Concentration polarization and nonequilibrium electroosmotic slip in dense multiparticle systems

Electrical field-induced concentration polarization (CP) and CP-based nonequilibrium electroosmotic slip are studied in fixed beds of strong cation-exchange particles using confocal laser scanning microscopy (CLSM) and the macroscopic electroosmotic flow (EOF) dynamics. A key property of the investigated fixed beds is the coexistence of quasi-electroneutral macroporous regions between the micrometer-sized particles and the ion-permselective (here, cation-selective) intraparticle mesopores with a mean size of 10 nm. The application of an external electrical field to the particles induces depleted and enriched CP zones along their anodic and cathodic interfaces, respectively, by the local interplay of diffusive and electrokinetic transport. The intensity and dimension of the CP zones depend on the applied electrical field strength and the fluid-phase ionic strength. With increasing field strength a limiting current density through a particle is approached, meaning that charge transport locally through a particle becomes controlled by the dynamics in the adjoining extraparticle convective-diffusion boundary layer (depleted CP zone). In this regime a nonequilibrium electrical double layer can be induced electrokinetically in the depleted CP zone and intraparticle pore space, resulting in nonlinear EOF in the interparticle macropore space. The local CP dynamics analyzed by CLSM is successfully correlated with the onset of nonlinearity in the macroscopic EOF dynamics. We further demonstrate that multiparticle effects arising in fixed beds (random close packings) of ion-permselective particles modulate significantly the local pattern of CP and intensity of the nonequilibrium electroosmotic slip with respect to the undisturbed single-particle picture.     

Dielectrophoresis of nanosized particle

The theory of dielectrophoresis is constructed with allowance for electroosmotic perturbances. Changes in the flow regime of electrolyte in the diffuse part of electrical double layer under the action of quadratic (with respect to external field) electric forces are considered. The expression for low-frequency limit of the dielectrophoretic velocity of a spherical particle, which is valid at the arbitrary thickness of electrical double layer and fairly small value of ζ-potential (< 50 mV), is derived. It is shown that electroosmotic perturbances appeared to be rather significant for nanosized particles and their dielectrophoretic velocity under the effect of electroosmotic perturbances changes by several times.     

Nonequilibrium electrokinetic effects in beds of ion-permselective particles

Electrokinetic transport of fluorescent tracer molecules in a bed of porous glass beads was investigated by confocal laser scanning microscopy. Refractive index matching between beads and the saturating fluid enabled a quantitative analysis of intraparticle and extraparticle fluid-side concentration profiles. Kinetic data were acquired for the uptake and release of electroneutral and counterionic tracer under devised conditions with respect to constant pressure-driven flow through the device and the effect of superimposed electrical fields. Transport of neutral tracer is controlled by intraparticle mass transfer resistance which can be strongly reduced by electroosmotic flow, while steady-state distributions and bead-averaged concentrations are unaffected by the externally applied fields. Electrolytes of low ionic strength caused the transport through the charged (mesoporous) beads to become highly ion-permselective, and concentration polarization is induced in the bulk solution due to the superimposed fields. The depleted concentration polarization zone comprises extraparticle fluid-side mass transfer resistance. Ionic concentrations in this diffusion boundary layer decrease at increasing field strength, and the flux densities approach an upper limit. Meanwhile, intraparticle transport of counterions by electromigration and electroosmosis continues to increase and finally exceeds the transport from bulk solution into the beads. A nonequilibrium electrical double layer is induced which consists of mobile and immobile space charge regions in the extraparticle bulk solution and inside a bead, respectively. These electrical field-induced space charges form the basis for nonequilibrium electrokinetic phenomena. Caused by the underlying transport discrimination (intraparticle electrokinetic vs extraparticle boundary-layer mass transfer), the dynamic adsorption capacity for counterions can be drastically reduced. Further, the extraparticle mobile space charge region leads to nonlinear electroosmosis. Flow patterns can become highly chaotic, and electrokinetic instability mixing is shown to increase lateral dispersion. Under these conditions, the overall axial dispersion of counterionic tracer can be reduced by more than 2 orders of magnitude, as demonstrated by pulse injections.     

Electroosmosis at spherical and cylindrical metal surfaces

The profiles and velocities of electroosmotic flows at spherical and cylindrical metal surfaces are experimentally studied. Main differences are established between electroosmotic flows at the surfaces of ionite granules and particles with electronic conductivity.     

Concentration polarization-based nonlinear electrokinetics in porous media: induced-charge electroosmosis

We have investigated induced-charge electroosmotic flow in a fixed bed of ion-permselective glass beads by quantitative confocal laser scanning microscopy. Externally applied electrical fields induce concentration polarization (CP) in the porous medium due to coupled mass and charge transport normal to the charge-selective interfaces. These data reveal the generation of a nonequilibrium electrical double layer in the depleted CP zones and the adjoining anodic hemispheres of the (cation-selective) glass beads above a critical field strength. This initiates CP-based induced-charge electroosmosis along curved interfaces of the quasi-electroneutral macropore space between glass beads. Caused by mutual interference of resulting nonlinear flow with (flow-inducing) space charge regions, an electrohydrodynamic instability can appear locally and realize turbulent flow behavior at low Reynolds numbers. It is characterized by a local destruction of the CP zones and concomitant removal of diffusion-limited mass transfer. More efficient pore-scale lateral mixing also improves macroscopic transport, which is reflected in the significantly reduced axial dispersion of a passive tracer.     

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.     

Measurement of electroosmotic and electrophoretic velocities using pulsed and sinusoidal electric fields

In this work, we explore two methods to simultaneously measure the electroosmotic mobility in microchannels and the electrophoretic mobility of micron‐sized tracer particles. The first method is based on imposing a pulsed electric field, which allows to isolate electrophoresis and electroosmosis at the startup and shutdown of the pulse, respectively. In the second method, a sinusoidal electric field is generated and the mobilities are found by minimizing the difference between the measured velocity of tracer particles and the velocity computed from an analytical expression. Both methods produced consistent results using polydimethylsiloxane microchannels and polystyrene micro‐particles, provided that the temporal resolution of the particle tracking velocimetry technique used to compute the velocity of the tracer particles is fast enough to resolve the diffusion time‐scale based on the characteristic channel length scale. Additionally, we present results with the pulse method for viscoelastic fluids, which show a more complex transient response with significant velocity overshoots and undershoots after the start and the end of the applied electric pulse, respectively.     

Influence of moderate Joule heating on electroosmotic flow velocity, retention, and efficiency in capillary electrochromatography

The influence of Joule heating on electroosmotic flow velocity, the retention factor of neutral analytes, and separation efficiency in capillary electrochromatography was investigated theoretically and experimentally. A plot of electrical current against the applied electrical field strength was used to evaluate the Joule heating effect. When the mobile phase concentration of Tris buffer exceeded 5.0 mM in the studied capillary electrochromatography systems using particulate and monolithic columns (with an accompanying power level of heat dissipation higher than 0.35 W/m), the Joule heating effect became clearly noticeable. Theoretical models for describing the variation of electroosmotic flow velocity with increasing applied field strength and the change of retention factors for neutral analytes with electrical field strength at higher Tris buffer concentrations were analyzed to explain consequences of Joule heating in capillary electrochromatography. Qualitative agreement between experimental data and implications of the theoretical model analysis was observed. The decrease of separation efficiency in capillary electrochromatography with macroporous octadecylsilica particles at high buffer concentration can be also attributed to Joule heating mainly via the increased axial diffusion of the analyte molecules and dispersion of solute bands by a nonuniform electroosmotic flow profile over the column cross-section. However, within a moderate temperature range, the contribution of the macroscopic velocity profile in the column arising from radial temperature gradients is insignificant.     

Electrically driven flow near a colloidal particle close to an electrode with a Faradaic current

To elucidate the nature of processes involved in electrically driven particle aggregation in steady fields, flows near a charged spherical colloidal particle next to an electrode were studied. Electrical body forces in diffuse layers near the electrode and the particle surface drive an axisymmetric flow with two components. One is electroosmotic flow (EOF) driven by the action of the applied field on the equilibrium diffuse charge layer near the particle. The other is electrohydrodynamic (EHD) flow arising from the action of the applied field on charge induced in the electrode polarization layer. The EOF component is proportional to the current density and the particle surface (zeta) potential, whereas our scaling analysis shows that the EHD component scales as the product of the current density and applied potential. Under certain conditions, both flows are directed toward the particle, and a superposition of flows from two nearby particles provides a mechanism for aggregation. Analytical calculations of the two flow fields in the limits of infinitesimal double layers and slowly varying current indicate that the EOF and EHD flow are of comparable magnitude near the particle whereas in the far field the EHD flow along the electrode is predominant. Moreover, the dependence of EHD flow on the applied potential provides a possible explanation for the increased variability in aggregation velocities observed at higher field strengths.     

Perspective on concentration polarization effects in electrochromatographic separations

This work illustrates the appearance and electrohydrodynamic consequences of concentration polarization in the particulate and monolithic fixed beds used in capillary electrochromatography and related electrical-field assisted processes. Key property of most porous materials is the co-existence of bulk, quasi-electroneutral macroporous regions and mesoporous compartments which are ion-permselective (due to electrical double-layer overlap) causing different transport numbers for co-ionic and counterionic species, e.g., background electrolyte components, or the analytes. For a cathodic electroosmotic flow the (cation) permselectivity, together with diffusive and electrokinetic transport induces depleted and enriched concentration polarization zones at the anodic and cathodic interfaces, respectively, in dependence of the mobile phase ionic strength and applied electrical fields. At high field strength a secondary, nonequilibrium electrical double layer may be created in the depleted concentration polarization zones of a material stimulating electroosmosis of the second kind. The potential of this induced-charge electroosmosis with respect to nonlinear flow velocities and electrokinetic instability mixing (basically destroying the concentration polarization zones) is analyzed in view of the pore space morphology in random-close packings of spherical-shaped, porous particles and hierarchically structured monoliths. Possible applications based on a fine-tuning of the illustrated effects emerge for microfluidic pumping and mixing, or the intensification of sample recovery in adsorption processes. With this perspective we want to focus the attention on concentration polarization in electrochromatographic systems by presenting and discussing original data acquired on relevant microscopic as well as macroscopic scales, and point towards the importance of related effects in colloid and membrane science.*     

Electrokinetic translocation of a deformable nanoparticle controlled by field effect in nanopores

Nanopores have become a popular single-molecule manipulation and detection technology. In this paper, we have constructed a continuum model of the nanopore; the arbitrary Lagrangian-Eulerian (ALE) method is used to describe the motion of particles and fluid. The mathematical model couples the stress-strain equation for the dynamics of a deformable particle, the Poisson equation for the electric field, the Navier-Stokes equations for the flow field, and the Nernst-Planck equations for ionic transport. Based on the model, the mechanism of field-effect regulation of particles passing through a nanopore is investigated. The results show that the transport of particles which is controlled by the field effect depends on the electroosmotic flow (EOF) generated by the gate electrode in the nanopore and the electrostatic interaction between the nanopore and particles. That also explains the asymmetry of particle transport velocity in the nanopore with a gate electrode. When the gate potential is negative, or the gate electrode length is small, the maximum deformation of the particles is increased. The field-effect regulation in the nanopore provides an active and compatible method for nanopore detection, and provides a convenient method for the active control of the particle deformation in the nanopore.     

Recent advances in direct current electrokinetic manipulation of particles for microfluidic applications

Microfluidic devices have been extensively used to achieve precise transport and placement of a variety of particles for numerous applications. A range of force fields have thus far been demonstrated to control the motion of particles in microchannels. Among them, electric field‐driven particle manipulation may be the most popular and versatile technique because of its general applicability and adaptability as well as the ease of operation and integration into lab‐on‐a‐chip systems. This article is aimed to review the recent advances in direct current (DC) (and as well DC‐biased alternating current) electrokinetic manipulation of particles for microfluidic applications. The electric voltages are applied through electrodes that are positioned into the distant channel‐end reservoirs for a concurrent transport of the suspending fluid and manipulation of the suspended particles. The focus of this review is upon the cross‐stream nonlinear electrokinetic motions of particles in the linear electroosmotic flow of fluids, which enable the diverse control of particle transport in microchannels via the wall‐induced electrical lift and/or the insulating structure‐induced dielectrophoretic force.     

Catalytic micropumps: microscopic convective fluid flow and pattern formation

As innovations continue to be made in the fields of microfluidics and the colloidal assembly, new strategies for moving particles and fluids may be needed. Heterogeneous catalysis provides means of locally converting the stored chemical energy of fuels to mechanical energy. We report an ambient temperature stationary "pump" that generates a proton concentration gradient through the bipolar electrochemical decomposition of hydrogen peroxide on patterned silver-gold surfaces. The resulting electric field drives convective fluid flow and pattern formation of colloidal tracer particles at the microscopic level by a combination of electroosmotic and electrophoretic forces.     

Electrophoresis of solid particles at large Peclet numbers

A theory of concentration polarization of a thin electrical double layer (DL) on a spherical particle is developed for the regime of large Peclet numbers which is realized in strong electric fields. In this regime, the concentration field arising outside DL is estimated under influence of diffusion and convection. According to the theory developed, polarization of DL at large Peclet numbers causes a change in the Stern potential, the formation of a dipole moment and the long-range potential. The diffuse layer deviates strongly from spherical symmetry and electroneutrality, and the screen of the surface charge is provided not only by the diffuse atmosphere but also by the charge induced in the convective-diffusion layer. The effect of electric field on the induced charge gives rise to the additional electroosmotic slip, that was called "secondary electroosmosis". Thus, a nonlinear additional term for the Smoluchowski formula of electrophoretic velocity is based on the changes of zeta-potential and on the secondary electroosmotic slip. The comparison of theory with experimental results revealed considerable fitting.     

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier-Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye-Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study.     

Electroosmotically enhanced mass transfer through polyacrylamide gels

We present an internal pumping strategy to enhance solute fluxes in polymer gels. The method is based on electroosmotic flow driven by an electric field applied across a gel that has been doped with charged colloidal inclusions. This work is motivated by the need to enhance the transport in gel-based biosensor devices whose response dynamics are often mass transfer limited. In this case, polyacrylamide gel slabs were doped with immobilized, charged silica colloids, and the flux of a fluorescent tracer was measured as a function of applied field strength, the volume fraction and size of the colloidal silica inclusions, and the bulk electrolyte composition. Significant flux enhancements were achieved with applied electric currents on the order of a few mA. Control experiments indicated that the flux enhancement was not due to any distortion of the gel diffusional properties in response to the presence of the inclusions. At a constant inclusion volume fraction, the electroosmotic solute flux enhancement was strongest for the smallest particle sizes that provide the highest total surface area, consistent with the electroosmotic mechanism whereby fluid flow is generated along the solid/liquid interface.     

Theoretical studies of microfluidic dispensing processes

The understanding of electrokinetic transport phenomena in microfluidic dispensers, an important component of biochips, is very important for designing and controlling biochips. A theoretical model to study the electrokinetic transport processes in microfluidic dispensers was developed in the work to study the controlling parameters for the dispensing process. The electrical field, the flow field, and the concentration field during dispensing processes were obtained by solving this theoretical model numerically. The effects of the electroosmotic mobility of the buffer solution, the diffusion coefficient and the electrophoretic mobility of the sample, the applied electrical field strength, and the channel size on the dispensing process are examined in this paper. The investigations show that optimal controlling parameter values can be found by using this model for dispensing any desired amount of the sample.     

Tradeoff between mixing and transport for electroosmotic flow in heterogeneous microchannels with nonuniform surface potentials

Electroosmotic flow (EOF) is a phenomenon associated with the movement of an aqueous solution induced by the application of an electric field in microchannels. The characteristics of EOF depend on the nature of the surface potential, i.e., whether it is uniform or nonuniform. In this paper, a lattice Boltzmann model (LBM) combined with the Poisson-Boltzmann equation is used to simulate flow field in a rectangular microchannel with nonuniform (step change) surface potentials. The simulation results indicate that local circulations can occur near a heterogeneous region with nonuniform surface potentials, in agreement with those by other authors. Largest circulations, which imply a highest mixing efficiency due to convection and short-range diffusion, were found when the average surface potential is zero, regardless of whether the distribution of the heterogeneous patches is symmetric or asymmetric. In this work, we have illustrated that there is a trade-off between the mixing and liquid transport in EOF microfluidics. One should not simply focus on mixing and neglect liquid transport, as performed in the literature. Excellent mixing could lead to a poor transport of electroosmotic flow in microchannels.     

Theoretical study on potential distribution and electroosmotic flow velocity in microscale channel

A developed mathematical model for calculating potential distribution inside the electrical double layer is explored in this paper based on the Poisson-Boltzmann equation. By modifying the ion concentration, we numerically simulated the potential profile inside the actual electrical double layer according to the zeta potential. Then a theoretical analysis on the streamwise electroosmotic velocity in microscale channel is presented. Furthermore, the expression of the electroosmotic velocity is significantly suppressed after considering the Helmboltz-Smolucbowski equation boundary conditions. The results show that the calculated electroosmotic values basically agree with the experimental ones. Therefore, this provides the data for micro- and nano-channels’ electrophoretic transport, as well as separation of neutral and charged electrolyte.     

Influence of the three-dimensional heterogeneous roughness on electrokinetic transport in microchannels

Surface roughness has been considered as a passive means of enhancing species mixing in electroosmotic flow through microfluidic systems. It is highly desirable to understand the synergetic effect of three-dimensional (3D) roughness and surface heterogeneity on the electrokinetic flow through microchannels. In this study, we developed a three-dimensional finite-volume-based numerical model to simulate electroosmotic transport in a slit microchannel (formed between two parallel plates) with numerous heterogeneous prismatic roughness elements arranged symmetrically and asymmetrically on the microchannel walls. We consider that all 3D prismatic rough elements have the same surface charge or zeta potential, the substrate (the microchannel wall) surface has a different zeta potential. The results showed that the rough channel's geometry and the electroosmotic mobility ratio of the roughness elements' surface to that of the substrate, epsilon(mu), have a dramatic influence on the induced-pressure field, the electroosmotic flow patterns, and the electroosmotic flow rate in the heterogeneous rough microchannels. The associated sample-species transport presents a tidal-wave-like concentration field at the intersection between four neighboring rough elements under low epsilon(mu) values and has a concentration field similar to that of the smooth channels under high epsilon(mu) values.