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Bubble-mediated transfer of dilute gas in turbulence

Published online by Cambridge University Press:  14 June 2021

Palas Kumar Farsoiya Open the ORCID record for Palas Kumar Farsoiya [Opens in a new window] ,
Stéphane Popinet Open the ORCID record for Stéphane Popinet [Opens in a new window]  and
Luc Deike Open the ORCID record for Luc Deike [Opens in a new window]
Palas Kumar Farsoiya
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
Stéphane Popinet
Affiliation:
Institut Jean Le Rond d'Alembert, CNRS UMR 7190, Sorbonne Université, Paris75005, France
Luc Deike*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA High Meadows Environmental Institute, Princeton University, Princeton, NJ08544, USA
*
†Email address for correspondence: ldeike@princeton.edu
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Abstract

Bubble-mediated gas exchange in turbulent flow is critical in bubble column chemical reactors as well as for ocean–atmosphere gas exchange related to air entrained by breaking waves. Understanding the transfer rate from a single bubble in turbulence at large Péclet numbers (defined as the ratio between the rate of advection and diffusion of gas) is important as it can be used for improving models on a larger scale. We characterize the mass transfer of dilute gases from a single bubble in a homogeneous isotropic turbulent flow in the limit of negligible bubble volume variations. We show that the mass transfer occurs within a thin diffusive boundary layer at the bubble–liquid interface, whose thickness decreases with an increase in turbulent Péclet number, $\widetilde {{Pe}}$. We propose a suitable time scale $\theta$ for Higbie (Trans. AIChE, vol. 31, 1935, pp. 365–389) penetration theory, $\theta = d_0/\tilde {u}$, based on $d_0$ the bubble diameter and $\tilde {u}$ a characteristic turbulent velocity, here $\tilde {u}=\sqrt {3}\,u_{{rms}}$, where $u_{{rms}}$ is the large-scale turbulence fluctuations. This leads to a non-dimensional transfer rate ${Sh} = 2(3)^{1/4}\sqrt {\widetilde {{Pe}}/{\rm \pi} }$ from the bubble in the isotropic turbulent flow. The theoretical prediction is verified by direct numerical simulations of mass transfer of dilute gas from a bubble in homogeneous and isotropic turbulence, and very good agreement is observed as long as the thin boundary layer is properly resolved.

JFM classification

Drops and Bubbles: Bubble dynamics Mass Transport: Coupled diffusion and flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A34
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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