A SIMILARITY SOLUTION TO A PROBLEM IN NONLINEAR ION TRANSPORT WITH A NONLOCAL CONDITION

Abstract

We derive an initial–boundary value problem with a nonlocal condition to model mass and charge transport in a controlled potential experiment called chronoamperometry. The charge is carried by ions set in motion by a change in the applied electrode potential. The resulting electric current is called the current response. When the charge flux arises from diffusion alone, the model reduces to an initial–boundary value problem for the heat equation. We consider diffusion and migration (motion under the influence of an electric field). This latter component of the total flux gives rise to a nonlinearity in the transport equations. Experimentalists have noted the current response to be proportional to the square root of the time with or without migration. It is shown that the initial–boundary value problem has a unique similarity solution that accounts for this observation.