Self-similar solution for laminar bubbly flow evolving from a vertical plate
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.
Cite
@article{arxiv.2401.13113,
title = {Self-similar solution for laminar bubbly flow evolving from a vertical plate},
author = {N. Valle and J. W. Haverkort},
journal= {arXiv preprint arXiv:2401.13113},
year = {2024}
}