AC-driven electro-osmotic flow in charged nanopores

Abstract

In this paper we report the theory describing the electro-osmotic flow in charged nanopores with constant radius and charge density driven by alternating current. We solve the ion and solution transport in unsteady conditions as described by the Navier-Stokes and Nernst-Planck equations considering the electrical potential inside the charged nanopore uniform in the radial direction (Uniform Potential model approximation). We derive the transport equation system in the case in which the pore is connected to two boundary diffusion layers and the cations and anions have different diffusion coefficients. This approach allows the theoretical description of the characteristic frequency dependence of the phase shift between the applied current density and the electro-osmotic flow. Additionally we show how the analysis of the dynamic response of the electro-osmotic coupling factor versus the AC frequency allows us to quantify the apparent ion diffusion coefficient in membranes. Notably, the frequency window where the phase-shift is predicted is well inside the commonly used sampling rate for electro-osmotic flow experiments f ∈ 10 −4 , 10 1 Hz, hence the proposed method can be useful to determine the apparent diffusion coefficient of ions (such as redox complex for flow batteries) in charged membranes.

Steady State and Dynamic Response of Voltage-Operated Membrane Gates

“…We attribute the relative maximum of φhyd at low frequencies to the diffusion-limited mass transfer. Indeed both the peak position, which is related to the apparent diffusion coefficient of the ions in the membrane (Dionapp), and its magnitude (order of 0.1 radians) are compatible with the predicted values from the theory of AC electro-osmotic flow in charged nanocapillary [39]. This non-monotonous behaviour is related to the ion transport through the selective membrane and the effect of the change in ion concentration (concentration polarization phenomena due to electro-osmosis) on the stagnant boundary diffusion layers at the membrane-solution interfaces.…”

Impedance Resonance in Narrow Confinement

“…The peculiar geometry has not yet been exploited experimentally but is in principle feasible . It should be noted though that applying our model to this case implies neglecting any specific solvent contributions to the AC electric field response as well as any structural details of the walls …”

Theory of Ion and Water Transport in Electron-Conducting Membrane Pores with p H-Dependent Chemical Charge

“…The equations of the UP model for transport of water and ions at steady-state with unequal diffusion coefficients and variable surface charge are given by [45]…”

“…Note that u, j s and j ch are constants along the pore in the current model, while for a dynamic problem, u and j ch are still invariants due to the continuity of fluid flow and electric current, but j s will vary along the pore. Furthermore, we neglect the possible relevance of upstream and downstream diffusion boundary layers [45].…”