A numerical analysis of finite Debye-length effects in induced-charge electro-osmosis

For a microchamber filled with a binary electrolyte and containing a flat un-biased center electrode at one wall, we employ three numerical models to study the strength of the resulting induced-charge electro-osmotic (ICEO) flow rolls: (i) a full nonlinear continuum model resolving the double layer, (ii) a linear slip-velocity model not resolving the double layer and without tangential charge transport inside this layer, and (iii) a nonlinear slip-velocity model extending the linear model by including the tangential charge transport inside the double layer. We show that compared to the full model, the slip-velocity models significantly overestimate the ICEO flow. This provides a partial explanation of the quantitative discrepancy between observed and calculated ICEO velocities reported in the literature. The discrepancy increases significantly for increasing Debye length relative to the electrode size, i.e. for nanofluidic systems. However, even for electrode dimensions in the micrometer range, the discrepancies in velocity due to the finite Debye length can be more than 10% for an electrode of zero height and more than 100% for electrode heights comparable to the Debye length.Comment: 11 pages, Revtex, 7 eps figure

Flow reversal at low voltage and low frequency in a microfabricated ac electrokinetic pump

Microfluidic chips have been fabricated to study electrokinetic pumping generated by a low voltage AC signal applied to an asymmetric electrode array. A measurement procedure has been established and followed carefully resulting in a high degree of reproducibility of the measurements. Depending on the ionic concentration as well as the amplitude of the applied voltage, the observed direction of the DC flow component is either forward or reverse. The impedance spectrum has been thoroughly measured and analyzed in terms of an equivalent circuit diagram. Our observations agree qualitatively, but not quantitatively, with theoretical models published in the literature.Comment: RevTex, 9 pages, 6 eps figure

Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients

We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal design, in particular shape and topology optimization, and are most often solved numerically utilizing a finite element approach. Within the FV framework for control in the coefficients problems the main difficulty we face is the need to analyze the convergence of fluxes defined on the faces of cells, whereas the convergence of the coefficients happens only with respect to the “volumetric” Lebesgue measure. Additionally, depending on whether the stationarity conditions are stated for the discretized or the original continuous problem, two distinct concepts of stationarity at a discrete level arise. We provide characterizations of limit points, with respect to FV mesh size, of globally optimal solutions and two types of stationary points to the discretized problems. We illustrate the practical behaviour of our cell-based FV discretization algorithm on a numerical example