A model of the growth of hydrogen bubbles in the electrolysis of water

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.