An analysis of steady/unsteady electroosmotic flows through charged cylindrical nano-channels

Abstract

The steady/unsteady electroosmotic flow in an infinitely extended cylindrical channel with diameters ranging from 10 to 100 nm has been investigated. A mixture of (NaCl + H2O) is considered for the numerical calculation of the mass, potential, velocity, and mixing efficiency. Results are obtained for the channel diameters are small, equal, or greater than the electric double layer (EDL) both for steady and unsteady cases. In the present discussion, a symmetrical distribution of mole fractions is considered at the wall interface. Hence, the velocity and potential are symmetrical in nature toward the centerline of the channel, and also identical in nature at maximum and minimum time levels (i.e., at π/2 and 3π/2 for a periodic function) in the transient case. In case of steady flows, the velocity and potential satisfy the chemical equilibrium condition at the centerline. It is observed that the electric double layer reaches a local equilibrium in the presence of electroosmosis when the channel length is long compared to the characteristic hydraulic diameter and the flow is essentially one-dimensional, which depends only on channel diameter. Comparisons of NP (Nernst Plank) model with PB (Poisson–Boltzmann) model are achieved out for different published results at larger channel diameters.