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

N. Valle Marchante*, J.W. Haverkort

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

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.
Original languageEnglish
Article numberA38
Number of pages18
JournalJournal of Fluid Mechanics
Volume996
DOIs
Publication statusPublished - 2024

Keywords

  • buoyant boundary layers
  • gas/liquid flow

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