Skip to main content
×
Home

Gas depletion through single gas bubble diffusive growth and its effect on subsequent bubbles

  • Álvaro Moreno Soto (a1), Andrea Prosperetti (a2), Detlef Lohse (a1) and Devaraj van der Meer (a1)
Abstract

When a gas bubble grows by diffusion in a gas–liquid solution, it affects the distribution of gas in its surroundings. If the density of the solution is sensitive to the local amount of dissolved gas, there is the potential for the onset of natural convection, which will affect the bubble growth rate. The experimental study of the successive quasi-static growth of many bubbles from the same nucleation site described in this paper illustrates some consequences of this effect. The enhanced growth due to convection causes a local depletion of dissolved gas in the neighbourhood of each bubble beyond that due to pure diffusion. The quantitative data of sequential bubble growth provided in the paper show that the radius-versus-time curves of subsequent bubbles differ from each other due to this phenomenon. A simplified model accounting for the local depletion is able to collapse the experimental curves and to predict the progressively increasing bubble detachment times.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Gas depletion through single gas bubble diffusive growth and its effect on subsequent bubbles
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Gas depletion through single gas bubble diffusive growth and its effect on subsequent bubbles
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Gas depletion through single gas bubble diffusive growth and its effect on subsequent bubbles
      Available formats
      ×
Copyright
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Corresponding author
Email addresses for correspondence: a.morenosoto@utwente.nl, d.vandermeer@utwente.nl
References
Hide All
Akin S. & Kovscek A. R. 2002 Heavy-oil solution gas drive: a laboratory study. J. Petrol. Sci. Engng 35, 3348.
Bataller H., Miqueu C., Plantier F., Daridon J.-L., Jaber T. J., Abbasi A., Saghir M. Z. & Bou-Ali M. M. 2009 Comparison between experimental and theoretical estimations of the thermal expansion, concentration expansion coefficients, and viscosity for binary mixtures under pressures up to 20 MPa. J. Chem. Engng Data 54, 17101715.
Bejan A. 1993 Heat Transfer, 1st edn. Willey.
Bergman T. L., Incropera F. P., DeWitt D. P. & Lavine A. S. 2011 Fundamentals of Heat and Mass Transfer, 7th edn. Willey.
Bisperink C. G. J. & Prins A. 1994 Bubble growth in carbonated liquids. Colloids Surf. A 85, 237253.
Chu S. & Prosperetti A. 2016 History effects on the gas exchange between a bubble and a liquid. Phys. Rev. Fluids 1 (064202), 120.
Clift R., Grace J. R. & Weber M. E. 1978 Bubbles, Drops and Particles. Academic.
Cussler E. L. 2009 Diffusion: Mass Transfer in Fluid Systems, 3rd edn.. Cambridge Series in Chemical Engineering. Cambridge University Press.
Dietrich E., Wildeman S., Visser C. W., Hofhuis K., Kooij E. S., Zandvliet H. J. W. & Lohse D. 2016 Role of natural convection in the dissolution of sessile droplets. J. Fluid Mech. 794, 4567.
Enríquez O. R., Hummelink C., Bruggert G.-W., Lohse D., Prosperetti A., van der Meer D. & Sun C. 2013 Growing bubbles in a slightly supersaturated liquid solution. Rev. Sci. Instrum. 84, 065111.
Enríquez O. R., Sun C., Lohse D., Prosperetti A. & van der Meer D. 2014 The quasi-static growth of CO˙2 bubbles. J. Fluid Mech. 741, R1.
Eötvös R. 1886 Ueber den Zusammenhang der Oberflächenspannung der Flüssigkeiten mit ihrem Molecularvolumen. Ann. Phys. 263, 448459.
Epstein P. S. & Plesset M. S. 1950 On the stability of gas bubbles in liquid–gas solutions. J. Chem. Phys. 18 (11), 15051509.
Frank M. J. W., Kuipers J. A. M. & van Swaaij W. P. M. 1996 Diffusion coefficients and viscosities of CO2 + H2O, CO2 + CH3OH, NH3 + H2O, and NH3 + CH3OH liquid mixtures. J. Chem. Engng Data 41, 297302.
Fritz W. 1935 Berechnung des Maximal Volume von Dampfblasen. Phys. Z. 36, 379388.
Hebach A., Oberhof A. & Dahmen N. 2004 Density of water + carbon dioxide at elevated pressures: measurements and correlation. J. Chem. Engng Data 49, 950953.
Henry W. 1803 Experiments on the quantity of gases absorbed by water, at different temperatures, and under different pressures. Phil. Trans. R. Soc. Lond. 93, 29–42 and 274–276.
International Association for the Properties of Water and Steam2014 Revised release on the IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use.
Kuchmaand A. E., Gor G. Yu. & Kuni F. M. 2009 Stages of steady diffusion growth of a gas bubble in strongly supersaturated gas–liquid solution. Colloid J. 71 (4), 520528.
Kuni F. M., Kuchma A. E. & Adjemyan L. T. 2009 Narrowness of the region of nonuniformity of strongly supersaturated liquid solution around the growing gas bubble. Colloid J. 71 (3), 360364.
Landau L. D. & Lifshitz E. M. 1980 Course of Theoretical Physics, Volume 5: Statistical Physics, 3rd edn. Pergamon.
Lee W. T., McKechnie J. S. & Devereux M. G. 2011 Bubble nucleation in stout beers. Phys. Rev. E 83 (051609), 15.
Li X. & Yortsos Y. C. 1995 Theory of multiple bubble growth in porous media by solute diffusion. Chem. Engng Sci. 50 (8), 12471271.
Liger-Belair G., Voisin C. & Jeandet P. 2005 Modelling nonclassical heterogeneous bubble nucleation from cellulose fibers: application to bubbling in carbonated beverages. J. Phys. Chem. B 109 (30), 1457314580.
Liu Y. & Zhang Y. 2000 Bubble growth in rhyolitic melt. Earth Planet. Sci. Lett. 181, 251264.
Lohse D. & Zhang X. 2015 Surface nanobubbles and nanodroplets. Rev. Mod. Phys. 87 (3), 9811035.
Lu W., Guo H., Chou I. M., Burruss R. C. & Li L. 2013 Determination of diffusion coefficients of carbon dioxide in water between 268 and 473 K in a high-pressure capillary optical cell with in situ Raman spectroscopic measurements. Geochim. Cosmochim. Acta 115, 183204.
Lubetkin S. D. & Akhtar M. 1996 The variation of surface tension and contact angle under applied pressure of dissolved gases, and the effects of these changes on the rate of bubble nucleation. J. Colloid Interface Sci. 180 (0272), 4360.
Oehmichen T., Datsevich L. & Jess A. 2010 Influence of bubble evolution on the effective kinetics of heterogeneously catalysed gas/liquid reactions. Part I: reactions with gaseous products. Chem. Engng Technol. 33 (6), 911920.
Og̃uz H. N. & Prosperetti A. 1993 Dynamics of bubble growth and detachment from a needle. J. Fluid Mech. 257, 111145.
Peñas-López P., Moreno Soto Á., Parrales M. A., van der Meer D., Lohse D. & Rodríguez-Rodríguez J. 2017 The history effect in bubble growth and dissolution. Part 2. Experiments and simulations of a spherical bubble attached to a horizontal flat plate. J. Fluid Mech. 820, 479510.
Peñas-López P., Parrales M. A., Rodríguez-Rodríguez J. & van der Meer D. 2016 The history effect in bubble growth and dissolution. Part 1. Theory. J. Fluid Mech. 800, 180212.
Pierantozzi R. 2007 Carbon dioxide. In Kirk-Othmer Encyclopedia of Chemical Technology, 22, 5th edn. (ed. Kirk-Othmer), vol. 4, pp. 803822. Willey.
Rahman S. U. 2013 Natural convection transport from sphere held in vertical cylindrical cavities. Arab. J. Sci. Eng. 38, 19511957.
Scriven L. E. 1959 On the dynamics of phase growth. Chem. Engng Sci. 10, 113.
Sillen C. W. M. P., Barendrecht E., Janssen L. J. J. & van Stralen S. J. D. 1982 Gas bubble behaviour during water electrolysis. Intl J. Hydrogen Energy 7 (7), 557587.
Somorjai G. A. & Li Y. 2010 Introduction to Surface Chemistry and Catalysis, 2nd edn. Willey.
Stricker L., Dollet B., Fernández Rivas D. & Lohse D. 2013 Interacting bubble clouds and their sonochemical production. J. Acoust. Soc. Am. 134 (3), 18541862.
Uzel S., Chappell M. A. & Payne S. J. 2006 Modeling the cycles of growth and detachment of bubbles in carbonated beverages. J. Phys. Chem. B 110, 75797586.
Verhaart H. F. A., de Jonge R. M. & van Stralen S. J. D. 1979 Growth rate of a gas bubble during electrolysis in supersaturated liquid. Intl J. Heat Mass Transfer 23, 293299.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 3
Total number of PDF views: 133 *
Loading metrics...

Abstract views

Total abstract views: 121 *
Loading metrics...

* Views captured on Cambridge Core between 13th October 2017 - 23rd November 2017. This data will be updated every 24 hours.