Abstract
The growth of attached bubbles during the electrochemical evolution of hydrogen at a horizontal cathode at the base of a quiescent, dilute aqueous solution is analysed using a simple model of the process that includes the Butler–Volmer reaction model, the diffusion and migration of electroactive species and a symmetry condition that approximately accounts for the presence of periodically spaced bubbles on the electrode surface. The diffusion controlled growth of a bubble approximately follows a $t^{1/2}$ law when the spacing of the bubbles on the electrode is large, departing slightly from it due to the non-uniformity of the concentration of dissolved hydrogen in the supersaturated solution into which the bubble grows, and approaches a $t^{1/3}$ law when the spacing decreases. The space- and time-averaged current density increases exponentially with the applied voltage for an alkaline solution when the consumption of water in the reaction is not taken into account. For an acidic solution, the average current density saturates to a transport limited value that depends on bubble spacing. For a given voltage, the presence of attached bubbles increases the average current density due to the decrease of the concentration overpotential caused by the bubbles. The spacing of the bubbles on the electrode surface decreases when the voltage increases if the maximum supersaturation at the electrode is imposed to be constant. The result suggests that coalescence of attached bubbles will occur above a certain voltage.
Highlights
Gas evolution reactions play an important role in many electrochemical processes of interest
The life cycle of a bubble at a gas-evolving electrode begins with the nucleation at a suitable site of the electrode surface of a cluster of gas molecules from a solution supersaturated with dissolved gas
The bubble grows by taking up dissolved gas that reaches its surface by diffusion (Brandon & Kelsall 1985; Enríquez et al 2014), and detaches from the electrode when the buoyancy force, aided by hydrodynamic forces if the liquid flows around the electrode (Eigeldinger & Vogt 2000), overcomes the surface tension and electric forces that keep the bubble on the electrode surface (Brandon et al 1985; Oguz & Prosperetti 1993; Lv et al 2017)
Summary
Gas evolution reactions play an important role in many electrochemical processes of interest. The local density of electric current passing between the electrode and the liquid is proportional to the local rate of the electrochemical gas-evolving reaction, which in turn depends on the local concentrations of reactants and products at the electrode and increases with the applied voltage (see section). The electric current density averaged over the electrode surface and over the time of growth of the bubble is computed as a function of the voltage applied between the upper boundary and the electrode of the simulated half-cell. This current density is found to increase with the voltage and, for a given voltage, it is larger than the current density in the absence of bubbles. The variation of the bubble spacing with applied voltage that leads to a constant maximum supersaturation on the electrode, which is the model prediction of bubble coverage, is computed
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