moreread less

1,343 citations

Book•

Heat transfer

[...]

Adrian Bejan

01 Jan 1960

1,030 citations

Journal Article•DOI•

The dynamics of bubble formation and growth in magmas: A review and analysis

[...]

R. S. J. Sparks¹•Institutions (1)

Lancaster University¹

01 Mar 1978-Journal of Volcanology and Geothermal Research

TL;DR: In this article, a numerical method has been developed to determine bubble growth rates during volcanic eruptions of basaltic and rhyolitic tephras, and the numerical solutions consider both diffusional and decompressional growth and the effects of magma ascent rates (0-400 cm s−1), magma viscosity (102 to 108 poise), gas solubility, gas content (0.25-5%), and gas diffusivity (10−6 to 10−9 cm2 s− 1) on growth rates.

...read moreread less

901 citations

Journal Article•DOI•

On the dynamics of phase growth

[...]

L. E. Scriven¹•Institutions (1)

Royal Dutch Shell¹

01 Dec 1995-Chemical Engineering Science

TL;DR: In this paper, the equations governing spherically symmetric phase growth in an infinite medium are first formulated for the general case and then simplified to describe growth controlled by the transport of heat and matter.

...read moreread less

832 citations

"The quasi-static growth of CO2 bubb..." refers background in this paper

...Theories, both including (Scriven 1959) and neglecting (Epstein & Plesset 1950) the advective transport induced by the radially expanding bubble interface, predict that the radius R grows proportionally to √ t (with a larger prefactor in the former case)....
[...]

Journal Article•DOI•

Bubble nucleation from gas cavities — a review

[...]

S.F. Jones¹, Geoffrey Evans¹, Kevin P. Galvin¹•Institutions (1)

University of Newcastle¹

28 Feb 1999-Advances in Colloid and Interface Science

TL;DR: In this article, a review of the nucleation of bubbles in solutions supersaturated with a gas, in particular the bubble nucleation that occurs at specific sites, as a cycle is presented.

...read moreread less

534 citations

"The quasi-static growth of CO2 bubb..." refers background or result in this paper

...This last phenomenon stands in contrast to previous experimental studies in which its effects were not detected and therefore explicitly discounted by the authors (Bisperink & Prins 1994; Jones et al. 1999)....
[...]
...At moderate supersaturation, bubbles take well under one minute to reach a 0.5 mm detachment radius and advection by the moving interface is significant (Bisperink & Prins 1994; Jones et al. 1999; Barker et al. 2002)....
[...]
...First, the bubble is no longer a full sphere, but rather a spherical cap pinned to the perimeter of the nucleation site (Bisperink & Prins 1994; Jones et al. 1999; Barker et al. 2002)....
[...]
...Although this phenomenon was considered by Jones et al. (1999) and related to the time it takes the following bubble to nucleate, alterations in the growth rate after nucleation were not reported....
[...]