Phase field modelling of the growth and detachment of bubbles in a hydrogen electrolyzer

TL;DR

The paper addresses the challenge of modeling $H_2$ bubble growth and detachment at a working electrode during water electrolysis. It develops a fully coupled diffuse-interface framework that combines the Cahn–Hilliard phase-field description with incompressible Navier–Stokes flow and electrochemical transport (protons and hydrogen) governed by Butler–Volmer kinetics, while accounting for gravity and a prescribed contact angle $\theta_Y$. Key findings show that detachment volume and time strongly depend on $\theta_Y$, whereas the detachment time is only weakly affected by the applied electrode potential, with larger effects at lower acidity; the model also highlights the role of near-wall hydrogen flux and remnant gas in nucleation. The work provides a computational tool to study bubble management in hydrogen electrolyzers and offers insights for electrode design and operation to optimize gas release and efficiency.

Abstract

We develop and implement numerically a phase field model for the growth and detachment of a gas bubble resting on an electrode and being filled with hydrogen produced by water electrolysis. The bubble is surrounded by a viscous liquid, has a prescribed static contact angle and is also subject to gravitational forces. We compute, as a function of the static contact angle, the time at which the bubble detaches from the substrate and what volume it has at that time. We also investigate de dependence of the detachment time on other parameters such as the applied voltage and the hydrogen ion concentration at the fluid bulk.

Figures (12)

• Figure 1: Sketch of physical settings: H$_2$ is produced at the electrode by water electrolysis using the electrons $e^-$ provided by the battery, and diffuses inside the bubble with the contact angle $\theta_Y$. The bubble will grow and detach once buoyancy forces due to gravity overcome the surface tension forces that attach the bubble to the surface.
• Figure 4: Bubble volume at lift-off instant for different contact angles. Each point in the graph corresponds to a single simulation were only the contact varies.
• Figure 5: Time to lift-off for different contact angles. Each point in the graph corresponds to a single simulation were only the contact varies. Overall time is represented in the horizontal axis, which takes into account the coalescence time plus the simulation time from the initial conditions until the moment when the bubbles lifts-off. The coalescence time has been assumed calculating the growth rate in the first instants and extrapolating this trend backwards.
• Figure 6: Lift-off times for different applied voltages. Graphs with different values of reference proton concentrations are shown in the figure, the figure shows the decay of the lift off time respect to the applied voltage. The effect is greater when the proton concentration at the electrode is lower.
• Figure : (a) $t=0.1\,\text{s}$