Three-dimensional numerical study on hydrogen bubble growth at electrode

TL;DR

This work investigates hydrogen bubble growth, coalescence, and detachment at electrodes using 3D direct numerical simulation with a VOF-based one-fluid Navier–Stokes formulation in Basilisk. It combines axisymmetric validation with fully 3D studies of single and multiple nucleation sites, analyzing diffusion-controlled growth ($R \propto t^{1/2}$), mass transfer quantified by Sherwood numbers, and detachment governed by Fritz’s relation. Key findings show that current density and contact angle modulate growth, while several bubbles suppress individual growth yet detach earlier upon coalescence; these insights advance understanding of gas removal efficiency in electrolysis. The results provide mechanistic guidance for electrode design and operation aimed at improving overall electrolysis efficiency by optimizing bubble management and surface-wettability strategies.

Abstract

Three-dimensional direct numerical simulation of electrolysis is applied to investigate the growth and detachment of bubbles at electrodes. The moving gas-liquid interface is modeled employing the VOF-based method. To ensure the accuracy of the simulations, a mesh-independence study has been performed. The simulations include the growth phase of the bubbles, followed by their detachment from the electrode surface, and the results are validated with analytical models and experimental data. The bubble growth is diffusion-controlled, leading to the scaling \(R\propto t^{1/2}\), but our simulation overpredicts the growth exponent during the initial stage. We further demonstrate that the number of nucleation sites significantly affects gas transport, as quantified by the Sherwood number. The influences of contact angle and nucleation site on bubble detachment are also examined. The predicted detachment radius varies linearly with contact angle, consistent with Fritz's linear relation between the volume-equivalent radius and contact angle, confirming that the surface tension is the dominant attachment force. Finally, as the nucleation sites increase, the induced bubble coalescence accelerates the bubble detachment. Taken together, these findings give us valuable insights into improving gas bubble removal and enhancing overall electrolysis efficiency.

Figures (19)

• Figure 1: Schematic representation of the two-phase electrochemical system with relevant chemical reactions and boundary conditions at the cathode.
• Figure 2: Sketch of the axisymmetric simulation setup.
• Figure 3: Sketch of the 3D simulation setup
• Figure 4: Sensitivity test on decreased surface tension (a), and increased hydrogen density (b).
• Figure 5: Frames show the dissolved hydrogen concentration for a bubble growing at the contact angle of $\theta=90 \degree$(with the current density of $I=\mathrm{1000 A/m^2}$). The color legend represents $\mathrm{H_2}$ concentration, while the upper limit is $0.2 \mathrm{mol/m^3}$.