Bubble coverage

H. Vogt, R.J. Balzer, The bubble coverage of gas-evolving electrodes in stagnant electrolytes, Electrochimica Acta, Volume 50, Issue 10 (2005) pp2073-2079... 

Electrochemical discharges have all the characteristics of arc discharges. They occur in a very similar voltage range with similar currents and at atmospheric pressure. The question remains as to how these arcs can be initiated. We have proposed the hypothesis that the ignition is thermal [123]. The cathode temperature required is probably reached before the gas film is totally formed,3 when the active electrode bubble coverage fraction reaches its maximum value. 

Note that, in this description, the shadowing of the surface by the bubbles in the adherence region was not considered. With increasing bubble coverage fraction 6, the resistance in the diffusion region ff will also increase. A possible ansatz is to write (3.44) as ... 

The evolution of bubbles on a gas evolving electrode is a dynamic process. As described in previous sections, percolation theory can help to quantify the bubble size distribution in the adherence region if the mean bubble coverage fraction 9 is known. In order to derive an equation describing the evolution of 6 for gas evolving electrodes, we will write a mass balance equation between the amount of gas produced and the quantity of gas leaving the adherence region [125,129]. Faraday s law computes VG, the amount of gas produced per unit time at an electrode ... 

The evolution equation of the bubble coverage fraction 9 is as follows ... 

The stationary mean bubble coverage fraction 0s is given by the stationary solution of Equation (3.61) ... 

To evaluate the sum from Equation (3.68), we will use the approximation smax = oo in the following paragraphs. As long as 9 is smaller than the percolation threshold pc, the stationary bubble coverage fraction is given by ... 

In a similar manner, one can write a relation between the terminal voltage and the stationary bubble coverage fraction (9s < pc) ... 

Increase in the nominal current density With increasing nominal current density I/A, the bubble coverage fraction increases. When it reaches a critical value, as computed by (4.16), a gas film is formed. Such a scenario happens, for example, in current-controlled cells or, as will be seen in Section 4.1.3, in a voltage-controlled cell if for some reason the inter-electrode resistance decreases. 

Figure 4.7 Step input for a terminal voltage lower than the critical voltage (a) bubble coverage fraction 0 step input (b) normalised current J step input.

For higher terminal voltages, the bubble coverage fraction will grow according to Equation (4.22) until it reaches the percolation threshold where the gas film forms. The time tf until pc is attained is given by the solution of 0 t f) — Pc One obtains for the gas film formation time (Fig. 4.8) ... 

Eigeldinger, X Vogt, H. The bubble coverage of gas-evolving electrodes in a flowing electrolyte. Electrochim. Acta 45 27 (2000), pp. 4449-4456. 

The foregoing is an equilibrium analysis, yet some transient effects are probably important to film resilience. Rayleigh [182] noted that surface freshly formed by some insult to the film would have a greater than equilibrium surface tension (note Fig. 11-15). A recent analysis [222] of the effect of surface elasticity on foam stability relates the nonequilibrium surfactant surface coverage to the foam retention time or time for a bubble to pass through a wet foam. The adsorption process is important in a new means of obtaining a foam by supplying vapor phase surfactants [223]. 

Precipitation and Generation Methods For a thorough understanding of the phenomena involved, bubble nucleation ould be considered. A discussion of nucleation phenomena is beyond the scope of this Handbook however, excellent coverages are presented by Blander and Katz. 

Figure 12.18 Voltammetric CO stripping from a Pt(l 11)/Ru electrode (Ru coverage approximately 0.2 ML) to aCO-free 0.1 M H2SO4 solution. The baseline voltammogramfromPt(lll)/ Ru after CO stripping is shown. The scan rate was 1 mV/s. CO was adsorbed at 0 V for 5 minutes, and was purged from solution by Ar bubbling for 25 minutes.

CO was adsorbed during 5 min. at 0.2 V (saturation coverage) and then eliminated from the bulk by bubbling Ar for 5 min. Then the solution was exchanged... 

Regular Perturbation Solution. To effect an analytical expression for the bubble-flow resistance, we consider fast sorption kinetics or equivalently, small deviations from equilibrium surfactant coverage making 0 large. Hence, a regular perturbation expansion is performed in 1/0 about the constant-tension case. The resulting equations for and rf are to zero and first order in 1/0 (21) ... 

In equation 5, C is amorphous carbon and CF2 changes to many perfluorocarbons, such as CF4, C2F6, etc., by secondary reactions. The surface coverage of graphite fluoride on the anode depends on the relative reaction rates of equations 4 and 5. Equation 6 has been introduced to analyze the wettability of the carbon surface with graphite fluoride formed on it.2 It shows the relationship between the fraction of effective surface for equation 3 per unit surface area of carbon (a) and the contact angle (0) of a fluorine gas bubble on the surface of the carbon electrode.2... 

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