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

We build and solve 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 the dependence of the detachment time on other parameters such as the applied voltage and the hydrogen ion concentration at the fluid bulk.