The role of external electric fields in enhancing ion mobility, drift velocity, and drift-diffusion rates in aqueous electrolyte solutions

Molecular simulations have been carried out using the method of molecular dynamics to investigate the role of external electric fields on the ion mobility, drift velocity, and drift-diffusion rate of ions in aqueous electrolyte solutions. These properties are critical for a range of processes including electrodialysis, electro-deionization, electrophoresis, and electroosmosis. Our results show that external electric fields relax the hydrated ion structure at significantly larger time scales (between 300 and 800 ps), than most other relaxation processes in solutions (generally of the order of 1 ps). Previous studies that did not account for the much longer relaxation times did not observe this behavior for ions even with very high electric fields. External electric fields must also overcome several (at least two or more) activation energy barriers to significantly change the structure of hydrated ions. As a result, the dynamic behavior changes almost in bands as a function of electric field strengths, rather than linearly. Finally, the effect of the field is much less dramatic on water than the ions. Thus electric fields will be of more significance in processes that involve the transport of ions (such as electro-deionization) than the transport of water (electroosmosis).     

Flow behavior of periodical electroosmosis in microchannel for biochips

This paper presents an analytical solution for periodical electroosmotic flows in two-dimensional uniform microchannel based on Poisson-Boltzmann equations for electric double layer (EDL) and Navier-Stokes equation for incompressible viscous fluid. Analytical results indicate that the velocity of periodical electroosmosis strongly depends on Reynolds number Re=omegah(2)/nu, as well as on EDL properties and applied electric field. Slip velocity of EDL decreases as the Reynolds number increases. Electroosmotic velocity outside the EDL decreases, and lag phase angle of velocity increases as distance away from the channel wall increases. A wavelike velocity profile across the channel is found. An asymptotic solution for low Reynolds number is given in this paper. Periodical electroosmosis with low Reynolds has same velocity amplitude and a pluglike velocity profile as that of steady electroosmosis. Based on Debye-Hückel approximation, this paper also obtains a solution of periodical electroosmosis applicable to cases where the thickness of EDL is of the same order as half of channel width.     

Analytical study of Joule heating effects on electrokinetic transportation in capillary electrophoresis

Electric fields are often used to transport fluids (by electroosmosis) and separate charged samples (by electrophoresis) in microfluidic devices. However, there exists inevitable Joule heating when electric currents are passing through electrolyte solutions. Joule heating not only increases the fluid temperature, but also produces temperature gradients in cross-stream and axial directions. These temperature effects make fluid properties non-uniform, and hence alter the applied electric potential field and the flow field. The mass species transport is also influenced. In this paper we develop an analytical model to study Joule heating effects on the transport of heat, electricity, momentum and mass species in capillary-based electrophoresis. Close-form formulae are derived for the temperature, applied electrical potential, velocity, and pressure fields at steady state, and the transient concentration field as well. Also available are the compact formulae for the electric current and the volume flow rate through the capillary. It is shown that, due to the thermal end effect, sharp temperature drops appear close to capillary ends, where sharp rises of electric field are required to meet the current continuity. In order to satisfy the mass continuity, pressure gradients have to be induced along the capillary. The resultant curved fluid velocity profile and the increase of molecular diffusion both contribute to the dispersion of samples. However, Joule heating effects enhance the sample transport velocity, reducing the analysis time in capillary electrophoretic separations.     

Open source simulation tool for electrophoretic stacking,focusing, and separation

We present the development, formulation, and performance of a new simulation tool for electrophoretic preconcentration and separation processes such as capillary electrophoresis, isotachophoresis, and field amplified sample stacking. The code solves the one-dimensional transient advection-diffusion equations for multiple multivalent weak electrolytes (including ampholytes) and includes a model for pressure-driven flow and Taylor–Aris dispersion. The code uses a new approach for the discretization of the equations, consisting of a high resolution compact scheme which is combined with an adaptive grid algorithm. We show that this combination allows for accurate resolution of sharp concentration gradients at high electric fields, while at the same time significantly reducing the computational time. We demonstrate smooth, stable, and accurate solutions at current densities as high as 5000 A/m² using only 300 grid points, and a 75-fold reduction in computational time compared with equivalent uniform grid techniques. The code is available as an open source for free at http://microfluidics.stanford.edu.     

弛豫理论对离子交换毛细管电色谱中峰压缩现象的研究

 在毛细管电色谱中,由于溶质在输运过程中所具有的电性质,常会产生一些特殊的现象。这些现象,如离子交换毛细管电色谱中产生超高柱效峰的现象,已经不能用一般的色谱理论加以解释。基于弛豫理论所建立的基本模型,在考虑溶质在两相中皆有可能发生正、反向迁移的情况下,得到了流出曲线一阶原点矩和二阶中心矩的理论表达式,并通过对溶质在两相中电扩散速率与电泳速率、电渗流速率关系的分析结果证实:溶质在固定相表面的电扩散行为可以使其保留变弱,出峰加快;而这种电扩散导致的超常柱效峰的出现具有不稳定性,只有在多方面因素综合影响匹配的情况下才可能出现。     

Electroosmosis in porous materials

Electroosmosis is the phenomenon of fluid flow induced by an applied electric field. This paper is concerned with electroosmosis in a porous material composed of closely-packed spheres immersed in a general electrolyte. A formula is obtained for the electroosmotic flow rate in the case when the double layer is much thinner than the particle radius. By combining this formula with electroosmosis measurements it is possible to determine the particle ζ potential. To test the validity of the model which underlies this, and most other electrokinetic calculations, ζ potentials obtained from Van der Put and Bijsterbosch's (J. Colloid Interface Sci. 92, 499, 1983) electroosmosis measurements are compared with potentials obtained from their conductivity and electrophoresis measurements.     

On ion transport regulation with field-effect nonlinear electroosmosis control in microfluidics embedding an ion-selective medium

We study herein numerically the use of induced-charge electrokinetic phenomena to enable a flexible control of ion transport of dilute electrolyte in a straight ion concentration polarization system. The effect of three convection modes of induced-charge electrokinetic phenomena, including induced-charge electroosmosis, flow-field effect transistor, and alternating-current electroosmosis (ACEO), on convective arrestment of diffusive wave-front propagation is investigated by developing a cross-scale and fully coupled transient numerical simulation model, wherein multiple frequency electrochemical polarization and nonlinear diffuse charge dynamics in spatiotemporally varying solution conductivity are taken into account. We demonstrate by detailed comparative simulation studies that ACEO vortex flow field above a metal strip array arranged along the anodic chamber's bottom surface serves as the most efficient way for adjusting the salt density distribution at micrometer and even millimeter dimension, due to its high flexibility in controlling the stirring flow state with the introduction of two extra electrical parameters. The specific operating status is determined by whether the electrode array is floating in potential (induced-charge electroosmosis) or biased to ground (flow-field effect transistor) or forced to oscillate at another Fourier mode (ACEO). These results prove useful for on-chip electric current control with electroconvective stirring.     

Sample transport and electrokinetic injection in a microchip device for chemical cytometry

Sample transport and electrokinetic injection bias are well characterized in capillary electrophoresis and simple microchips, but a thorough understanding of sample transport on devices combining electroosmosis, electrophoresis, and pressure-driven flow is lacking. In this work, we evaluate the effects of electric fields from 0 to 300 V/cm, electrophoretic mobilities from 10(-4) to 10(-6) cm(2)/Vs, and pressure-driven fluid velocities from 50 to 250 μm/s on sample injection in a microfluidic chemical cytometry device. By studying a continuous sample stream, we find that increasing electric field strength and electrophoretic mobility result in improved injection and that COMSOL simulations accurately predict sample transport. The effects of pressure-driven fluid velocity on injection are complex, and relative concentration values lie on a surface defined by pressure-driven flow rates. For high-mobility analytes, this surface is flat, and sample injection is robust despite fluctuations in flow rate. For lower mobility analytes, the surface becomes steeper, and injection depends strongly on pressure-driven flow. These results indicate generally that device design must account for analyte characteristics and specifically that this device is suited to high-mobility analytes. We demonstrate that for a suitable pair of peptides fluctuations in injection volume are correlated; electrokinetic injection bias is minimized; and electrophoretic separation is achieved.     

Electrokinetic particle translocation through a nanopore containing a floating electrode

Electrokinetic particle translocation through a nanopore containing a floating electrode is investigated by solving a continuum model, composed of the coupled Poisson-Nernst-Planck (PNP) equations for the ionic mass transport and the modified Stokes equations for the flow field. Two effects due to the presence of the floating electrode, the induced-charge electroosmosis (ICEO) and the particle-floating electrode electrostatic interaction, could significantly affect the electrokinetic mobility of DNA nanoparticles. When the electrical double layers (EDLs) of the DNA nanoparticle and the floating electrode are not overlapped, the particle-floating electrode electrostatic interaction becomes negligible. As a result, the DNA nanoparticle could be trapped near the floating electrode arising from the induced-charge electroosmosis when the applied electric field is relatively high. The presence of the floating electrode attracts more ions inside the nanopore resulting in an increase in the ionic current flowing through the nanopore; however, it has a limited effect on the deviation of the current from its base current when the particle is far from the pore.     

径向电场调制毛细管电泳法用于蛋白质分离

利用自制的双向电场控制毛细管电泳新系统,考察了蛋白质的分离情况.结果发现,在低pH值下,通过施加径向电场,不仅可改变电渗流的大小和方向,而且能抑制蛋白质的吸附,进而实现对蛋白质分离效率和分离速度的调控.研究结果表明,可通过物理化学方法实现毛细管电泳的动态或随机调控,这对许多生物样品分离有实际意义.     

Hybrid continuum-atomistic approach to model electrokinetics in nanofluidics

In this study, for the first time, a hybrid continuum-atomistic based model is proposed for electrokinetics, electroosmosis and electrophoresis, through nanochannels. Although continuum based methods are accurate enough to model fluid flow and electric potential in nanofluidics (in dimensions larger than 4 nm), ionic concentration is too low in nanochannels for the continuum assumption to be valid. On the other hand, the non-continuum based approaches are too time-consuming and therefore is limited to simple geometries, in practice. Here, to propose an efficient hybrid continuum-atomistic method of modelling the electrokinetics in nanochannels; the fluid flow and electric potential are computed based on continuum hypothesis coupled with an atomistic Lagrangian approach for the ionic transport. The results of the model are compared to and validated by the results of the molecular dynamics technique for a couple of case studies. Then, the influences of bulk ionic concentration, external electric field, size of nanochannel, and surface electric charge on the electrokinetic flow and ionic mass transfer are investigated, carefully. The hybrid continuum-atomistic method is a promising approach to model more complicated geometries and investigate more details of the electrokinetics in nanofluidics.     

调控双电层电渗流数值研究

在通道壁面垂直施加一个调控电场可以改变双电层电荷密度和Zeta电位势,实现对电渗流的调控.采用电场Poisson方程、动量守恒的Navier-Stokes方程、电解质离子输运的Nernst-Planck方程和液体混合反应的组分浓度输运方程,本文对微通道壁面离散布置调控电极的情况进行了数值分析.数值算例包括单电极、双电极...     

Comparison of the Nernst-Planck model and the Poisson-Boltzmann model for electroosmotic flows in microchannels

In the analysis of electroosmotic flows, the internal electric potential is usually modeled by the Poisson-Boltzmann equation. The Poisson-Boltzmann equation is derived from the assumption of thermodynamic equilibrium where the ionic distributions are not affected by fluid flows. Although this is a reasonable assumption for steady electroosmotic flows through straight microchannels, there are some important cases where convective transport of ions has nontrivial effects. In these cases, it is necessary to adopt the Nernst-Planck equation instead of the Poisson-Boltzmann equation to model the internal electric field. In the present work, the predictions of the Nernst-Planck equation are compared with those of the Poisson-Boltzmann equation for electroosmotic flows in various microchannels where the convective transport of ions is not negligible.     

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.     

Mass transport characteristics and chromatographic behavior of preparative electrochromatography on hydroxyapatite.

Introducing an electric field into chromatography on hydroxyapatite (HAP) was attempted in order to enhance mass transfer and separation performance. A membrane spaced multicompartment electrolyzer was developed for electrochromatography on HAP. The high performance of liquid transport by electroosmotic flux was identified and described in terms of dynamic electroosmotic pressure. The application of the electric field resulted in an improved adsorption of bovine serum albumin as shown by the breakthrough curve as function of the electric field. An improved elution was also obtained in the presence of the electric field. The results show that electroosmosis is a powerful tool of liquid transport and dispersion in a packed bed of fine particles and has potential in the large-scale chromatography of biological molecules.     

Joule heating effects on electrokinetic flows with conductivity gradients

Instability occurs in the electrokinetic flow of fluids with conductivity and/or permittivity gradients if the applied electric field is beyond a critical value. Understanding such an electrokinetic instability is significant for both improved transport (via the suppressed instability) and enhanced mixing (via the promoted instability) of liquid samples in microfluidic applications. This work presents the first study of Joule heating effects on electrokinetic microchannel flows with conductivity gradients using a combined experimental and numerical method. The experimentally observed flow patterns and measured critical electric fields under Joule heating effects to different extents are reasonably predicted by a depth-averaged numerical model. It is found that Joule heating increases the critical electric field for the onset of electrokinetic instability because the induced fluid temperature rise and in turn the fluid property change (primarily the decreased permittivity) lead to a smaller electric Rayleigh number.     

Theoretical prediction of fast 3D AC electro-osmotic pumps

AC electro-osmotic (ACEO) pumps in microfluidics currently involve planar electrode arrays, but recent work on the underlying phenomenon of induced-charge electro-osmosis (ICEO) suggests that three-dimensional (3D) geometries may be exploited to achieve faster flows. In this paper, we present some new design principles for periodic 3D ACEO pumps, such as the "fluid conveyor belt" of ICEO flow over a stepped electrode array. Numerical simulations of these designs (using the standard low-voltage model) predict flow rates almost twenty times faster than existing planar ACEO pumps, for the same applied voltage and minimum feature size. These pumps may enable new portable or implantable lab-on-a-chip devices, since rather fast (mm s(-1)), tuneable flows should be attainable with battery voltages (<10 V).     

Biomarker-mediated disruption of coffee-ring formation as a low resource diagnostic indicator

The ring pattern resulting from the unique microfluidics in an evaporating coffee drop is a well-studied mass transport phenomenon generating interest in the research community mostly from a mechanistic perspective. In this report, we describe how biomarker-induced particle-particle assemblies, magnetic separation, and evaporation-driven ring formation can be combined for simple pathogen detection. In this assay design, the presence of biomarkers causes self-assembly of a magnetic nanoparticle and a fluorescently labeled micrometer-sized particle. A small spherical magnet under the center of the drop prevents these assemblies from migrating to the drop's edge while a nonreactive control particle flows to the edge forming a ring pattern. Thus the presence or absence of biomarker results in distinctly different distributions of particles in the dried drop. Proof-of-principle studies using poly-L-histidine, a peptide mimic of the malaria biomarker pfHRPII, show that the predicted particle distributions occur with a limit of detection of approximately 200-300 nM.     

Electrohydrodynamics of a drop under nonaxisymmetric electric fields

We consider the electrohydrodynamics of a spherical drop in a nonaxisymmetric electric field, which can be approximated by the sum of a uniform field and a linear straining field. We obtain the analytic solution of the three-dimensional flow fields inside and outside a drop for the Stokes flow regime by using Lamb's general solution and the leaky dielectric model. With the analytic solution, the dielectrophoretic migration velocity of a drop is obtained as a function of the type and the frequency of the imposed electric field. The direction of drop motion is found to be parallel to the dielectrophoretic force. The analytic solution is also used to investigate the characteristics of the interfacial flow under various nonaxisymmetric electric fields. While investigating the interfacial flow, we find a surface vortex structure under certain nonaxisymmetric electric fields, which is found to be related to the chaotic mixing inside the drop. Finally, we consider the chaotic features of three-dimensional flows inside the drop under static nonaxisymmetric electric fields.     

A simple mechanism for reliable particle sorting in a microdevice with combined electroosmotic and pressure-driven flow

Selective transport and sorting of particles in microfluidic devices by electroosmosis is complicated due to superposition of uncontrolled hydrodynamic pressure contributions on the electroosmotic force. In this paper, we present a microfluidic concept for the reliable and simple separation and sorting of particles in a microchip by electroosmosis combined with pressure-driven flow. The presented device allows fluid quantities to be switched and particles to be sorted within a channel manifold using only a single power supply with fixed voltage and an electric switch. Consequently, chip operation and fluid switching procedure are greatly simplified compared to a situation, in which several independent power sources are used for flow balancing, as is the common procedure. With the triple-T channel design presented, backpressure flow disturbing the electrokinetic fluid and particle separation process is eliminated by introducing controlled opposed hydrodynamic flow of buffer from side channels. This pressure-driven flow is generated on-chip by setting up differences in the reservoir pressures in a defined manner. A detailed flow analysis based on the equivalence of fluid flow and electric current is performed and the conditions for reliable chip function are worked out.