Characterization of porous membranes by zeta-potential under an ac electric field: analytical treatment of time-dependent electroosmostic flow

Electroosmosis has been used to determine zeta-potentials of porous membranes with nano-pores. In order to eliminate the influence of electrode polarization and concentration polarization on the membrane surface, one should employ an alternating electric field instead of a direct electric field. However, theoretical study of time-dependent electroosmosis flow is limited. In this work, we obtained an analytical solution of oscillating electroosmosis flow that is based on the Debye–Hückel approximation. The derived analytical solutions are useful for more general time-dependent problems through superposition of time-harmonic solutions weighted by the appropriate Fourier coefficients. We have provided a new formula for the determination of zeta-potentials for porous membranes under an alternating electric field. Our results suggest that the use of a steady-state equation to interpret zeta-potentials of nano-pores by means of the amplitude or plateau value of an oscillating sinusoidal and step function electric field can be misleading only when the frequency of oscillation is as high as 108 Hz.