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

Multiphysics analytical and numerical studies of biomolecule preconcentration utilizing ion concentration polarization: a case study of convergent microchannels

A convergent sector in microfluidic devices utilizing ion concentration polarization (ICP) can help increase the preconcentration rate and the concentration enhancement factor (CEF) of biomolecules. In this work, we present a detailed study of the nozzle-like-squeeze effect of a convergent channel on the preconcentration of biomolecules. By numerically solving coupled Nernst-Planck-Poisson-Navier-Stokes governing equations for the 2D channel model, we report the first study on the critical width of a convergent region in the channel to retain the advantage of the nozzle-like-squeeze effect in speeding up preconcentration and augmenting CEF. In addition, we investigated the impact of the location and the dimensions of a convergent sector on the mechanism of biomolecule preconcentration. The location of an ion-selective membrane was also determined to ensure that biomolecules are focused on the convergent region of the channel. Moreover, we introduce analytical studies to compare and verify simulation findings. Specifically, the formulas for the critical dimensions of a convergent channel, location of a preconcentrated biomolecule plug, and position of an ion-selective membrane are presented. Furthermore, important working parameters, including electric potentials and hydrostatic pressures, were examined to scrutinize their effect on convergent concentrators. These detailed analytical solutions and numerical simulation results are consistent with experimental observations, providing deep insights into the ICP phenomenon and the preconcentration mechanism of biomolecules in convergent microfluidic concentration devices.

Determination of Critical Dimensions of Microchannels to Ensure the Electrokinetic Biomolecule Preconcentration: Analytical and Numerical Studies

Preconcentration of biomolecules based on ion concentration polarization (ICP) has been splendidly applied to various biomedical and chemical processes. However, in many circumstances, biomolecule preconcentration could not occur due to the lack of full studies on the preconcentration mechanism, especially on the effect of microchannel dimensions. In this work, we provide analytical studies on the critical dimensions (minimum and maximum) of microchannels for the preconcentration of biomolecules. These formulas are verified with the numerical results by fully solving the coupled governing equations: Poisson-Nernst-Planck and Navier-Stokes experiments with appropriate boundary conditions and assumptions. In addition, we examine the impact of operational parameters, such as electric potentials and critical external pressures, on the formation of the preconcentration. Moreover, two important results are provided for the first time, including the position of the preconcentrated biomolecule region and the concentration enhancement factor of the biomolecules. These analytical and numerical results are consistent with experimental observations and, therefore, could provide sharp insight into the mechanism of biomolecule preconcentration and give useful guidelines to better design and optimize ICP-based microfluidic preconcentration devices.

Theoretical Analysis of the Influence of Spacers on Salt Ion Transport in Electromembrane Systems Considering the Main Coupled Effects

This article considers a theoretical analysis of the influence of the main coupled effects and spacers on the transfer of salt ions in electromembrane systems (EMS) using a 2D mathematical model of the transfer process in a desalting channel with spacers based on boundary value problems for the coupled system of Nernst-Planck-Poisson and Navier-Stokes equations. The basic patterns of salt ion transport have been established, taking into account diffusion, electromigration, forced convection, electroconvection, dissociation/recombination reactions of water molecules, as well as spacers located inside the desalting channel. It has been shown that spacers and taking into account the dissociation/recombination reaction of water molecules significantly change both the formation and development of electroconvection. This article confirms the fact of the exaltation of the limiting current studied by Harkatz, where it is shown that the current (flux) of salt ions increases when the dissociation reaction begins by a certain value called the exaltation current, which is proportional to the flow of water dissociation products. A significant combined effect of electroconvection and dissociation/recombination reactions as well as the spacer system in the desalting channel on the transport of salt ions are shown. The complex, nonlinear, and non-stationary interaction of all the main effects of concentration polarization and spacers in the desalting channel are also considered in the work.

Ion Transport in Electromembrane Systems under the Passage of Direct Current: 1D Modelling Approaches

For a theoretical analysis of mass transfer processes in electromembrane systems, the Nernst-Planck and Poisson equations (NPP) are generally used. In the case of 1D direct-current-mode modelling, a fixed potential (for example, zero) is set on one of the boundaries of the considered region, and on the other-a condition connecting the spatial derivative of the potential and the given current density. Therefore, in the approach based on the system of NPP equations, the accuracy of the solution is significantly affected by the accuracy of calculating the concentration and potential fields at this boundary. This article proposes a new approach to the description of the direct current mode in electromembrane systems, which does not require boundary conditions on the derivative of the potential. The essence of the approach is to replace the Poisson equation in the NPP system with the equation for the displacement current (NPD). Based on the system of NPD equations, the concentration profiles and the electric field were calculated in the depleted diffusion layer near the ion-exchange membrane, as well as in the cross section of the desalination channel under the direct current passage. The NPD system, as well as NPP, allows one to describe the formation of an extended space charge region near the surface of the ion-exchange membrane, which is important for describing overlimiting current modes. Comparison of the direct-current-mode modelling approaches based on NPP and NPD showed that the calculation time is less for the NPP approach, but the calculation accuracy is higher for the NPD approach.

Experimental Study on Ion Transport in Microfluidic Electrodialysis Using Partially Masked Ion Exchange Membranes

Electrodialysis using anion-exchange membranes (AEMs) and cation-exchange membranes (CEMs) has been widely used for water desalination and the management of various ionic species. During commercial electrodialysis, the available area of an ion-exchange membrane is reduced by a non-conductive spacer that is in contact with the AEM/CEM. Although multiple reports have described the advantages or disadvantages of spacers, fewer studies have explored the effects of spacers on the mass transport effect of the reduced membrane area excluding the fluid flow change. In this paper, we present our experimental studies concerning mass transport in microfluidic electrodialysis systems with partially masked ion-exchange membranes. Six different types of masking membranes were prepared by the deposition of non-conductive films on parts of the membranes. The experimental results showed that the overlapped types (in which masking was vertically aligned in the AEM/CEM) exhibited a larger electrical conductance and better current/energy efficiency, compared with the non-overlapped types (in which masking was vertically dislocated in the AEM/CEM). We also observed that a reduction in the unit length of the unmasked ion-exchange membrane enhanced overall mass transport. Our results demonstrate the effects of patterned membranes on electrical resistance and desalination performance; they also identify appropriate arrangements for electromembrane systems.

Comprehensive Electrokinetic-Assisted Separation of Oil Emulsion with Ultrahigh Flux

Many industries have a significant but largely unmet need for efficient and high-flux emulsion separation, particularly for nanoemulsions. Conventional separation membranes rely on size-based separation mainly utilizing a sieving mechanism plus a wetting phenomenon, resulting in a dramatic trade-off between separation efficiency and separation flux. Herein we address this challenge by adapting electrokinetics to membrane-based separation, using a charge-based mechanism capable of separating even nanoemulsions with a demonstrated separation efficiency of >99% and ultrahigh flux up to 40 000 L/H·m². Our device arrests nano-oil droplets, allowing them to coalesce into larger droplets which are then able to be filtered by coarser membranes. This hybrid technology makes electrokinetic-assisted filtration scalable and commercially viable and allows for a better understanding of the multiphysics underlying dynamic separation.

Transport and Electrochemical Characteristics of CJMCED Homogeneous Cation Exchange Membranes in Sodium Chloride, Calcium Chloride, and Sodium Sulfate Solutions

Recently developed and produced by Hefei Chemjoy Polymer Material Co. Ltd., homogeneous CJMC-3 and CJMC-5 cation-exchange membranes (CJMCED) are characterized. The membrane conductivity in NaCl, Na2SO4, and CaCl2 solutions, permeability in respect to the NaCl and CaCl2 diffusion, transport numbers, current-voltage curves (CVC), and the difference in the pH (DpH) of the NaCl solution at the desalination compartment output and input are examined for these membranes in comparison with a well-studied commercial Neosepta CMX cation-exchange membrane produced by Astom Corporation, Japan. It is found that the conductivity, CVC (at relatively low voltages), and water splitting rate (characterized by DpH) for both CJMCED membranes are rather close to these characteristics for the CMX membrane. However, the diffusion permeability of the CJMCED membranes is significantly higher than that of the CMX membrane. This is due to the essentially more porous structure of the CJMCED membranes; the latter reduces the counterion permselectivity of these membranes, while allowing much easier transport of large ions, such as anthocyanins present in natural dyes of fruit and berry juices. The new membranes are promising for use in electrodialysis demineralization of brackish water and natural food solutions.

Electrodialysis Applications in Wastewater Treatment for Environmental Protection and Resources Recovery: A Systematic Review on Progress and Perspectives

This paper presents a comprehensive review of studies on electrodialysis (ED) applications in wastewater treatment, outlining the current status and the future prospect. ED is a membrane process of separation under the action of an electric field, where ions are selectively transported across ion-exchange membranes. ED of both conventional or unconventional fashion has been tested to treat several waste or spent aqueous solutions, including effluents from various industrial processes, municipal wastewater or salt water treatment plants, and animal farms. Properties such as selectivity, high separation efficiency, and chemical-free treatment make ED methods adequate for desalination and other treatments with significant environmental benefits. ED technologies can be used in operations of concentration, dilution, desalination, regeneration, and valorisation to reclaim wastewater and recover water and/or other products, e.g., heavy metal ions, salts, acids/bases, nutrients, and organics, or electrical energy. Intense research activity has been directed towards developing enhanced or novel systems, showing that zero or minimal liquid discharge approaches can be techno-economically affordable and competitive. Despite few real plants having been installed, recent developments are opening new routes for the large-scale use of ED techniques in a plethora of treatment processes for wastewater.

Shear electroconvective instability in electrodialysis channel under extreme depletion and its scaling laws

The electroconvective instability (ECI) in an electrodialysis channel under a strong electric field is studied here. The phenomenon of ECI with extreme depletion (ECI-HD) is reported; that is, the overlapping vortices cause the extreme depletion zone to propagate in the horizontal direction. Using scaling theory and direct numerical simulation, we indicate a series of features under the ECI-HD. The decrease in ion transport rate with voltage in ECI-HD is different from the enhancement in the ECI with moderate depletion (ECI-MD), which results in a unique peak in the voltage-current curve. More importantly, we reveal that the ECI is regulated by a scaling factor consisting of the electric field, hydrodynamic coupling coefficient, and Péclet number. For the ECI-HD, the scaling factor has an opposite effect on the vortex size and overlimiting current as that on the ECI-MD. The extreme depletion zone of the ECI-HD also has an uncommon diffusion self-similar dynamics. These unique scaling laws allow one to establish the quantitative bridge between the ion concentration, electric field, and vortex size by the overlimiting current.

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.

Free Flow Ion Concentration Polarization Focusing (FF-ICPF)

Electrokinetic separation techniques in microfluidics are a powerful analytical chemistry tool, although an inherent limitation of microfluidics is their low sample throughput. In this article we report a free-flow variant of an electrokinetic focusing method, namely ion concentration polarization focusing (ICPF). The analytes flow continuously through the system via pressure driven flow while they separate and concentrate perpendicularly to the flow by ICPF. We demonstrate free flow ion concentration polarization focusing (FF-ICPF) in two operating modes, namely peak and plateau modes. Additionally, we showed the separation resolution could be improved by the use of an electrophoretic spacer. We report a concentration factor of 10 in human blood plasma in continuous flow at a flow rate of 15 μL min^-1.

Potentiodynamic and Galvanodynamic Regimes of Mass Transfer in Flow-Through Electrodialysis Membrane Systems: Numerical Simulation of Electroconvection and Current-Voltage Curve

Electromembrane devices are usually operated in two electrical regimes: potentiodynamic (PD), when a potential drop in the system is set, and galvanodynamic (GD), when the current density is set. This article theoretically investigates the current-voltage curves (CVCs) of flow-through electrodialysis membrane systems calculated in the PD and GD regimes and compares the parameters of the electroconvective vortex layer for these regimes. The study is based on numerical modelling using a basic model of overlimiting transfer enhanced by electroconvection with a modification of the boundary conditions. The Dankwerts’ boundary condition is used for the ion concentration at the inlet boundary of the membrane channel. The Dankwerts’ condition allows one to increase the accuracy of the numerical implementation of the boundary condition at the channel inlet. On the CVCs calculated for PD and DG regimes, four main current modes can be distinguished: underlimiting, limiting, overlimiting, and chaotic overlimiting. The effect of the electric field regime is manifested in overlimiting current modes, when a significant electroconvection vortex layer develops in the channel.

Three-dimensional electroconvective vortices in cross flow

This study focuses on the three-dimensional (3D) electrohydrodynamic flow instability between two parallel electrodes driven by unipolar charge injection with and without cross flow. Lattice Boltzmann method with a two-relaxation time model is used to compute flow patterns. In the absence of cross flow, the base-state solution is hydrostatic, and the electric field is one-dimensional. With strong charge injection and high electrical Rayleigh number, the system exhibits electroconvective vortices. Disturbed by perturbation patterns, such as rolling pattern, square pattern, and hexagon pattern, the flow develops corresponding to the most unstable mode. The growth rate and pattern transitions are studied using dynamic mode decomposition of the transient numerical solutions. The interactions between cross flow and electroconvective vortices lead to suppression and disappearance of structures with velocity components in the direction of cross flow, while the other components are not affected. Surprisingly, the transition from a 3D to a 2D flow pattern enhances the convective charge transport, marked by an increase in the electric Nusselt number. Hysteresis in the 3D to 2D transition is characterized by the nondimensional parameter Y, a ratio of the electrical force term to the viscous term in the momentum equation.

Electro-Kinetic Instability in a Laminar Boundary Layer Next to an Ion Exchange Membrane

The electro-kinetic instability in a pressure driven shear flow near an ion exchange membrane is considered. The electrochemical system, through which an electrical potential drop is applied, consists in a polarization layer in contact with the membrane and a bulk. The numerical investigation contained two aspects: analysis of the instability modes and description of the Lagrangian transport of fluid and ions. Regarding the first aspect, the modes were analyzed as a function of the potential drop. The analysis revealed how the spatial distribution of forces controls the dynamics of vortex association and dissociation. In particular, the birth of a counter-clockwise vortex between two clockwise vortices, and the initiation of clusters constituting one or two envelopes wrapping a vortex group, were examined. In regards to the second aspect, the trajectories were computed with the fourth order Runge Kutta scheme for the time integration and with the biquadratric upstream scheme for the spatial and time interpolation of the fluid velocity and the ion flux. The results for the periodic mode showed two kinds of trajectories: the trochoidal motion and the longitudinal one coupled with a periodic transverse motion. For the aperiodic modes, other mechanisms appeared, such as ejection from the mixing layer, trapping by a growing vortex or merging vortices. The analysis of the local velocity field, the vortices’ shape, the spatial distribution of the forces and the ion flux components explained these trajectories.

2D Mathematical Modelling of Overlimiting Transfer Enhanced by Electroconvection in Flow-Through Electrodialysis Membrane Cells in Galvanodynamic Mode

Flow-through electrodialysis membrane cells are widely used in water purification and the processing of agricultural products (milk, wine, etc.). In the research and operating practice of such systems, a significant place is occupied by a galvanodynamic (or galvanostatic) mode. 2D mathematical modelling of ion transfer in the galvanodynamic mode requires solving the problem of setting the average current density equal to a certain value, while the current density distribution in the system is uneven. This article develops a 2D mathematical model of the overlimiting transfer enhanced by electroconvection in a flow-through electrodialysis cell in the galvanodynamic mode. The model is based on the system of Navier–Stokes, Nernst–Planck, Poisson equations and equations for the electric current stream function. To set the electric mode we use a boundary condition, relating the electric field strength and current density. This approach allows us to describe the formation of the extended space charge region and development of electroconvection at overlimiting currents. For the first time, chronopotentiograms and current–voltage characteristics of the membrane systems are calculated for the galvanodynamic mode taking into account the forced flow and development of electroconvection. The behaviors of the calculated chronopotentiograms and current–voltage characteristic coincide qualitatively with experimental data. The effects of the electrolyte concentration, forced flow velocity and channel size on the mass transfer at overlimiting currents are estimated.

1D Mathematical Modelling of Non-Stationary Ion Transfer in the Diffusion Layer Adjacent to an Ion-Exchange Membrane in Galvanostatic Mode

The use of the Nernst–Planck and Poisson (NPP) equations allows computation of the space charge density near solution/electrode or solution/ion-exchange membrane interface. This is important in modelling ion transfer, especially when taking into account electroconvective transport. The most solutions in literature use the condition setting a potential difference in the system (potentiostatic or potentiodynamic mode). However, very often in practice and experiment (such as chronopotentiometry and voltammetry), the galvanostatic/galvanodynamic mode is applied. In this study, a depleted stagnant diffusion layer adjacent to an ion-exchange membrane is considered. In this article, a new boundary condition is proposed, which sets a total current density, i, via an equation expressing the potential gradient as an explicit function of i. The numerical solution of the problem is compared with an approximate solution, which is obtained by a combination of numerical solution in one part of the diffusion layer (including the electroneutral region and the extended space charge region, zone (I) with an analytical solution in the other part (the quasi-equilibrium electric double layer (EDL), zone (II). It is shown that this approach (called the “zonal” model) allows reducing the computational complexity of the problem tens of times without significant loss of accuracy. An additional simplification is introduced by neglecting the thickness of the quasi-equilibrium EDL in comparison to the diffusion layer thickness (the “simplified” model). For the first time, the distributions of concentrations, space charge density and current density along the distance to an ion-exchange membrane surface are computed as functions of time in galvanostatic mode. The calculation of the transition time, τ, for an ion-exchange membrane agree with an experiment from literature. It is suggested that rapid changes of space charge density, and current density with time and distance, could lead to lateral electroosmotic flows delaying depletion of near-surface solution and increasing τ.

Mass Transfer Phenomena during Electrodialysis of Multivalent Ions: Chemical Equilibria and Overlimiting Currents

Electrodialysis is utilized for the deionization of saline streams, usually formed by strong electrolytes. Recently, interest in new applications involving the transport of weak electrolytes through ion-exchange membranes has increased. Clear examples of such applications are the recovery of valuable metal ions from industrial effluents, such as electronic wastes or mining industries. Weak electrolytes give rise to a variety of ions with different valence, charge sign and transport properties. Moreover, development of concentration polarization under the application of an electric field promotes changes in the chemical equilibrium, thus making more complex understanding of mass transfer phenomena in such systems. This investigation presents a set of experiments conducted with salts of multivalent metals with the aim to provide better understanding on the involved mass transfer phenomena. Chronopotentiometric experiments and current-voltage characteristics confirm that shifts in chemical equilibria can take place simultaneous to the activation of overlimiting mass transfer mechanisms, that is, electroconvection and water dissociation. Electroconvection has been proven to affect the type of precipitates formed at the membrane surface thus suppressing the simultaneous dissociation of water. For some electrolytes, shifts in the chemical equilibria forced by an imposed electric field generate new charge carriers at specific current regimes, thus reducing the system resistance.

Continuous and High-Throughput Electromechanical Lysis of Bacterial Pathogens Using Ion Concentration Polarization

Electrical lysis of mammalian cells has been a preferred method in microfluidic platforms because of its simple implementation and rapid recovery of lysates without additional reagents. However, bacterial lysis typically requires at least a 10-fold higher electric field (∼10 kV/cm), resulting in various technical difficulties. Here, we present a novel, low-field-enabled electromechanical lysis mechanism of bacterial cells using electroconvective vortices near ion selective materials. The vortex-assisted lysis only requires a field strength of ∼100 V/cm, yet it efficiently recovers proteins and nucleic acids from a variety of pathogenic bacteria and operates in a continuous and ultrahigh-throughput (>1 mL/min) manner. Therefore, we believe that the electromechanical lysis will not only facilitate microfluidic bacterial sensing and analysis but also various high-volume applications such as the energy-efficient recovery of valuable metabolites in biorefinery pharmaceutical industries and the disinfection of large-volume fluid for the water and food industries.