Self-similar solution for laminar bubbly flow evolving from a vertical plate

The development of a bubble plume from a vertical gas-evolving electrode is driven by buoyancy and hydrodynamic bubble dispersion. This canonical fluid mechanics problem is relevant for both thermal and electrochemical processes. We adopt a mixture model formulation for the two-phase flow, consideri...

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Bibliographic Details
Published in:Journal of fluid mechanics 2024-10, Vol.996, Article A38
Main Authors: Valle, N., Haverkort, J.W.
Format: Article
Language:English
Subjects:
Boundary layer equations
Boundary layers
Boussinesq approximation
Boussinesq equations
Bubbles
Density
Dispersion
Electrochemistry
Fluid flow
Fluid mechanics
Height
Hydrodynamics
JFM Papers
Laminar boundary layer
Laminar flow
Laminar mixing
Multiphase flow
Scaling
Self-similarity
Specific volume
Thickness
Two phase flow
Velocity
Viscosity
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Summary:The development of a bubble plume from a vertical gas-evolving electrode is driven by buoyancy and hydrodynamic bubble dispersion. This canonical fluid mechanics problem is relevant for both thermal and electrochemical processes. We adopt a mixture model formulation for the two-phase flow, considering variable density (beyond Boussinesq), viscosity and hydrodynamic bubble dispersion. Introducing a new change of coordinates, inspired by the Lees–Dorodnitsyn transformation, we obtain a new self-similar solution for the laminar boundary layer equations. The results predict a wall gas fraction and gas plume thickness that increase with height to the power of 1/5 before asymptotically reaching unity and scaling with height to the power 2/5, respectively. The vertical velocity scales with height to the power of 3/5. Our analysis shows that self-similarity is only possible if gas conservation is entirely formulated in terms of the gas specific volume instead of the gas fraction.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2024.793