Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-17T13:19:53.306Z Has data issue: false hasContentIssue false
  • English
  • Français

The history effect on bubble growth and dissolution. Part 2. Experiments and simulations of a spherical bubble attached to a horizontal flat plate

Published online by Cambridge University Press:  11 May 2017

Pablo Peñas-López ,
Álvaro Moreno Soto Open the ORCID record for Álvaro Moreno Soto [Opens in a new window] ,
Miguel A. Parrales ,
Devaraj van der Meer ,
Detlef Lohse Open the ORCID record for Detlef Lohse [Opens in a new window]  and
Javier Rodríguez-Rodríguez Open the ORCID record for Javier Rodríguez-Rodríguez [Opens in a new window]
Pablo Peñas-López*
Affiliation:
Fluid Mechanics Group, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés (Madrid), Spain
Álvaro Moreno Soto*
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Miguel A. Parrales
Affiliation:
Departamento de Ingeniería Energética y Fluidomecánica, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, C. José Gutiérrez Abascal 2, 28006 Madrid, Spain
Devaraj van der Meer
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Detlef Lohse
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Javier Rodríguez-Rodríguez
Affiliation:
Fluid Mechanics Group, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés (Madrid), Spain
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The accurate description of the growth or dissolution dynamics of a soluble gas bubble in a super- or undersaturated solution requires taking into account a number of physical effects that contribute to the instantaneous mass transfer rate. One of these effects is the so-called history effect. It refers to the contribution of the local concentration boundary layer around the bubble that has developed from past mass transfer events between the bubble and liquid surroundings. In Part 1 of this work (Peñas-López et al., J. Fluid Mech., vol. 800, 2016b, pp. 180–212), a theoretical treatment of this effect was given for a spherical, isolated bubble. Here, Part 2 provides an experimental and numerical study of the history effect regarding a spherical bubble attached to a horizontal flat plate and in the presence of gravity. The simulation technique developed in this paper is based on a streamfunction–vorticity formulation that may be applied to other flows where bubbles or drops exchange mass in the presence of a gravity field. Using this numerical tool, simulations are performed for the same conditions used in the experiments, in which the bubble is exposed to subsequent growth and dissolution stages, using stepwise variations in the ambient pressure. Besides proving the relevance of the history effect, the simulations highlight the importance that boundary-induced advection has to accurately describe bubble growth and shrinkage, i.e. the bubble radius evolution. In addition, natural convection has a significant influence that shows up in the velocity field even at short times, although given the supersaturation conditions studied here, the bubble evolution is expected to be mainly diffusive.

JFM classification

Drops and Bubbles: Bubble dynamics Convection: Convection Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 820 , 10 June 2017 , pp. 479 - 510
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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 (6), 1710–1715.Google Scholar
Batchelor, G. K. 1979 Mass transfer from a particle suspended in fluid with a steady linear ambient velocity distribution. J. Fluid Mech. 95, 369–400.Google Scholar
Chu, S. & Prosperetti, A. 2016a Dissolution and growth of a multicomponent drop in an immiscible liquid. J. Fluid Mech. 798, 787–811.Google Scholar
Chu, S. & Prosperetti, A. 2016b History effects on the gas exchange between a bubble and a liquid. Phys. Rev. Fluids 1, 064202.Google Scholar
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, 45–67.Google Scholar
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.Google Scholar
Enríquez, O. R., Sun, C., Lohse, D., Prosperetti, A. & van der Meer, D. 2014 The quasi-static growth of CO2 bubbles. J. Fluid Mech. 741, R1.Google Scholar
Epstein, P. S. & Plesset, M. S. 1950 On the stability of gas bubbles in liquid–gas solutions. J. Chem. Phys. 18 (11), 1505–1509.Google Scholar
Gelderblom, H., Bloemen, O. & Snoeijer, J. H. 2012 Stokes flow near the contact line of an evaporating drop. J. Fluid Mech. 709, 69–84.Google Scholar
Harvey, A. H., Kaplan, S. G. & Burnett, J. H. 2005 Effect of dissolved air on the density and refractive index of water. Intl J. Thermophys. 26 (5), 1495–1514.CrossRefGoogle Scholar
Koumoutsakos, P., Leonard, A. & Pépin, F. 1994 Boundary conditions for viscous vortex methods. J. Comput. Phys. 113 (1), 52–61.Google Scholar
Lighthill, M. J. 1963 Laminar Boundary Layers (ed. Rosenhead, L.), pp. 46–57. Oxford University Press.Google Scholar
Lohse, D. 2016 Towards controlled liquid–liquid microextraction. J. Fluid Mech. 84, 1–4.Google Scholar
Lundgren, T. & Koumoutsakos, P. 1999 On the generation of vorticity at a free surface. J. Fluid Mech. 382, 351–366.Google Scholar
Michaelides, E. E. 2003 Hydrodynamic force and heat/mass transfer from particles, bubbles, and drops – the Freeman scholar lecture. J. Fluid Engng 125, 209–238.Google Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1–18.Google Scholar
Moon, P. & Spencer, D. E. 1988 Field Theory Handbook – Including Coordinate Systems, Differential Equations and Their Solutions, 2nd edn. p. 104. Springer.Google Scholar
Peñas-López, P., van Elburg, B., Parrales, M. A. & Rodríguez-Rodríguez, J. 2016a Diffusion of dissolved CO2 in water propagating from a cylindrical bubble in a horizontal Hele–Shaw cell. Phys. Rev. Fluids (submitted).Google Scholar
Peñas-López, P., Parrales, M. A. & Rodríguez-Rodríguez, J. 2015 Dissolution of a CO2 spherical cap bubble adhered to a flat surface in air-saturated water. J. Fluid Mech. 775, 53–76.Google Scholar
Peñas-López, P., Parrales, M. A., Rodríguez-Rodríguez, J. & van der Meer, D. 2016b The history effect in bubble growth and dissolution. Part 1. Theory. J. Fluid Mech. 800, 180–212.Google Scholar
Rosner, D. E. & Epstein, M. 1972 Effects of interface kinetics, capillarity and solute diffusion on bubble growth rates in highly supersaturated liquids. Chem. Engng Sci. 27 (1), 69–88.Google Scholar
Scriven, L. E. 1959 On the dynamics of phase growth. Chem. Engng Sci. 10 (1), 1–13.Google Scholar
Shim, S., Wan, J., Hilgenfeldt, S., Panchal, P. D. & Stone, H. A. 2014 Dissolution without disappearing: multicomponent gas exchange for CO2 bubbles in a microfluidic channel. Lab on a Chip 14, 2428–2436.Google Scholar
Sun, R. & Cubaud, T. 2011 Dissolution of carbon dioxide bubbles and microfluidic multiphase flows. Lab on a Chip 11, 2924–2928.Google Scholar
Szekely, J. & Martins, G. P. 1971 Non equilibrium effects in the growth of spherical gas bubbles due to solute diffusion. Chem. Engng Sci. 26 (1), 147–159.Google Scholar
Takemura, F., Liu, Q. & Yabe, A. 1996 Effect of density-induced natural convection on the absorption process of single bubbles under a plate. Chem. Engng Sci. 51 (20), 4551–4560.Google Scholar
Thom, A. 1933 The flow past circular cylinders at low speeds. Proc. R. Soc. Lond. A 141 (845), 651–669.Google Scholar
Volk, A., Rossi, M., Kähler, C. J., Hilgenfeldt, S. & Marín, A. 2015 Growth control of sessile microbubbles in PDMS devices. Lab on a Chip 15, 4607–4613.Google Scholar
Weinan, E. & Liu, J.-G. 1996 Vorticity boundary condition and related issues for finite difference schemes. J. Comput. Phys. 124 (2), 368–382.Google Scholar