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

• Electro-osmotic flow through microchannels with undulated surfaces is analyzed.
• Lattice Boltzmann simulation for electrokinetic flows is carried out.
• Analytical model is derived via the lubrication approximation theory.
• Flow reduction due to the surface structure is demonstrated.
• One-way flow induced in a channel with zero net surface charge is confirmed.

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.