A similarity solution to a problem in nonlinear ion transport with a nonlocal condition

We derive an initial-boundary value problem with a nonlocal condition to mo del mass and charge transport in a controlled potential experiment called c hronoamperometry. The charge is carried by ions set in motion by a change i n the applied electrode potential. The resulting electric current is called the current response. When the charge flux arises from diffusion alone, th e model reduces to an initial-boundary value problem for the heat equation. We consider diffusion and migration (motion under the influence of an elec tric field). This latter component of the total flux gives rise to a nonlin earity 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.