Of course, the volume fraction of hydrogen gas bubbles cannot exceed 100%. Consider spherical gas bubbles of equal size, the maximum theoretical packing fraction is much lower at about 74 %, or even roughly 64 % for a random packing. The space between bubbles can be taken up by smaller bubbles and the space between those smaller bubbles again by smaller bubbles, so that theoretically there is no strict limit below 100%. Also, gas bubbles could coalesce to form a big bubble filling the entire electrolyser space so that the gas fraction could approach 100%.
However, it turns out that bubbles in strong electrolytes do not coalesce so easily and prefer to stay at a small distance from each other. This makes that these hydrogen and oxygen bubbles behave somewhat like solid particles. Therefore, we introduced into our models what in granular matter modelling is called solid pressure. As the gas fraction increases, a repulsive pressure avoids a further increase.
Figure: Simulations of the gas fraction near a zero-gap electrode. Red is about 60%.
We find that a maximum gas fraction around 65 % corresponds well with experimental results on the bubble-induced resistance. In this way, the extra ingredient of a solid pressure helps simulations correspond more to reality and as a result converge more easily as extremely high gas fractions are avoided.
