Mathias B. Andersen

Streaming current and wall dissolution over 48 h in silica nanochannels

We present theoretical and experimental studies of the streaming current induced by a pressure-driven flow in long, straight, electrolyte-filled nanochannels. The theoretical work builds on our recent one-dimensional model of electro-osmotic and capillary flow, which self-consistently treats both the ion concentration profiles, via the nonlinear Poisson-Boltzmann equation, and the chemical reactions in the bulk electrolyte and at the solid-liquid interface. We extend this model to two dimensions and validate it against experimental data for electro-osmosis and pressure-driven flows, using eight 1-μm-wide nanochannels of heights varying from 40 nm to 2000 nm. We furthermore vary the electrolyte composition using KCl and borate salts, and the wall coating using 3-cyanopropyldimethylchlorosilane. We find good agreement between prediction and experiment using literature values for all parameters of the model, i.e., chemical reaction constants and Stern-layer capacitances. Finally, by combining model predictions with measurements over 48 h of the streaming currents, we develop a method to estimate the dissolution rate of the silica walls, typically around 0.01 mg/m(2)/h, equal to 45 pm/h or 40 nm/yr, under controlled experimental conditions.

Surface-dependent chemical equilibrium constants and capacitances for bare and 3-cyanopropyldimethylchlorosilane coated silica nanochannels

We present a combined theoretical and experimental analysis of the solid-liquid interface of fused-silica nanofabricated channels with and without a hydrophilic 3-cyanopropyldimethylchlorosilane (cyanosilane) coating. We develop a model that relaxes the assumption that the surface parameters C(1), C(2), and pK(+) are constant and independent of surface composition. Our theoretical model consists of three parts: (i) a chemical equilibrium model of the bare or coated wall, (ii) a chemical equilibrium model of the buffered bulk electrolyte, and (iii) a self-consistent Gouy-Chapman-Stern triple-layer model of the electrochemical double layer coupling these two equilibrium models. To validate our model, we used both pH-sensitive dye-based capillary filling experiments as well as electro-osmotic current-monitoring measurements. Using our model we predict the dependence of ζ potential, surface charge density, and capillary filling length ratio on ionic strength for different surface compositions, which can be difficult to achieve otherwise.

Numerical analysis of finite Debye-length effects in induced-charge electro-osmosis.

For a microchamber filled with a binary electrolyte and containing a flat unbiased 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.

Spatiotemporal pH dynamics in concentration polarization near ion-selective membranes.

We present a detailed analysis of the transient pH dynamics for a weak, buffered electrolyte subject to voltage-driven transport through an ion-selective membrane. We show that pH fronts emanate from the concentration polarization zone next to the membrane and that these propagating fronts change the pH in the system several units from its equilibrium value. The analysis is based on a 1D model using the unsteady Poisson-Nernst-Planck equations with nonequilibrium chemistry and without assumptions of electroneutrality or asymptotically thin electric double layers. Nonequilibrium chemical effects, especially for water splitting, are shown to be important for the dynamical and spatiotemporal evolution of the pH fronts. Nonetheless, the model also shows that at steady state the assumption of chemical equilibrium can still lead to good approximations of the global pH distribution. Moreover, our model shows that the transport of the hydronium ion in the extended space charge region is governed by a balance between electromigration and water self-ionization. On the basis of this observation, we present a simple model showing that the net flux of the hydronium ion is proportional to the length of the extended space charge region and the water self-ionization rate. To demonstrate these effects in practice, we have adopted the experiment of Mai et al. (Mai, J.; Miller, H.; Hatch, A. V. Spatiotemporal Mapping of Concentration Polarization Induced pH Changes at Nanoconstrictions. ACS Nano 2012, 6, 10206) as a model problem, and by including the full chemistry and transport, we show that the present model can capture the experimentally observed pH fronts. Our model can, among other things, be used to predict and engineer pH dynamics, which can be essential to the performance of membrane-based systems for biochemical separation and analysis.

Coupling between Buoyancy Forces and Electroconvective Instability near Ion-Selective Surfaces.

Recent investigations have revealed that ion transport from aqueous electrolytes to ion-selective surfaces is subject to electroconvective instability that stems from coupling of hydrodynamics with electrostatic forces. These systems inherently involve fluid density variation set by salinity gradients. However, the coupling between the buoyancy effects and electroconvective instability has not yet been investigated although a wide range of electrochemical systems are naturally prone to these interplaying effects. In this study we thoroughly examine the interplay of gravitational convection and chaotic electroconvection. Our results reveal that buoyant forces can significantly influence the transport rates, otherwise set by electroconvection, when the Rayleigh number Ra of the system exceeds a value Ra∼1000. We show that buoyancy forces can significantly alter the flow patterns in these systems. When the buoyancy acts in the stabilizing direction, it limits the extent of penetration of electroconvection, but without eliminating it. When the buoyancy destabilizes the flow, it alters the electroconvective patterns by introducing upward and downward fingers of respectively light and heavy fluids.

Confinement effects on electroconvective instability

We present an analysis of hydrodynamic effects in systems involving ion transport from an aqueous electrolyte to an ion‐selective surface. These systems are described by the Poisson–Nernst–Planck and Navier–Stokes equations. Historically, such systems were modeled by one‐dimensional geometries with spatial coordinate in the direction of transport and normal to the ion‐selective surface. Rubinstein and Zaltzman [JFM 579, 173–226 (2007)] showed that when such systems are unbounded in the transverse directions, a hydrodynamic instability can occur. This instability, referred to as electroconvective instability, leads to advective mixing, which results in overlimiting transport rates significantly beyond what is predicted from one‐dimensional models. In this study, we present an analysis of electroconvection in confined systems, considering a broad range of applications including microfluidic systems and porous media. Our analysis reveals that full confinement in the transverse directions significantly suppresses electroconvection and overlimiting current. However, when at least one transverse direction allows for flow escape, such as in thin but wide channels or in porous media, the onset of instability is only weakly affected by confinement. We will also present a review of relevant literature and discuss how the present study resolves the contradictory contrasts between the results of recent work on this topic.

Nanofluidic carbon-dioxide sensor using nanoscale hydronium-dominated ion transport theory

We demonstrate a nanofluidic-based carbon dioxide sensor through corroboration with our nanochannel hydronium-dominated ion transport model. We verify the predictive power of our model by comparing calculated and measured conductances of solutions with added HCl in both bulk and in nanochannel geometries. From thus model, we use our experimental system to determine the carbon-dioxide content in the ambient atmosphere.