Common Approximations for the Current Distribution

Even when applying the thin boundary layer approximation, the equations required for solving the current and potential distributions in the electrochemical cell yield a nonlinear system requiring iterative solution. The reason is that the boundary conditions incorporate the unknown term (the electrostatic potential or the current density). While this presents no serious hurdle for computer-implemented numerical solutions, analytical solutions of nonlinear systems are difficult and generally require a linearization procedure. To analytically characterize features of the current distribution, some simplifying approximations are frequently applied. These are summarized in Table 1, and are discussed below. 

Approximation Prevailing overpotential Controlling equation Boundary conditions 

---