Changes in zeta potential caused by a dc electric current for thin double layers

An asymptotic solution was obtained to describe one-dimensional, steady-state transport of a symmetric binary electrolyte normal to two large parallel electrodes, in the limit in which the Debye length is infinitesimal compared to the distance separating the two electrodes. Despite the nonzero ion flux, Boltzmann's equation continues to describe the relationship between either ion concentration and the electrostatic potential inside the diffuse part of the double layer, while local electroneutrality applies outside, even for current densities approaching the limiting value. In the absence of ion adsorption or dissociation reactions at the electrodes, the magnitude of any charge or zeta potential arising on the electrodes at zero current is determined by the equilibrium constant for the redox reactions which would exchange ionic charge carriers for electric charge carriers at the electrode surface. Nonzero current causes the ionic strength of the bulk to vary with position. This perturbs the Debye length of the diffuse cloud on either electrode: it is the local ionic strength just outside the cloud which determines the Debye length for that cloud. Nonzero current also changes the zeta potential. The dimensionless rate of change dζ/dJ was as large as 30.