Polarization of disc and ring electrodes in high-conductivity electrolyte solutions

Studies of electrical double layers near charged surfaces in electrolyte solutions are important for a wide range of applications including biophysics, colloidal science, and micro/nanofluidics. We investigate the polarization of disc and ring electrodes immersed in an electrolyte solution and subjected to a small external AC voltage governed by the Debye−Falkenhagen equation (a linearization of the Nernst−Planck equations) and the Poisson equation. Based on integral transforms, analytical techniques are developed for predicting the space charge density and complex impedance of the system. The effect of electrode dimension on the impedance is examined and compared with experiments. These mathematical models enable uncovering detailed knowledge of the surface charge densities on the electrodes from experimental impedance spectroscopy measurements.