Analysis of electro-osmotic flow in a microchannel with undulated surfaces

Abstract

The electro-osmotic flow through a channel between two undulated surfaces induced by an external electric field is investigated. The gap of the channel is very small and comparable to the thickness of the electrical double layers. A lattice Boltzmann simulation is carried out on the model consisting of the Poisson equation for electrical potential, the Nernst-Planck equation for ion concentration, and the Navier-Stokes equations for flows of the electrolyte solution. An analytical model that predicts the flow rate is also derived under the assumption that the channel width is very small compared with the characteristic length of the variation along the channel. The analytical results are compared with the numerical results obtained by using the lattice Boltzmann method. In the case of a constant surface charge density along the channel, the variation of the channel width reduces the electro-osmotic flow, and the flow rate is smaller than that of a straight channel. In the case of a surface charge density distributed inhomogeneously, one-way flow occurs even under the restriction of a zero net surface charge along the channel.

Driving an electrolyte through a corrugated nanopore

“…Plots of the functions ∆Υ1 (downward triangles) and ∆Υ3 (upward triangles), as a function of ∆S (panel a) and k0h (panel b) for the channel shape given in Eq (44)…”

Electroosmotic flow of a two-layer fluid in a slit channel with gradually varying wall shape and zeta potential

“…The pressure gradients at each pointK 1 (x i ) andK 2 (x i ) can then be calculated from Eqs. (26) and (27). Third, the pressure drop over one wavelength ∆P (n) can be evaluated from the integral ofK 1 orK 2 .…”

“…For given η,κ,ζ 1 , ∆P ,ŵ(x) andζ 2 (x), the problem is solved whenĥ(x),q i andK i (x) (i = 1, 2) are found through Eqs. (26), (27), (29), (30) and (31). It is a highly nonlinear system of equations, which can be solved by a trial-and-error numerical scheme.…”

“…Their numerical results suggest that the mixing performance can be remarkably improved by increasing either the wave amplitude or the length of the wavy surface or the magnitude of the heterogeneous zeta potential. Other authors who also looked into the combined effect of wall shape and charge patterns on EO flow include, among others, Xuan and Li [22], Bhattacharyya and Nayak [23], Ng and Qi [24], Bhattacharyya and Bera [25], and Yoshida et al [26]. All these studies, however, only considered single-fluid EO flow.…”

Molecular dynamics and continuum analyses of the electrokinetic zeta potential in nanostructured slit channels

“…[12,13,14] Conventional theoretical descriptions for electrokinetic flows, and thus analytical models for the zeta potential, have been developed based on the classical continuum assumptions of sharp liquid-solid interfaces of plane or spherical surfaces that are physically smooth and chemically homogeneous. As a result, and despite insightful theoretical and computational studies, [15,16,17,18,19,20,21] there are no well-established analytical models to account for experimental observations and/or predict analytically the zeta potential for surfaces with nanoscale physical structures or roughness of arbitrary shape and dimensions comparable to the Debye length λ D .…”