Geometric Requirements for Uniform Current Densities at Surface-Conductive Insulators or Resistive Electrodes

The conditions for practically uniform current densities in the presence of ohmic potential drops along electrode surfaces are established for several configurations. Perfectly uniform current flow lines in the electrolyte can be obtained within limited ranges, with electrodes having cylindrical surfaces traced by Eq. [9], or be closely approximated with electrodes in the form of parabolic cylindrical or paraboloid segments traced by Eq. [11] or [20] or [22]. For practically uniform current densities at either curved or flat electrodes, the areas must be limited to narrow bands, rings, or small circles, as indicated in Fig. 2 or by Eq. [38], [49], [68], or [92]. For identical flat narrow‐band electrodes perpendicular to the cell walls, a mirror‐symmetric arrangement of external current‐collecting contacts is shown to require a fourfold larger minimum electrode spacing than a line‐symmetric arrangement.