  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.
