Electrokinetic actuation of an uncharged polarizable dielectric droplet in charged hydrogel medium

Electrokinetic transport of an uncharged nonconducting microsized liquid droplet in a charged hydrogel medium is studied. Dielectric polarization of the liquid drop under the action of an externally imposed electric field induces a non-homogeneous charge density at the droplet surface. The interactions of the induced surface charge of the droplet with the immobile charges of the hydrogel medium generates an electric force to the droplet, which actuates the drop through the charged hydrogel medium. A numerical study based on the first principle of electrokinetics is adopted. Dependence of the droplet velocity on its dielectric permittivity, bulk ionic concentration, and immobile charge density of the gel is analyzed. The surface conduction is significant in presence of charged gel, which creates a concentration polarization. The impact of the counterion saturation in the Debye layer due to the dielectric decrement of the medium is addressed. The modified Nernst–Planck equation for ion transport and the Poisson equation for the electric field is considered to take into account the dielectric polarization. A quadrupolar vortex around the uncharged droplet is observed when the gel medium is considered to be uncharged, which is similar to the induced charge electroosmosis around an uncharged dielectric colloid in free-solution. We find that the induced charge electrokinetic mechanism creates a strong recirculation of liquid within the droplet and the translational velocity of the droplet strongly depends on its size for the dielectric droplet embedded in a charged gel medium.     

The effects of electrostatic correlations on the ionic current rectification in conical nanopores

Ion‐ion electrostatic correlations are recognized to play a significant role in the presence of concentrated multivalent electrolytes. To account for their impact on ionic current rectification phenomenon in conical nanopores, we use the modified continuum Poisson‐Nernst‐Planck (PNP) equations by Bazant et al. Coupled with the Stokes equations, the effects of the EOF are also included. We thoroughly investigate the dependence of the ionic current rectification ratios as a function of the double layer thickness and the electrostatic correlation length. By considering the electrostatic correlations, the modified PNP model successfully captures the ionic current rectification reversal in nanopores filled with lanthanum chloride LaCl₃. This finding qualitatively agrees with the experimental observations that cannot be explained by the standard PNP model, suggesting that ion‐ion electrostatic correlations are responsible for this reversal behavior. The modified PNP model not only can be used to explain the experiments, but also go beyond to provide a design tool for nanopore applications involving multivalent electrolytes.     

Electrokinetic ion transport in confined micro‐nanochannel

In this paper, a confined micronanochannel is presented to concentrate ions in a restricted zone. A general model exploiting the Poisson–Nernst–Plank equations coupled with the Navier–Stokes equation is employed to simulate the electrokinetic ion transport. The influences of the micronanochannel dimension and the surface charge density on the potential distribution, the ion concentration, and the fluid flow are investigated. The numerical results show that the potential drop depends mainly on the nanochannel, instead of the confined channel. Both decreasing the width and increasing the length enhance the ion enrichment performance. For a given nanochannel, ultimate value of ion concentration may be determined by the potential at the center point of the nanochannel. The study also shows that the enrichment stability can be improved by increasing the micronanochannel width, decreasing the micronanochannel length and reducing the surface charge density.     

Stationary electrodiffusion–adsorption processes in membranes including diffuse double layer effects: A network approach

Ion transport across membranes with surface charge due to ion adsorption, including the diffuse double layer effects, is analysed using the network simulation method. The membrane system under study is a multilayer one constituted by a membrane and two diffusion boundary layers on both sides of the membrane. The ion transport processes are described by the Nernst–Planck and Poisson equations not only in the membrane–solution interfaces, but also in the membrane bulk and in the two diffusion boundary layers. The membrane has a negative surface charge due to an anion adsorption process. The structure of the equilibrium diffuse double layers and the steady-state current–voltage characteristic have been analysed for the case of an adsorption process described by a Langmuir-type adsorption isotherm. The evolution of the electric potential difference across the membrane system in the equilibrium state of the system as a function of the bathing concentrations, have been also analysed.     

Theoretical Analysis of the Effect of Ion Concentration in Solution Bulk and at Membrane Surface on the Mass Transfer at Overlimiting Currents

Overlimiting current modes are of considerable interest for the practice of electrodialysis (ED). However, the economical expedience of such ED modes is evident only for desalination of dilute solutions. Here, we show the theoretical analysis of the effect of concentration on the behavior of an ED cell with homogeneous ion-exchange membranes. The study is based on numerical solution of the two-dimensional system of coupled equations of Nernst–Planck–Poisson–Navier–Stokes. It is shown that as the electrolyte concentration in solution that enters the ED desalination chamber increases, the intensity of electroconvection decreases, which induces a decrease in the relative mass-transfer rate (the decrease in the ratio of current density to its limiting value). This effect is stronger in the region of high potential differences where the electroconvective instability of Rubinstein–Zaltzman is realized under the conditions of a nonuniform concentration field caused by solution desalination. In contrast, the increase in the counterion concentration at the membrane surface (associated with the increase in the surface charge) intensifies the electroconvection.     

Modeling and simulation of nanoparticle separation through a solid-state nanopore

Recent experimental studies show that electrokinetic phenomena such as electroosmosis and electrophoresis can be used to separate nanoparticles on the basis of their size and charge using nanopore‐based devices. However, the efficient separation through a nanopore depends on a number of factors such as externally applied voltage, size and charge density of particle, size and charge density of membrane pore, and the concentration of bulk electrolyte. To design an efficient nanopore‐based separation platform, a continuum‐based mathematical model is used for fluid. The model is based on Poisson–Nernst–Planck equations along with Navier–Stokes equations for fluid flow and on the Langevin equation for particle translocation. Our numerical study reveals that membrane pore surface charge density is a vital parameter in the separation through a nanopore. In this study, we have simulated high‐density lipoprotein (HDL) and low‐density lipoprotein (LDL) as the sample nanoparticles to demonstrate the capability of such a platform. Numerical results suggest that efficient separation of HDL from LDL in a 0.2 M KCL solution (resembling blood buffer) through a 150 nm pore is possible if the pore surface charge density is ～ ?4.0 mC/m². Moreover, we observe that pore length and diameter are relatively less important in the nanoparticle separation process considered here.     

Molecularly imprinted SPE coupled with HPLC for the selective separation and enrichment of alkyl imidazolium ionic liquids in environmental water samples

A novel 1‐butyl‐3‐methylimidazolium chloride ionic liquid surface imprinted solid‐phase sorbent was synthesized. The as‐prepared material was characterized by SEM, Brunauer–Emmett–Teller surface area analysis and Fourier Transform IR measurements. Then its adsorption properties for alkyl imidazolium ionic liquids, including adsorption capacities, adsorption kinetics, and properties of selective separation and enrichment were studied in detail. It was shown that the ionic liquid surface imprinted polymer exhibited high selective recognition characteristics for the imidazolium chloride ionic liquids with short alkyl chains (C_nmimCl, n = 2, 4, 6, 8) and the adsorption equilibrium was achieved within 25 min. Various parameters were optimized for the 1‐butyl‐3‐methylimidazolium chloride ionic liquid surface imprinted polymer SPE column, such as flow rate, eluent solvent, selectivity, and reusability of the column. Then, the SPE column coupled with HPLC was used for the determination of alkyl imidazolium ionic liquids. Experimental results showed that the existence of their structural analogs and common concomitants in environmental matrices did not affect the enrichment of 1‐butyl‐3‐methyl imidazolium chloride ionic liquid. The average recoveries of 1‐butyl‐3‐methylimidazolium chloride ionic liquid in spiked water samples were in the range of 92.0–102.0% with the RSD lower than 5.8%.     

Predicting ion concentration polarization and analyte stacking/focusing at nanofluidic interfaces

We report on the investigation of electropreconcentration phenomena in micro-/nanofluidic devices integrating 100 μm long nanochannels using 2D COMSOL simulations based on the coupled Poisson–Nernst–Planck and Navier–Stokes system of equations. Our numerical model is used to demonstrate the influence of key governing parameters such as electrolyte concentration, surface charge density, and applied axial electric field on ion concentration polarization (ICP) dynamics in our system. Under sufficiently extreme surface-charge-governed transport conditions, ICP propagation is shown to enable various transient and stationary stacking and counter-flow gradient focusing mechanisms of anionic analytes. We resolve these spatiotemporal dynamics of analytes and electrolyte ICP over disparate time and length scales, and confirm previous findings that the greatest enhancement is observed when a system is tuned for analyte focusing at the charge, excluding microchannel, nanochannel electrical double layer (EDL) interface. Moreover, we demonstrate that such tuning can readily be achieved by including additional nanochannels oriented parallel to the electric field between two microchannels, effectively increasing the overall perm-selectivity and leading to enhanced focusing at the EDL interfaces. This approach shows promise in providing added control over the extent of ICP in electrokinetic systems, particularly under circumstances in which relatively weak ICP effects are observed using only a single channel.     

A parallel finite element simulator for ion transport through three‐dimensional ion channel systems

A parallel finite element simulator, ichannel, is developed for ion transport through three‐dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson–Nernst–Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I – V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α‐Hemolysin (α‐HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size‐modified PNP (SMPNP) model on VDAC and α‐HL. It is shown that the size effects in SMPNP can effectively lead to reduced current in the channel, and the results are closer to BD simulation results. © 2013 Wiley Periodicals, Inc.     

Electroviscous Effects in Ceramic Nanofiltration Membranes

Membrane permeability and salt rejection of a γ‐alumina nanofiltration membrane were studied and modeled for different salt solutions. Salt rejection was predicted by using the Donnan‐steric pore model, in which the extended Nernst–Planck equation was applied to predict ion transport through the pores. The solvent flux was modeled by using the Hagen–Poiseuille equation by introducing electroviscosity instead of bulk viscosity. γ‐Alumina particles were used for ζ‐potential measurements. The ζ‐potential measurements show that monovalent ions did not adsorb on the γ‐alumina surface, whereas divalent ions were highly adsorbed. Thus, for divalent ions, the model was modified, owing to pore shrinkage caused by ion adsorption. The ζ‐potential lowered the membrane permeability, especially for membranes with a pore radius lower than 3 nm, a ζ‐potential higher than 20 mV, and an ionic strength lower than 0.01 m . The rejection model showed that, for a pore radius lower than 3 nm and for solutions with ionic strengths lower than 0.01 m , there is an optimum ζ‐potential for rejection, because of the concurrent effects of electromigration and convection. Hence, the model can be used as a prediction tool to optimize membrane perm‐selectivity by designing a specific pore size and surface charge for application at specific ionic strengths and pH levels.     

Effects of fluid slippage on pressure-driven electrokinetic energy conversion in conical nanochannels

The effects of fluid slippage on the pressure-driven electrokinetic energy conversion in conical nanochannels are systematically investigated in this paper. We present a multiphysical model that couples the Planck–Nernst–Poisson equations and the Navier–Stokes equation with a Navier slip condition to fulfill this purpose. We systematically look into the variation of various performance indicators of electrokinetic energy conversion, for example, streaming current, streaming potential, generation power, energy conversion efficiency, regulation parameter, and enchantment ratio, with the conicity of nanochannels and the slip length for two pressure differences of the same magnitude but opposite directions. Particularly, enhancement ratios related to streaming current, streaming potential, generation power, and energy conversion efficiency are defined to comprehensively measure the enhancement of the performance of electrokinetic energy conversion due to the slip length. The results demonstrate that a combination of large slip length and small conicity enhances the electrokinetic energy conversion performance significantly. Furthermore, the fluid slippage-induced enhancement of the electrokinetic energy conversion in the backward pressure difference mode is stronger than that in the forward pressure difference mode. Our results provide design and operation guidelines for pressure-driven electrokinetic energy conversion devices.     

Robust and high‐resolution simulations of nonlinear electrokinetic processes in variable cross‐section channels

We present a model and an associated numerical scheme to simulate complex electrokinetic processes in channels with nonuniform cross‐sectional area. We develop a quasi‐1D model based on local cross‐sectional area averaging of the equations describing unsteady, multispecies, electromigration‐diffusion transport. Our approach uses techniques of lubrication theory to approximate electrokinetic flows in channels with arbitrary variations in cross‐section; and we include chemical equilibrium calculations for weak electrolytes, Taylor–Aris type dispersion due of nonuniform bulk flow, and the effects of ionic strength on species mobility and on acid–base equilibrium constants. To solve the quasi‐1D governing equations, we provide a dissipative finite volume scheme that adds numerical dissipation at selective locations to ensure both unconditional stability and high accuracy. We couple the numerical scheme with a novel adaptive grid refinement algorithm that further improves the accuracy of simulations by minimizing numerical dissipation. We benchmark our numerical scheme with existing numerical schemes by simulating nonlinear electrokinetic problems, including ITP and electromigration dispersion in CZE. Simulation results show that our approach yields fast, stable, and high‐resolution solutions using an order of magnitude less grid points compared to the existing dissipative schemes. To highlight our model's capabilities, we demonstrate simulations that predict increase in detection sensitivity of ITP in converging cross‐sectional area channels. We also show that our simulations of ITP in variable cross‐sectional area channels have very good quantitative agreement with published experimental data.     

Microwave‐assisted preparation of poly(ionic liquids)‐modified magnetic nanoparticles for pesticide extraction

Novel poly(ionic liquids) were synthesized and immobilized on prepared magnetic nanoparticles, which were used to extract pesticides from fruit and vegetable samples by dispersive solid‐phase extraction prior to high‐performance liquid chromatography analysis. Compared with monomeric ionic liquids, poly(ionic liquids) have a larger effective contact area and higher viscosity, so they can achieve higher extraction efficiency and be used repeatedly without a decrease in analyte recovery. The immobilized poly(ionic liquids) were rapidly separated from the sample matrix, providing a simple approach for sample pretreatment. The nature and volume of the desorption solvent and amount of poly(ionic liquid)‐modified magnetic material were optimized for the extraction process. Under optimum conditions, calibration curves were linear (R² > 0.9988) for pesticide concentrations in the range of 0.100–10.000 μg/L. The relative standard deviations for repeated determinations of the four analytes were 2.29–3.31%. The limits of detection and quantification were 0.29–0.88 and 0.97–2.93 μg/L, respectively. Our results demonstrate that the developed poly(ionic liquid)‐modified material is an effective absorbent to extract pesticides from fruit and vegetable samples.     

On the dilemma of the use of the electroneutrality constraint in electrochemical calculations

A simple treatment is developed to demonstrate that invoking the electroneutrality assumption to solve electrochemical transport problems is equivalent to invoking the limit of the exact (Nernst–Planck–Poisson) treatment when certain charge-density-related terms become negligibly small.     

Electric double layer theory for room temperature ionic liquids on charged electrodes: Milestones and prospects

In this review, we shortly summarize the basic theoretical milestones achieved in the mean-field theory of room temperature ionic liquids on charged electrodes since the publication of Kornyshev's seminal article in 2007. We pay special attention to the behavior of the differential capacitance profile and the microscopic parameters of ions that can have a substantial influence on it. Among them are parameters of short-range specific interactions, ionic diameters, static polarizabilities, and permanent dipole moments. We also discuss the recent ‘nonlocal’ mean-field theories that can describe the overscreening behavior of the local ionic concentrations, as well as the crossover from overscreening to crowding.     

Extended Poisson–Nernst–Planck modeling of membrane blockage via insoluble reaction products

A generalized time-dependent mathematical model is developed for a diffusion–migration–reaction system incorporating a pore blockage effect due to generation of insoluble precipitates in a porous membrane. The system behavior is investigated via direct numerical solution of an extended, highly non-linear equation set based on the classical Poisson–Nernst–Planck equations for ion transport. In order to treat the buildup of solid reaction products in the membrane, this novel formulation incorporates both a reaction term and a space- and time-dependent diffusivity expression based on a simple precipitation model. The model is demonstrated for a generalized case and then extended to cover the well-known reaction of silver and chloride ions to form insoluble AgCl. Time-dependent concentration profiles of all ions in the membrane are obtained and the effects of precipitate buildup in the pore space are investigated. The role of counterions in the transient behavior of the system is also clarified.     

Recent progress of task‐specific ionic liquids in chiral resolution and extraction of biological samples and metal ions

Ionic liquids have been functionalized for modern applications. The functional ionic liquids are also called task‐specific ionic liquids. Various task‐specific ionic liquids with certain groups have been constructed and exploited widely in the field of separation. To take advantage of their properties in separation science, task‐specific ionic liquids are generally used in techniques such as liquid–liquid extraction, solid‐phase extraction, gas chromatography, high‐performance liquid chromatography, and capillary electrophoresis. This review mainly covers original research papers published in the last five years, and we will focus on task‐specific ionic liquids as the chiral selectors in chiral resolution and as extractant or sensor for biological samples and metal ion purification.     

Molecularly imprinted polymers for the solid‐phase extraction of four fluoroquilones from milk and lake water samples

A method based on molecular crowding and ionic liquids as reaction solvents has been used for the synthesis of molecularly imprinted polymers. Levofloxacin was selected as the template, polymethyl methacrylate was the molecular crowding agent, and 1‐butyl‐3‐methylimidazolium tetrafluoroborate (ionic liquid) was selected as the reaction solvent and porogen. The optimized proportion for the mixed porogen was dimethyl sulfoxide/ionic liquid/polymethyl methacrylate 1:1.6:5 in chloroform (150 mg mL^?1). The morphology and chemical composition of levofloxacin imprinted polymers were assessed by scanning electron microscopy and Fourier transform infrared spectroscopy. The absorption experiments demonstrated that the levofloxacin imprinted polymers possess high selective recognition property to levofloxacin and analogs, including enrofloxacin, ciprofloxacin and gatifloxacin, which all belong to fluoroquinolones. An extraction method using levofloxacin imprinted polymers as sorbent followed by high‐performance liquid chromatography analysis was optimized for the determination of four fluoroquinolones in milk and lake water samples. Under the optimized conditions, good linearity was observed in a range of 5–1000 ng g^?1 with the limit of detection between 0.3 and 0.5 ng g^?1 for the four fluoroquinolones. The recoveries at three spiked levels ranged 82.4–98.3% with the relative standard deviation ≤4.9.     

Ionic Ingress and Charge‐Neutralization Phenomena of Conducting‐Polymer Films

Ionic ingress and diffusion through a conducting‐polymer (CP) film containing embedded charges under potential and concentration gradients is studied. Electroneutrality, a common assumption in modeling of similar systems, is not justified in this case or similar diffusion‐limited processes, as the timescale of ionic diffusion in the solid matrix is quite large. Counter ions therefore cannot move instantaneously for effective neutralization of excess charges. Poisson–Nernst–Planck (PNP) equations have to be solved for such cases without any simplifying assumption. Analytical solution shows the existence of a charge boundary layer, which limits and strongly influences the ionic flux. A general numerical method for solution is also developed for the dynamic modeling, analysis, and design of these types of systems. The numerical results are validated by comparison with analytical solutions as well as with some experimental results available in the literature. With this modeling framework, the basic features of controlled release of molecules across a CP film under an applied electrical potential can be explained quantitatively.