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

TL;DR

This paper investigates electro-osmotic flow in microchannels with undulated surfaces using lattice Boltzmann simulations and analytical modeling, revealing how surface charge distribution and channel geometry influence flow rates.

Contribution

It introduces an analytical model for electro-osmotic flow in undulated microchannels and compares it with lattice Boltzmann simulation results, highlighting effects of surface charge and geometry.

Findings

Undulated surfaces reduce flow rate compared to straight channels.

Homogeneous surface charge distribution can induce one-way flow.

Flow behavior depends on surface charge density and channel geometry.

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 {\color{black}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 in homogeneously, one-way flow occurs even under the restriction of a zero net surface charge along the channel.