The Bipolar Analysis of a Single Sphere in an Electrolytic Cell

The bipolar behavior of a single sphere in an electrolytic cell is investigated in this study. A mathematical model is proposed for two surface conditions: linear polarized kinetics and the Butler‐Volmer kinetics. Analytical current and potential distributions are obtained for a reversible reaction and linear polarized kinetics. Semianalytical potential and current distributions for the Butler‐Volmer kinetics are also obtained by the boundary collocation method. The current enhancement factor is defined as the ratio of the bipolar current to the applied current, and its value is predicted theoretically for linear polarization. The effective conductivity of a dilute dispersion is also formulated and related to the first coefficient of the series expression of the potential in a continuous medium. The influences of various parameters, including dimensionless potential drop, Ψ, conductivity ratio of electrolyte to solid phase, α, ratio of exchange current density to applied current, β, and transfer coefficients, and , are respectively discussed. The suitability of assuming linear polarized kinetics is also evaluated by comparing it with the Butler‐Volmer kinetics.