Electrokinetic flow in a nanochannel with an overlapped electrical double layer

Electrokinetic flows within an overlapped Electrical Double Layer (EDL), which are not well-understood, were theoretically investigated in this study with the particular attention on the consideration of hydronium ions in the EDL. Theoretical models for fully-developed steady pressure-driven flow for salt-free water or a binary salt solution in a slit-like nanochannel connecting to two reservoirs were developed. The transient flow in such a domain was also simulated from static state to the final steady state. In these models, the Poisson equation and the Nernst-Planck equation were solved either by analytic methods or by the finite element method. Surface adsorption-desorption equilibrium and water equilibrium were considered to account for the proton exchange at the surface and in the fluid. These models were the first to include those comprehensive processes that are uniquely important for overlapped EDL scenarios.;This study improves the understanding of electrokinetic flows within an overlapped EDL by demonstrating the profound impact of hydronium ions on the EDL structure. In the steady flow of potassium chloride solutions, hydronium ions are more enriched than potassium ions by up to 2~3 orders of magnitude, making the electrokinetic effects greatly depressed. The unequal enrichment effects of counterions were omitted in the traditional theory partially because the transient is extremely slow. The simulation results show that a concentration hump of hydronium ions initially forming at the channel entrance gradually expands over the whole channel in a way similar to the concentration plug flow moving downstream. The time required for the flow to reach the steady state could be as long as thousands of times the hydraulic retention time, dependent on the degree of the EDL overlap. This study improves the fundamental understanding for nanofluidic flows.