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Turbulent two-phase plumes with bubble-size reduction owing to dissolution or chemical reaction

Published online by Cambridge University Press:  25 January 2013

Mariana G. Domingos  and
Silvana S. S. Cardoso
Mariana G. Domingos
Affiliation:
Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK
Silvana S. S. Cardoso*
Affiliation:
Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK
*
†Email address for correspondence: [email protected]
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Abstract

Turbulent two-phase plumes consisting of a continuous phase of entrained fluid and a dispersed phase, in the form of buoyant droplets/bubbles, are investigated. Chemical reaction or dissolution causes both a decrease in the size of the droplets/bubbles and a change in the buoyancy of the plume. The behaviours of such a plume in environments with uniform and stratified density are considered. We show that the dynamics of the plume are determined by two dimensionless groups: $N/ T$ and $G/ T$. Here, $N$ is the buoyancy frequency of the environment, $G$ measures the ability of the reaction to change buoyancy and $T$ reflects the effect of reaction on the size of the droplets/bubbles. We identify four regimes of behaviour of a plume in a stratified environment depending on whether the dominant effect on buoyancy arises from reaction or stratification, and on the occurrence of either multiple or single zero-buoyancy levels. For a uniform environment, perturbation solutions for the fluxes of volume, momentum, buoyancy and chemical species as a function of ascent distance are obtained. We apply our findings to understand the dynamics of both of the cases of a release of methane and a release of carbon dioxide in the ocean. For a methane release in the Gulf of Mexico, the motion of the plume is shown to be controlled by external density stratification for a bubble diameter of methane above ${\sim }1$–2 mm. In the case of a carbon dioxide release in the Norwegian Sea, dissolution determines the motion of the plume when the bubble diameter is smaller than ${\sim }0. 5$–3.5 cm. In both scenarios, the plume releases seawater enriched with the chemical at multiple levels.

JFM classification

Convection: Plumes/thermals Turbulent Flows: Turbulent convection Reacting Flows: Turbulent reacting flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 716 , 10 February 2013 , pp. 120 - 136
Copyright
©2013 Cambridge University Press

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