Improved current-voltage approximations for currents exceeding the diffusion limit

Direct ionic current flows through a binary electrolyte solution bounded by two reactive electrodes which are connected to a voltage source. At sufficiently large voltages, the classical boundary-layer structure of the one-dimensional transport problem breaks down, resulting in currents exceeding Nernst's diffusion limit. While the asymptotic structure at these high voltages is well understood [B. Zaltzman and I. Rubinstein, J. Fluid Mech., 579(2007), pp. 173-226], the direct calculation of the pertinent current-voltage relation for the electrochemical cell is thwarted by the appearance of nonconverging integrals. We describe a systematic regularization procedure which allows this calculation.