Bulk electroconvection in electrolyte

Adhesive lift method for patterning arbitrary-shaped thin ion-selective films in micro/nanofluidic device

Micro/nanofluidic platforms with nanoporous films have been utilized as research tools for studying electrokinetic phenomena occurring not only in macro-scale systems such as electro-desalination but also in micro-scale systems such as bio-molecular preconcentrators. However, due to the limitations of fabrication techniques, studies with nanoporous films are mainly limited to vary the physicochemical properties of the films such as surface charge and pore size, despite the enormous effect of the membrane morphology on the phenomena that is to be expected. Therefore, we propose an economic and feasible nanofabrication method called the "adhesive lift method" for patterning thin arbitrarily-shaped nanoporous film to integrate it into micro/nanofluidic platforms. The conformal patterning of the nanoporous films (Nafion or poly(3,4-ethylenedioxythiophene)polystyrene sulfonate (PEDOT:PSS) in this work) was accomplished with spin coating, oxygen plasma treatment and the "adhesive lift technique". Using the fabricated platforms, the initiation of ion concentration polarization along the film with various shapes was demonstrated. In particular, various electrokinetic characteristics of overlimiting conductance depending on the length scale of the microchannels were successfully demonstrated. Therefore, the presented adhesive lift method would provide platforms which can nearly mimic practical macro-scale fluidic systems so that the method would be very useful for studying various electrokinetic phenomena inside it.

Semi-Continuous Desalination and Concentration of Small-Volume Samples

Electrodialysis is an electric-field-mediated process separating ions exploiting selective properties of ion-exchange membranes. The ion-exchange membranes create an ion-depleted zone in an electrolyte solution adjacent to the membrane under DC polarization. We constructed a microfluidic system that uses the ion-depleted zone to separate ions from the processed water solution. We tested the separation performance by desalting a model KCl solution spiked with fluorescein for direct observation. We showed both visually and by measuring the conductivity of the output solutions that the system can work in three modes of operation referred to as continuous desalination, desalination by accumulation, and unsuccessful desalination. The mode of operation can easily be set by changing the control parameters. The desalination factors for the model KCl solution reached values from 80 to 100%, depending on the mode of operation. The concentration factor, given as a ratio of concentrate-to-feed concentrations, reached zero for desalination by accumulation when only diluate was produced. The water recovery, therefore, was infinite at these conditions. Independent control of the diluate and concentrate flow rates and the DC voltage turned our system into a versatile platform, enabling us to set proper conditions to process various samples.

Investigation of ion-exchange membranes by means of chronopotentiometry: A comprehensive review on this highly informative and multipurpose technique

Electrodialysis is mostly used for drinking water production but it has gained applicability in different new fields in recent decades. Membrane characteristics and ion transport properties strongly influence the efficiency of electrodialysis and must be evaluated to avoid an intense energy consumption and ensure long membrane times of usage. To this aim, conducting studies on ion transport across membranes is essential. Several dynamic characterization methods can be employed, among which, chronopotentiometry has shown special relevance because it allows a direct access to the contribution of the potential in different states of the membrane/solution system. The present paper provides a critical review on the use of chronopotentiometry to determine the main membrane transport properties and to evaluate mass transfer phenomena. Properties, such as limiting current density, electrical resistances, plateau length, transport number of counter-ions in the membrane, transition times, and apparent fraction of membrane conductive area have been intensively discussed in the literature and are presented in this review. Some of the phenomena evaluated using this technique are concentration polarization, gravitational convection, electroconvection, water dissociation, and fouling/scaling, all of them also shown herein. Mathematical and experimental studies were considered. New trends in chronopotentiometric studies should include ion-exchange membranes that have been recently developed (presenting anti-fouling, anti-microbial, and monovalent-selective properties) and a deeper discussion on the behaviour of complex solutions that have been often treated by electrodialysis, such as municipal wastewaters. New mathematical models, especially 3D ones, are also expected to be developed in the coming years.

Overlimiting Current in Nonuniform Arrays of Microchannels: Recirculating Flow and Anticrystallization

Overlimiting current (OLC) through electrolytes interfaced with perm-selective membranes has been extensively researched for understanding fundamental nano-electrokinetics and developing efficient engineering applications. This work studies how a network of microchannels in a nonuniform array, which mimics a natural pore configuration, can contribute to OLC. Here, micro/nanofluidic devices are fabricated with arrays of parallel microchannels with nonuniform size distributions, which are faced with a perm-selective membrane. All cases maintain the same surface and bulk conduction to allow probing of the sensitivity only by the nonuniformity. Rigorous experimental and theoretical investigation demonstrates that overlimiting conductance has a maximum value depending on the nonuniformity. Furthermore, in operando visualization reveals that the nonuniform arrays induce flow loops across the microchannel network enhancing advective transport. This recirculating flow eliminates local salt accumulations so that it can effectively suppress undesirable salt crystallization. Therefore, these results can significantly advance not only the fundamental understanding of the driving mechanism of the OLC but also the design rule of electrochemical membrane applications.

Pulsed electric field-assisted overlimiting current enhancement through a perm-selective membrane

Overlimiting current through a perm-selective membrane has been actively researched not only for the fundamental advancement of electrokinetics but also for energy/environmental applications such as electrodialysis, fuel cells, etc. In particular, various strategies were reported for the enhancement of overlimiting current because these applications demand efficient mass transport through the membrane. In this work, we presented in operando visualization and rigorous numerical study for the overlimiting current density enhancement using a pulsed electric field which is one of the most cost-effective parameters to be externally controlled. We clearly demonstrated that the current density had a peak value as a function of the pulse frequency and would suggest its correlation to a concentration profile and diffusion relaxation time ([small tau, Greek, tilde]diff). As the pulse frequency was chosen which is similar to ([small tau, Greek, tilde]diff)-1, the concentration profiles (i.e. established current paths) were maintained even in off-state due to remnant current paths helping the fast ion transportation. The fundamental evidence presented in this work would provide a strategical design of a perm-selective membrane system for a higher mass transportation efficiency.

Pattern Formation of Three-Dimensional Electroconvection on a Charge Selective Surface

When a charge selective surface consumes or transports only cations or anions in the electrolyte, biased ion rejection initiates hydrodynamic instability, resulting in vortical fluid motions called electroconvection. In this Letter, we describe the first laboratory observation of three-dimensional electroconvection on a charge selective surface. Combining experiment and scaling analysis, we successfully categorized three distinct patterns of 3D electroconvection according to [(Ra_{E})/(Re^{2}Sc)] [electric Rayleigh number (Ra_{E}), Reynolds number (Re), Schmidt number (Sc)] as (i) polygonal, (ii) transverse, or (iii) longitudinal rolls. If Re increases or Ra_{E} decreases, pure longitudinal rolls are presented. On the other hand, transverse rolls are formed between longitudinal rolls, and two rolls are transformed as polygonal one at higher Ra_{E} or lower Re. In this pattern selection scenario, Sc determines the critical electric Rayleigh number (Ra_{E}^{*}) for the onset of each roll, resulting in Ra_{E}^{*}∼Re^{2}Sc. We also verify that convective ion flux by electroconvection (represented by an electric Nusselt number Nu_{E}) is fitted to a power law, Nu_{E}∼[(Ra_{E}-Ra_{E}^{*})/(Re^{2}Sc)]^{α_{1}}Re^{α_{2}}Pe^{α_{3}} [Péclet number (Pe)], where each term represents the characteristics of electroconvection, shear flow, and ion transport.

Controllable pH Manipulations in Micro/Nanofluidic Device Using Nanoscale Electrokinetics

Recently introduced nanoscale electrokinetic phenomenon called ion concentration polarization (ICP) has been suffered from serious pH changes to the sample fluid. A number of studies have focused on the origin of pH changes and strategies for regulating it. Instead of avoiding pH changes, in this work, we tried to demonstrate new ways to utilize this inevitable pH change. First, one can obtain a well-defined pH gradient in proton-received microchannel by applying a fixed electric current through a proton exchange membrane. Furthermore, one can tune the pH gradient on demand by adjusting the proton mass transportation (i.e., adjusting electric current). Secondly, we demonstrated that the occurrence of ICP can be examined by sensing a surrounding pH of electrolyte solution. When pH > threshold pH, patterned pH-responsive hydrogel inside a straight microchannel acted as a nanojunction to block the microchannel, while it did as a microjunction when pH < threshold pH. In case of forming a nanojunction, electrical current significantly dropped compared to the case of a microjunction. The strategies that presented in this work would be a basis for useful engineering applications such as a localized pH stimulation to biomolecules using tunable pH gradient generation and portable pH sensor with pH-sensitive hydrogel.

Surface conduction and electroosmotic flow around charged dielectric pillar arrays in microchannels

Dielectric microstructures have been reported to have a negative influence on permselective ion transportation because ions do not migrate in areas where the structures are located. However, the structure can promote the transportation if the membrane is confined to a microscopic scale. In such a scale where the area to volume ratio is significantly large, the primary driving mechanisms of the ion transportation transition from electro-convective instability (EOI) to surface conduction (SC) and electroosmotic flow (EOF). Here, we provide rigorous evidence on how the SC and EOF around the dielectric microstructures can accelerate the ion transportation by multi-physics simulations and experimental visualizations. The microstructures further polarize the ion distribution by SC and EOF so that ion carriers can travel to the membrane more efficiently. Furthermore, we verified, for the first time, that the arrangements of microstructures have a critical impact on the ion transportation. While convective flows are isolated in the crystal pillar configuration, the flows show an elongated pattern and create an additional path for ion current in the aligned pillar configuration. Therefore, the fundamental findings of the electrokinetic effects on the dielectric microstructures suggest an innovative application in micro/nanofluidic devices with high mass transport efficiency.

Dynamics of driftless preconcentration using ion concentration polarization leveraged by convection and diffusion

Over the past several decades, separation and preconcentration methods of (bio)molecules have been actively developed for various biomedical and chemical processes such as disease diagnostics, point of care test and environmental monitoring. Among the great developments of the electrokinetic method in a micro/nanofluidic platform is the ion concentration polarization (ICP) phenomenon, in which a target molecule is accumulated near a permselective nanoporous membrane under an applied electric field. ICP method has been actively studied due to its easy implementation and high preconcentration/separation efficiency. However, the dynamic behavior of preconcentrated analytes has not yet been fully studied, especially driftless migration, where the applied electric field is orthogonal to the direction of the drift migration. Here, we demonstrate anomalous shapes of preconcentrated analytes (either plug or dumbbell shape) and the morphologies were analytically modeled by the leverage of convection and diffusion migration. This model was experimentally verified with various lengths of DNA and the limiting cases (convection-free environment in paper-based microfluidic device and extremely low diffusivity of red blood cells) were also shown to confirm the model. Thus, this study not only provides an insight into the fundamental electrokinetic dynamics of molecules in an ICP platform but also plays a guiding role for the design of a nanofluidic preconcentrator for a lab on a chip application.

Nanoelectrokinetic bufferchannel-less radial preconcentrator and online extractor by tunable ion depletion layer

Among various preconcentration strategies using nanofluidic platforms, a nanoscale electrokinetic phenomenon called ion concentration polarization (ICP) has been extensively utilized due to several advantages such as high preconcentration factor and no need of complex buffer exchange process. However, conventional ICP preconcentrator had difficulties in the recovery of preconcentrated sample and complicated buffer channels. To overcome these, bufferchannel-less radial micro/nanofluidic preconcentrator was developed in this work. Radially arranged microchannel can maximize the micro/nano membrane interface so that the samples were preconcentrated from each microchannel. All of preconcentrated plugs moved toward the center pipette tip and can be easily collected by just pulling out the tip installed at the center reservoir. For a simple and cost-effective fabrication, a commercial printer was used to print the nanoporous membrane as "Nafion-junction device." Various analytes such as polystyrene particle, fluorescent dye, and dsDNA were preconcentrated and extracted with the recovery ratio of 85.5%, 79.0%, and 51.3%, respectively. Furthermore, we used a super inkjet printer to print the silver electrode instead of nanoporous membrane to preconcentrate either type of charged analytes as "printed-electrode device." A Faradaic reaction was used as the main mechanism, and we successfully demonstrated the preconcentration of either negatively or positively charged analytes. The presented bufferchannel-less radial preconcentrator would be utilized as a practical and handy platform for analyzing low-abundant molecules.

Surface Conduction in a Microchannel

Ionic current through a microchannel has drawn significant attention not only for fundamental electrokinetic research but also for the development of novel micro/nanofluidic applications. Among various ion transport mechanisms, surface conduction, which is a predominant mechanism in micro/nanofluidic devices, has been theoretically characterized based on two-dimensional analysis. However, its infinite axis assumption has become a barrier for direct application in practical micro/nanochannel networks. In this work, we conducted rigorous experiments to include all of the three-dimensional length scales. There, L/ A, the perimeter to area ratio of the microchannel cross-section, came up as a single parameter to quantitatively interpret the surface conductive ion transportation. Overlimiting conductance of microchannel devices increased with larger perimeter, which is equivalent to specific surface area, even with the same cross sectional area. Finally, a micro/nanofluidic diode with a different L/ A value on its forward and reverse channel was demonstrated as a simple application. The analysis presented could provide a practical guideline to design a micro/nanofluidic application.

Ion Concentration Polarization by Bifurcated Current Path

Ion concentration polarization (ICP) is a fundamental electrokinetic process that occurs near a perm-selective membrane under dc bias. Overall process highly depends on the current transportation mechanisms such as electro-convection, surface conduction and diffusioosmosis and the fundamental characteristics can be significantly altered by external parameters, once the permselectivity was fixed. In this work, a new ICP device with a bifurcated current path as for the enhancement of the surface conduction was fabricated using a polymeric nanoporous material. It was protruded to the middle of a microchannel, while the material was exactly aligned at the interface between two microchannels in a conventional ICP device. Rigorous experiments revealed out that the propagation of ICP layer was initiated from the different locations of the protruded membrane according to the dominant current path which was determined by a bulk electrolyte concentration. Since the enhancement of surface conduction maintained the stability of ICP process, a strong electrokinetic flow associated with the amplified electric field inside ICP layer was significantly suppressed over the protruded membrane even at condensed limit. As a practical example of utilizing the protruded device, we successfully demonstrated a non-destructive micro/nanofluidic preconcentrator of fragile cellular species (i.e. red blood cells).

Stabilization of ion concentration polarization layer using micro fin structure for high-throughput applications

Ion concentration polarization (ICP) has been extensively researched concerning new fundamentals in nanoscale electrokinetics and novel engineering applications. While biomedical and environmental ICP applications have a number of advantages compared to conventional methods, the technique has suffered from the critical limitation of low processing capacity because it has been usually presented in a micro/nanofluidic platform. In this paper, we devised micro fin structures inside a macroscale high-throughput ICP device and successfully demonstrated a stable formation of ICP layer and its performance. Since the fin structures created surface conductive fluidic circumstances and assisted in physically suppressing undesirable electrokinetic vortices generated in this fluidic regime, ICP was stably generated even in this macroscale system. Finally, batch-type droplet ICP preconcentrator and continuous-type ICP separator were introduced as examples for high-throughput millimeter-scale ICP devices using the implanted fin structures.

Numerical simulation of electrochemical desalination

We present an effective numerical approach to simulate electrochemically mediated desalination of seawater. This new membraneless, energy efficient desalination method relies on the oxidation of chloride ions, which generates an ion depletion zone and local electric field gradient near the junction of a microchannel branch to redirect sea salt into the brine stream, consequently producing desalted water. The proposed numerical model is based on resolution of the 3D coupled Navier-Stokes, Nernst-Planck, and Poisson equations at non-uniform spatial grids. The model is implemented as a parallel code and can be employed to simulate mass-charge transport coupled with surface or volume reactions in 3D systems showing an arbitrarily complex geometrical configuration.

Capillarity ion concentration polarization as spontaneous desalting mechanism

To overcome a world-wide water shortage problem, numerous desalination methods have been developed with state-of-the-art power efficiency. Here we propose a spontaneous desalting mechanism referred to as the capillarity ion concentration polarization. An ion-depletion zone is spontaneously formed near a nanoporous material by the permselective ion transportation driven by the capillarity of the material, in contrast to electrokinetic ion concentration polarization which achieves the same ion-depletion zone by an external d.c. bias. This capillarity ion concentration polarization device is shown to be capable of desalting an ambient electrolyte more than 90% without any external electrical power sources. Theoretical analysis for both static and transient conditions are conducted to characterize this phenomenon. These results indicate that the capillarity ion concentration polarization system can offer unique and economical approaches for a power-free water purification system.

Helical vortex formation in three-dimensional electrochemical systems with ion-selective membranes

The rate of electric-field-driven transport across ion-selective membranes can exceed the limit predicted by Nernst (the limiting current), and encouraging this "overlimiting" phenomenon can improve efficiency in many electrochemical systems. Overlimiting behavior is the result of electroconvectively induced vortex formation near membrane surfaces, a conclusion supported so far by two-dimensional (2D) theory and numerical simulation, as well as experiments. In this paper we show that the third dimension plays a critical role in overlimiting behavior. In particular, the vortex pattern in shear flow through wider channels is helical rather than planar, a surprising result first observed in three-dimensional (3D) simulation and then verified experimentally. We present a complete experimental and numerical characterization of a device exhibiting this recently discovered 3D electrokinetic instability, and show that the number of parallel helical vortices is a jump-discontinuous function of width, as is the overlimiting current and overlimiting conductance. In addition, we show that overlimiting occurs at lower fields in wider channels, because the associated helical vortices are more readily triggered than the planar vortices associated with narrow channels (effective 2D systems). These unexpected width dependencies arise in realistic electrochemical desalination systems, and have important ramifications for design optimization.

Shear flow of an electrically charged fluid by ion concentration polarization: scaling laws for electroconvective vortices

We consider electroconvective fluid flows initiated by ion concentration polarization (ICP) under pressure-driven shear flow, a scenario often found in many electrochemical devices and systems. Combining scaling analysis, experiment, and numerical modeling, we reveal unique behaviors of ICP under shear flow: a unidirectional vortex structure, its height selection, and vortex advection. Determined by both the external pressure gradient and the electric body force, the dimensionless height of the sheared electroconvective vortex is shown to scale as (ϕ(2)/U(HP))(1/3), which is a clear departure from the previous diffusion-drift model prediction. To the best of our knowledge, this is the first microscopic characterization of ion concentration polarization under shear flow, and it firmly establishes electroconvection as the mechanism for an overlimiting current in realistic, large-area ion exchange membrane systems such as electrodialysis. The new scaling law has significant implications on the optimization of electrodialysis and other electrochemical systems.

Numerical study on the bulk instability of constant-current conduction in cation-exchange membranes

Numerical simulation of two-dimensional bulk instability of the one-dimensional conduction state in an electrolyte confined between a pair of cation-exchange membranes subjected to an external voltage is conducted under an assumption of constant current. By employing variable grids, we resolve the problem of sensitive dependence of the numerical solutions to the grid refinement in particular at a current close to the limiting value. In fact, the full range of parameters, i.e., Schmidt number, Peclet number, diffusivity ratio, and current, is considered in this study in obtaining the stability chart. It turns out that the Schmidt number exerts almost no influence on the results. From the neutral curves in the chart of the parameter space (current versus diffusivity ratio, i.e., cation diffusivity divided by anion diffusivity) we confirm that the system tends to be unstable at high Peclet numbers, high currents, and low diffusivity ratios. As the diffusivity ratio is increased the instability mode switches from the monotonic to the oscillatory type, and the critical diffusivity ratio for the switching is found to be decreased as the Peclet number decreases. At the switching, no jump in the neutral curves is found, contrary to the earlier result, because the wave number is set free to change in this study. The stability chart obtained in this study represents the true boundaries in discriminating the stable from the unstable parameter sets because the critical eigenvalues constituting the chart are sought for the entire possible range of the wave numbers and the frequencies.

Electrohydrodynamic flow and colloidal patterning near inhomogeneities on electrodes

Current density inhomogeneities on electrodes (of physical, chemical, or optical origin) induce long-range electrohydrodynamic fluid motion directed toward the regions of higher current density. Here, we analyze the flow and its implications for the orderly arrangement of colloidal particles as effected by this flow on patterned electrodes. A scaling analysis indicates that the flow velocity is proportional to the product of the applied voltage and the difference in current density between adjacent regions on the electrode. Exact analytical solutions for the streamlines are derived for the case of a spatially periodic perturbation in current density along the electrode. Particularly simple asymptotic expressions are obtained in the limits of thin double layers and either large or small perturbation wavelengths. Calculations of the streamlines are in good agreement with particle velocimetry experiments near a mechanically generated inhomogeneity (a "scratch") that generates a current density larger than that of the unmodified electrode. We demonstrate that proper placement of scratches on an electrode yields desired patterns of colloidal particles.

Bulk electroconvective instability at high Péclet numbers

Bulk electroconvection pertains to flow induced by the action of a mean electric field upon the residual space charge in the macroscopic regions of a locally quasielectroneutral strong electrolyte. For a long time, controversy has existed in the literature as to whether quiescent electric conduction from such an electrolyte into a uniform charge-selective solid, such as a metal electrode or ion exchange membrane, is stable with respect to bulk electroconvection. While it was recently claimed that bulk electroconvective instability could not occur, this claim pertained to an aqueous, low-molecular-weight electrolyte characterized by an order-unity electroconvection Péclet number. In this paper, we show that the bulk electroconvection model transforms into the leaky dielectric model in the limit of infinitely large Péclet number. For the leaky dielectric model, conduction of the above-mentioned type is unstable, and so it is in the bulk electroconvection model for sufficiently large Péclet numbers. Such instability is sensitive to the ratio of the diffusivity of the cations to the anions. For infinite Péclet number, the case with equal ionic diffusivities is a bifurcation point separating stable and unstable regimes at the low-current limit. Further, for a cation-selective solid, when the Péclet number is finite and the anions are much more diffusive than the cations, an unreported bulk electroconvective instability is possible at low current. At higher currents and large Péclet numbers, we found that the system is unstable for all cation-to-anion diffusivity ratios, but passes from a monotonic instability to an oscillatory one as this ratio passes through unity.

Colloidal electroconvection in a thin horizontal cell. II. Bulk electroconvection of water during parallel-plate electrolysis

We recently have reported [J. Chem. Phys. 122, 164701 (2005)] a family of electroconvective patterns that arise when charge-stabilized colloidal dispersions are driven by constant (dc) vertical electric fields. Competition between gravity and electrokinetic forces acting on the individual spheres in this system leads to the formation of highly organized convective instabilities involving hundreds of spheres. Here, we report a distinct class of electroconvective patterns that emerge in confined aqueous dispersions at higher biases. These qualitatively resemble the honeycomb and labyrinthine patterns formed during thermally driven Rayleigh-Benard convection, but arise from a distinct mechanism. Unlike the localized colloidal electroconvective patterns observed at lower biases, moreover, these system-spanning patterns form even without dispersed colloidal particles. Rather, they appear to result from an underlying electroconvective instability during electrolysis in the parallel plate geometry. This contrasts with recent theoretical results suggesting that simple electrolytes are linearly stable against electroconvection.