Numerical investigation of field-effect control on hybrid electrokinetics for continuous and position-tunable nanoparticle concentration in microfluidics

We introduce herein an effective way for continuous delivery and position-switchable trapping of nanoparticles via field-effect control on hybrid electrokinetics (HEK). Flow field-effect transistor exploiting HEK delicately combines horizontal linear electroosmosis and transversal nonlinear electroosmosis of a shiftable flow stagnation line (FSL) on gate terminals under DC-biased AC forcing. The microfluidic nanoparticle concentrator proposed herein makes use of a simple device geometry, in which an individual or a series of planar metal strips serving as gate electrode (GE) are subjected to a hybrid gate voltage signal and arranged in parallel between a pair of 3D driving electrodes. On the application of a DC-biased AC electric field across channel length direction, all the GE are electrochemically polarized, and the action of imposed hybrid electric field on the multiple-frequency bipolar counterions within the composite-induced double layer generates two counter-rotating induced-charge electroosmotic (ICEO) micro-vortices on top of each GE. Symmetry breaking in ICEO flow profile occurs once the gate voltage deviates from natural floating potential of corresponding GE. The gate voltage offset not only results in an additional pump motion of working fluid for enhanced electroosmotic transport but also directly changes the location of FSL where nanoparticles are preferentially collected by field-effect HEK. Our results of field-effect control on HEK are supposed to guide an elaborate design of flexible electrokinetic frameworks embedding coplanar metal strips for a high degree of freedom analyte manipulation in modern micro-total-analytical systems.     

Behavior of neutral solutes in pressurized flow driven electrochromatography using a mixed stationary phase of ODS and anion-exchange

The behavior of neutral sample solutes in pressurized flow driven electrochromatography using a mixed stationary phase, which consisted of ODS and anion-exchange (ODS-SAX), was studied. Applications of both positive and negative voltage on a column induced increases in retention factors of sample solutes. The direction of an electroosmotic flow under applications of positive and negative voltage were the same, therefore, the sign of the surface charge density under positive and negative voltage was opposite. We proposed a new equation for the relationship between applied voltage and surface charge density, and the practical electroosmotic flow conformed to this equation. Studying the electroosmotic flow using our proposed equation revealed that the applied negative voltage accelerates the protonation of the quaternary ammonium group and dissociation of the silanol group on packing materials. The retention behavior of a neutral solute was affected by the existence of the charged functional groups. We propose that this phenomenon is applicable to the control of the retention behavior of a sample solute using an electric field.     

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.     

Scaling behavior in on‐chip field‐amplified sample stacking

Field amplified sample stacking (FASS) uses differential electrophoretic velocity of analyte ions in the high‐conductivity background electrolyte zone and low conductivity sample zone for increasing the analyte concentration. The stacking rate of analyte ions in FASS is limited by molecular diffusion and convective dispersion due to nonuniform electroosmotic flow (EOF). We present a theoretical scaling analysis of stacking dynamics in FASS and its validation with a large set of on‐chip sample stacking experiments and numerical simulations. Through scaling analysis, we have identified two stacking regimes that are relevant for on‐chip FASS, depending upon whether the broadening of the stacked peak is dominated by axial diffusion or convective dispersion. We show that these two regimes are characterized by distinct length and time scales, based on which we obtain simplified nondimensional relations for the temporal growth of peak concentration and width in FASS. We first verify the theoretical scaling behavior in diffusion‐ and convection‐dominated regimes using numerical simulations. Thereafter, we show that the experimental data of temporal growth of peak concentration and width at varying electric fields, conductivity gradients, and EOF exhibit the theoretically predicted scaling behavior. The scaling behavior described in this work provides insights into the effect of varying experimental parameters, such as electric field, conductivity gradient, electroosmotic mobility, and electrophoretic mobility of the analyte on the dynamics of on‐chip FASS.     

A quantitative model to evaluate the ion-enrichment and ion-depletion effect at microchannel-nanochannel junctions

In a nanometer-scale fluidic channel (nanochannel), coions are depleted while counterions are concentrated due to the electric double layer (EDL) overlap. When an electric field is applied across the nanochannel, ions are enriched at one end and depleted at the other end of the nanochannel. This phenomenon is termed the ion-enrichment and ion-epletion (IEID) effect. In this paper, we develop a theoretical model to evaluate this effect. The model takes into accounts not only the biased electrophoretic migrations but also the net charge transportation caused by electroosmotic flow. In addition, we consider the conductance change inside the nanochannel in assessing the electric field strength across it. We employ our recently developed protocol to measure these values. We establish a protocol to measure/quantitate the IEID effect. Finally, we compare the calculated results with the experimentally measured data and show good agreements between them.     

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.     

Effect of multivalent ions on electroosmotic flow in micro- and nanochannels

In this work, the effect of multivalent ions on electroosmotic flow is investigated for multiple electrolyte components. The cases studied include incorporating Ca2+ and HPO4(2-) and other monovalent ions, such as K+ and H2PO4-, into an aqueous NaCl solution. The governing equations are derived and solved numerically. The boundary conditions for the governing equations are obtained from the electrochemical equilibrium requirements. In comparison with monovalent ions, the results show that in micro- and nanochannels having fixed surface charges, multivalent counterions, even in very small amounts, reduce electroosmotic flow significantly, while the multivalent co-ions have little effect on the electroosmotic flow. Due to the enhanced ion-wall interactions multivalent counterions compose the majority of ions in the electric double layer (EDL), causing a decrease of net charge at the surface.     

Tunable Bidirectional Electroosmotic Flow for Diffusion‐Based Separations

We present a new concept for on‐chip separation that leverages bidirectional flow, to tune the dispersion regime of molecules and particles. The system can be configured so that low diffusivity species experience a ballistic transport regime and are advected through the chamber, whereas high diffusivity species experience a diffusion dominated regime with zero average velocity and are retained in the chamber. We detail the means of achieving bidirectional electroosmotic flow using an array of alternating current (AC) field‐effect electrodes, experimentally demonstrate the separation of particles and antibodies from dyes, and present a theoretical analysis of the system, providing engineering guidelines for its design and operation.     

Electric polarizability of DNA in aqueous salt solution

Monte Carlo simulations are performed to determine the anisotropy of the electric polarizability of a model DNA fragment in aqueous salt solution. By taking into consideration the participation of coions in the electroneutrality condition, at every simulation step, we obtain a list of counterions constituting the net charge arranged in increasing order of their distance from the DNA and calculate the contribution to the dipole moment from the first n counterions in the list. We define a partial polarizability tensor due to these n counterions to understand the origin of the polarizability in close relation to the solution structure. The ionic distributions are described by the counterion condensation theory. Characteristic features of the electric properties of polyelectrolytes are reproduced. The anisotropy of the electric polarizability Deltaalpha of DNA decreases with the addition of salt, yielding values comparable to experiment. The effect of electrophoretic motion of the polyion is examined by estimating its upper limit.     

Joule heating induced transient temperature field and its effects on electroosmosis in a microcapillary packed with microspheres

The Joule heating induced transient temperature field and its effect on the electroosmotic flow in a capillary packed with microspheres is analyzed numerically using the control-volume-based finite difference method. The model incorporates the coupled momentum equation for the electroosmotic velocity, the energy equations for the Joule heating induced temperature distributions in both the packed column and the capillary wall, and the mass and electric current continuity equations. The temperature-dependent physical properties of the electrolyte solution are taken into consideration. The characteristics of the Joule heating induced transient development of temperature and electroosmotic flow fields are studied. Specifically, the simulation shows that the presence of Joule heating causes a noticeable axial temperature gradient in the thermal entrance region and elevates a significant temperature increment inside the microcapillary. The temperature changes in turn greatly affect the electroosmotic velocity by means of the temperature-dependent fluid viscosity, dielectric constant, and local electric field strength. Furthermore, the model predicts an induced pressure gradient to counterbalance the axial variation of the electroosmotic velocity so as to maintain the fluid mass continuity. In addition, under specific conditions, the present model is validated by comparing with the existing analytical model and experimental data from the literature.     

Electroosmotic flow in microchannels with arbitrary geometry and arbitrary distribution of wall charge

General solutions are developed for direct current (DC) and alternating current (AC) electroosmotic flows in microfluidic channels with arbitrary cross-sectional geometry and arbitrary distribution of wall charge (zeta potential). The applied AC electric field can also be of arbitrary waveform. By proposing a nondimensional time scale varpi defined as the ratio of the diffusion time of momentum across the electric double-layer thickness to the period of the applied electric field, we demonstrate analytically that the Helmholtz-Smoluchowski electroosmotic velocity is an appropriate slip condition for AC electroosmotic flows in typical microfluidic applications. With this slip condition approach, electroosmotic flows in rectangular and asymmetric trapezoidal microchannels with nonuniform wall charge, as examples, are investigated. The unknown constants in the proposed general solutions are numerically determined with a least-squares method through matching the boundary conditions. We find that the wall charge affects significantly the electroosmotic flow while the channel geometry does not. Moreover, the flow feature is characterized by another nondimensional time scale Omega defined as the ratio of the diffusion time of momentum across the channel hydraulic radius to the period of the applied electric field. The onset of phase shift between AC electroosmotic velocity and applied electric field is also examined analytically.     

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.     

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.     

Remotely powered distributed microfluidic pumps and mixers based on miniature diodes

We demonstrate new principles of microfluidic pumping and mixing by electronic components integrated into a microfluidic chip. The miniature diodes embedded into the microchannel walls rectify the voltage induced between their electrodes from an external alternating electric field. The resulting electroosmotic flows, developed in the vicinity of the diode surfaces, were utilized for pumping or mixing of the fluid in the microfluidic channel. The flow velocity of liquid pumped by the diodes facing in the same direction linearly increased with the magnitude of the applied voltage and the pumping direction could be controlled by the pH of the solutions. The transverse flow driven by the localized electroosmotic flux between diodes oriented oppositely on the microchannel was used in microfluidic mixers. The experimental results were interpreted by numerical simulations of the electrohydrodynamic flows. The techniques may be used in novel actively controlled microfluidic-electronic chips.     

Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows

Many biofluids such as blood and DNA solutions are viscoelastic and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. However, the governing equations for viscoelastic flows are not easily solvable, especially for electroosmotic flows where the streamwise velocity varies rapidly from zero at the wall to a nearly uniform velocity at the outside of the very thin electric double layer. In the present investigation, we have devised a simple method to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels. It is based on the concept of the Helmholtz-Smoluchowski velocity which is widely adopted in the electroosmotic flows of Newtonian fluids. It is shown that the Helmholtz-Smoluchowski velocity for viscoelastic fluids can be found by solving a simple cubic algebraic equation. The volumetric flow rate obtained using this Helmholtz-Smoluchowski velocity is found to be almost the same as that obtained by solving the governing partial differential equations for various viscoelastic fluids.     

Separation of single-stranded DNA fragments at a 10-nucleotide resolution by stretching in microfluidic channels

We report a novel DNA separation method by tethering DNA chains to a solid surface and then stretching the DNA chains with an electric field. The anchor is such designed that the critical force to detach a DNA chain is independent of its size. Because the stretching force is proportional to the DNA net charge, a gradual increase of the electric field leads to size-based removal of the DNA strands from the surface and thus DNA separation. Here we show that this method, originally proposed for separation of long double-stranded DNA chains (>10,000 base pairs), is also applicable to single-stranded (ss) DNA fragments with less than 100 nucleotides (nt). Theoretical analysis indicates that the separation resolution is limited by the fluctuation forces on tethered DNA chains. By employing a microfluidic platform with narrow channels filled with a buffer of low ionic conductivity, we are able to apply a strong electric field to the DNA fragments with negligible Joule heating. Upon stepwise increments of the electric field, we demonstrate efficient separation of short ssDNA fragments at a 10-nt resolution.     

Effect of electrospray needle voltage on electroosmotic flow in capillary electrophoresis-mass spectrometry

The effect of the electrospray ionization (ESI) needle voltage on the electroosmotic flow (EOF) in capillary electrophoresis (CE)-mass spectrometry (MS) was investigated. The radial electric field that penetrates across the CE capillary wall imposed by the ESI needle voltage modifies the typical EOF. This effect was investigated for buffers commonly used in CE-MS. Variations as high as ±30% were observed.     

Numerical analysis of the thermal effect on electroosmotic flow and electrokinetic mass transport in microchannels

Joule heating is present in electrokinetically driven flow and mass transport in microfluidic systems. Nowadays, there is a trend of replacing costly glass-based microfluidic systems by the disposable, cheap polymer-based microfluidic systems. Due to poor thermal conductivity of polymer materials, the thermal management of the polymer-based microfluidic systems may become a problem. In this study, numerical analysis is presented for transient temperature development due to Joule heating and its effect on the electroosmotic flow (EOF) and mass species transport in microchannels. The proposed model includes the coupling Poisson-Boltzmann (P-B) equation, the modified Navier-Stokes (N-S) equations, the conjugate energy equation, and the mass species transport equation. The results show that the time development for both the electroosmotic flow field and the Joule heating induced temperature field are less than 1 s. The Joule heating induced temperature field is strongly dependent on channel size, electrolyte concentration, and applied electric field strength. The simulations reveal that the presence of the Joule heating can result in significantly different characteristics of the electroosmotic flow and electrokinetic mass transport in microchannels.     

Capillary zone electrophoresis with electroosmotic flow controlled by external radial electric field.

A new way of regulation of electroosmotic flow (EOF) in capillary zone electrophoresis (CZE) by external electric field has been developed. A set of three high-voltage power supplies is used to form a radial electric field across the capillary wall. One power supply is applied in the usual way as a driving force of CZE and EOF to the ends of the inner capillary compartment dipped into the electrode vessels and filled with background electrolyte. Two power supplies are connected to the ends of the outer low-conductivity coating of the capillary which is formed by the dispersion of copolymer of aniline and p-phenylenediamine in polystyrene matrix. The difference between electric potentials on the outer capillary surface and inside the capillary determines the voltage of radial electric field across the capillary wall and affects the electrokinetic potential at the solid-liquid interface inside the capillary. The effect of magnitude and polarity of external radial electric field on the flow rate of EOF, on the migration times of charged analytes and on the separation efficiency and resolution of CZE separations of synthetic oligopeptides, diglycine, triglycine and octapeptide fragments of human insulin was evaluated. Through the EOF control by external electric field the dynamic effective length of the capillary was obtained and the speed of analysis and resolution of CZE separations of peptide analytes could be optimized.     

Ionic Polymerization under an Electric Field as a Relaxational Method for the Investigation of Kinetics. I. On Results of the Change in Space Distribution of Ions

Abstract

Investigations were made which show that the change in the dynamics of polymerization and in molecular weight of the polymer under an electric field is connected with the redistribution of the ions growing macromolecules and counterions. Analysis of the equations obtained showed that the field can either increase or decrease the rate of the process. The effect's trend and magnitude depend on the ratio of the mobilities of macroions and counterions, degree of dissociation of active centers, and the ratio of rate constants of free ions and ion pairs. An analysis of literature data relevant to polymerization under an electric field was made.