Calculation of mass transfer to and from electrodes when homogeneous reactions occur in the mass-transfer boundary layer often requires numerical solution because the transport equations are generally nonlinear. Although finite-difference or finite-element methods are common, they may sometimes fail if the model equations are too stiff, for example, when a thin reaction zone is established by fast reactions. The structure of such problems is examined analytically by a perturbation analysis of a simplified model system. Numerical calculations of aqueous carbonate-species concentration profiles and interfacial pH are done for the boundary layer on a cathode where hydroxide ion is produced by the reduction of oxygen and reacts rapidly with the carbonates. These examples demonstrate how such problems may be formulated when very fast homogeneous reversible reactions are involved. Many electrode processes involve homogeneous reactions that occur simultaneously in the mass-transfer boundary layer. These reactions include breaking or formation of metal-ligand complexes during deposition or dissolution, ion association and dissociation, and cycling of soluble redox mediators. Quantitative analyses of electrode-kinetics experiments as well as modeling of processes in electrochemical reactors require identification of species concentrations at the electrode surface, and these can be affected strongly by such homogeneous reactions.The calculation of concentration profiles in the solution boundary layer near electrodes is based on the species conservation equationwhere c i is the molar concentration of species i, and R i is the net rate of production of i locally by homogeneous reactions. The molar flux N គ i is usually represented bywhich accounts for species transport by diffusion and convection as well as migration of ions in an electric field.1 The homogeneousreaction-rate terms often follow the form of the mass-action law, especially for reversible reactions such as ion association. That is, for a reaction such asthe rate of production of M i z i would be written asEquations 1-4 are written for each species in solution and combined with the electroneutrality conditionwhen charged species are involved and must be calculated. Their solution then requires application of appropriate boundary conditions on the electrode and in the bulk solution. Problems of this form have been solved for many important situations, including cyclic voltammetry, rotating disk and ring-disk electrodes, chronopotentiometry, and various boundary-layer flows with a variety of geometries, system chemistries, flow conditions, and electrode boundary conditions.2-6 The purpose of this paper is to investigate a limiting case where the homogeneous reactions are fast and reversible such that they establish a reaction zone very close to the electrode that requires modification of standard calculation procedures. To illustrate the issue of concern, we first consider a simple model problem. Then the conclusions are applied to the calculation of concentratio...
The precipitation of calcium carbonate from water containing 3 mM CaCO3 has been studied on a rotating disk electrode made of 304 stainless steel. When the electrode is polarized at potentials where hydrogen is produced or dissolved oxygen is reduced, the reduction reaction raises the interfacial pH sufficiently to precipitate the carbonate. The effects of current density and modulation on the precipitation process have been examined. This paper reports on the nature of the precipitates formed. Depending on the experimental conditions, one may obtain calcite, vaterite or aragonite. A mathematical model has been developed to describe the transport phenomena in the boundary layer on the rotating disk electrode. This model takes into account convection, diffusion, and migration as well as the homogeneous ionic equilibria in order to estimate the degree of supersaturation at the surface.
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