Bubble departure radius

The detachment of the bubble occurs if the condition FB = Fc is satisfied. It follows that the mean bubble departure radius (Rd) is well defined for a given electrode—electrolyte configuration (typical values are around 50 pm [115]). It may be expected that the mean bubble departure radius is mainly a property of the electrode (the electrode surface roughness which influences D), the electrode wettability (through the contact angle i9), and the electrolyte (density and surface tension of the electrolyte), but not of the current density j. However, the question is whether a cavity (nucleation site) is active or non-active. The current density may influence the activation of the nucleation sites. 

Several authors have studied the dependence of the mean bubble departure radius (Rd) on the current density. Venczel [109] found that for small current densities (typically j < 2 kA/m2) the radius decreases with decreasing current density. It seems to become independent of the current density for higher values, while the number of growing bubbles increases. Vogt [115] observed a similar behaviour for small current densities. Other authors [18,38,42] found that the mean departure radius increases with the current density j according to the following empirical power law ... 

It has to be stressed that all these empirical laws were obtained for relatively small current densities (j < 10 kA/m2). Gabrielli et al. [38] observed that for sufficiently high current densities the departure radius becomes independent of j. Depending on the nature of the gas, there seems to be a maximum bubble diameter. They found that this maximum diameter would be reached for j 90 kA/m2 in the case of hydrogen bubbles. 

Another important point to realise is that R depends not only on the equilibrium condition between the buoyancy force and the capillary force, but also on the bubble coalescence. Coalescence becomes more and more important for higher current densities. As measured by Janssen and van Stralen [66], the number of growing bubbles increases with the current density and thus coalescence becomes more and more probable. In the same paper, Janssen showed that the mean departure radius of bubbles can strongly depend on the quality of the electrode (he compared unused electrodes with used electrodes of the same type). 

Once the bubbles leave the electrode surface (when they have a radius equal to the departure radius) they diffuse into the bubble diffusion region. This region has a very high bubble concentration [12] with a typical thickness of a few millimetres. The bubbles can still grow. 

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