Asymptotic solutions for the electric potential and complex impedance of disc electrodes in high-conductivity electrolyte solutions

The study of electrical double layers near charged surfaces in electrolyte solutions is crucial for a range of applications, such as biophysics, colloidal science, and micro/nanofluidics. We derive asymptotic formulas for the electric potential and complex impedance of polarized disc electrodes in an electrolyte solution subject to a small external AC voltage based on the Debye–Falkenhagen approximation to the coupled Poisson–Nernst–Planck equations. Results from asymptotic formulas for the complex impedance are compared with experimental data, and scales for impedance and frequency are identified that lead to self-similar behavior. This analytical modeling can aid in optimizing electrode design and inform the use of dielectrophoresis techniques for manipulating and characterizing biological analytes in microfluidic devices.