REDUCING NONLINEAR-SYSTEMS OF TRANSPORT-EQUATIONS TO LAPLACES-EQUATION

Steady-state systems of coupled nonlinear transport equations are considered with boundary conditions determined by an electrochemical reaction (or reactions) on an electrode surface. A heuristic method for reducing such systems to a single Laplace equation with a nonlinear boundary condition is illustrated on several different examples. Flux distributions on the electrodes are derived by integral-equation techniques. The examples concern transport in a dilute electrochemical solution, where fluxes are given by the Nernst-Planck equation for diffusion and migration in an electric field, and a gas transport problem where fluxes are given by the Stefan-Maxwell equations. The effects of nonlinearities at transport-limited current conditions are characterized in a way that is independent of electrode geometry.