During electrolysis, the mechanism by which bubbles form on the electrodes, develop, and detach, is not fully understood. This is an issue because the size and persistence of bubbles have an impact on electrolysis efficiency because bubbles significantly reduce the electrode surface area in direct contact with the electrolyte, and can result in increased circuit path resistance.
Let us look at the process in a little more detail, though still rather simplistically. A hydrogen ion in the vicinity of the cathode may gain an electron and become a free hydrogen atom which immediately dissolves in the electrolyte. Two hydrogen atoms will combine to form a hydrogen molecule in solution (releasing energy). Once the liquid becomes supersaturated with hydrogen, bubbles of gas will start forming around nucleation sites. The process is dynamically extremely complex but can be modelled effectively just by assuming the gas being generated finds its way into the growing bubbles through a quasi-equilibrium process; it is not necessary to track the movement of each hydrogen atom. The bubble is initially attached to the electrode because the total adhesion force is greater than the combination of surface tension and gravity, but as the bubble grows, the balance shifts and the bubble will eventually detach.
Building a model of the process is useful as it illustrates of the effect of bubble formation on efficiency. With this knowledge it is possible to develop novel strategies for rapidly dispersing the bubbles, perhaps by forced electrolyte circulation. The bubble formation process for a stagnant electrolyte is illustrated above for a cathode with a roughened surface that is placed flat along the bottom of the cell. A much simplified 2-D model is presented that ignores the movement of the electrolyte, internal pressure, and heat and mass transfer (essentially a 1 mm deep electrode). The blue indicates the concentration of dissolved gas.
We will bear in mind the effect of bubbles later when we look at the factors that affect the efficiency of an alkaline electrolyser.
You may wish to develop a more realistic model yourself. A key parameter is the bubble contact angle θ (measured through the gas phase) which will range from 90 degrees for the smallest bubbles increasing towards 180 degrees at the point of detachment (in practice, the bubble detaches when the angle is about 150 degrees). As the angle increases the surface tension force in the direction normal to the surface decreases as a fraction of the force magnitude (per unit contact length). However, the line of contact changes and can increase, though as a fraction of bubble radius it will decrease, affecting surface tension and adhesion together. Bubble buoyancy and drag also needs to be taken into account.
Even in this approximation, there are a lot of effects changing in complex ways, and building an accurate model is very difficult; really, commercial software like ANSYS should be used. However, you can get a better understanding of the underlying concepts just from the force balance to first order accuracy; the forces at work whilst the bubble is growing are balanced as follows:
FAdhesion(ro) + FSurface Tension(ro) + FBuoyancy(r, ro) = 0,
where ro is the radius of the contact circle and r is the bubble radius. Taking the upward direction as positive the equation can be rewritten in terms of three positive constants (after calculating ro from r and θ ):
-2 π k1 r sin θ + 2 π k2 r sin2θ + f(r, ro) k3 r3 = 0
The function f(r, ro) describes the change in volume because of the contact region and bubble distortion effects. As r increases, the angle will increase from an initial 90 degrees, heading towards 180 degrees. After dividing through by r, the sum of the first two terms becomes smaller as expected. The tendency will therefore be for the bubble to eventually detach once it is no longer possible to get the equation to balance.
A full analysis gives the detachment radius from Fritz's formula:
rd3 = 3roσ sin θ / 2Δρg
where σ is the hydrogen gas-electrolyte surface tension.
For more information refer to this paper.