Electrokinetic transport through nanochannels

Abstract

This article presents a numerical study of the electrokinetic transport phenomena (electroosmosis and electrophoresis) in a three-dimensional nanochannel with a circular cross-section. Due to the nanometer dimensions, the Boltzmann distribution of the ions is not valid in the nanochannels. Therefore, the conventional theories of electrokinetic flow through the microchannels such as Poisson-Boltzmann equation and Helmholtz-Smoluchowski slip velocity approach are no longer applicable. In the current study, a set of coupled partial differential equations including Poisson-Nernst-Plank equation, Navier-Stokes, and continuity equations is solved to find the electric potential field, ionic concentration field, and the velocity field in the three-dimensional nanochannel. The effects of surface electric charge and the radius of nanochannel on the electric potential, liquid flow, and ionic transport are investigated. Unlike the microchannels, the electric potential field, ionic concentration field, and velocity field are strongly size-dependent in nanochannels. The electric potential gradient along the nanochannel also depends on the surface electric charge of the nanochannel. More counter ions than the coions are transported through the nanochannel. The ionic concentration enrichment at the entrance and the exit of the nanochannel is completely evident from the simulation results. The study also shows that the flow velocity in the nanochannel is higher when the surface electric charge is stronger or the radius of the nanochannel is larger.

Electroosmotic flow in single PDMS nanochannels

“…These new transport phenomena facilitate various novel applications and studies of the nanofluidics [9][10][11][12] . Theoretically, in nanochannels with overlapped EDLs, traditional Poisson-Boltzmann equation and Helmholtz-Smoluchowski equation used in microchannel systems are not applicable anymore 13 . For the case of extremely small nanochannels, even the continuum hypothesis can hardly survive when the channel size is in the order of the interaction length of the fluid molecules 12 .…”

Dielectric properties of a single nanochannel investigated by high-frequency impedance spectroscopy

“…[12], [13] Compared to the classical microfluidic field, the nanometer dimension of the channel requires specific theoretical predictions and experimental discussions. [14], [15], [16], [17]. The conductance law through nanochannels depends on the ionic strength of the background electrolyte.…”

Global Well-Posedness and Stability of Electrokinetic Flows

“…Even the more general approach to describe the electric potential via the Poisson-Boltzmann equation may not be accurate enough, since the Boltzmann statistics does not apply in overlapping double layers; cf. [30].…”