Unsteady electroosmosis in a microchannel with Poisson-Boltzmann charge distribution

The present study is concerned with unsteady electroosmotic flow (EOF) in a microchannel with the electric charge distribution described by the Poisson-Boltzmann (PB) equation. The nonlinear PB equation is solved by a systematic perturbation with respect to the parameter λ which measures the strength of the wall zeta potential relative to the thermal potential. In the small λ limits (λ<1), we recover the linearized PB equation - the Debye-Hückel approximation. The solutions obtained by using only three terms in the perturbation series are shown to be accurate with errors <1% for λ up to 2. The accurate solution to the PB equation is then used to solve the electrokinetic fluid transport equation for two types of unsteady flow: transient flow driven by a suddenly applied voltage and oscillatory flow driven by a time-harmonic voltage. The solution for the transient flow has important implications on EOF as an effective means for transporting electrolytes in microchannels with various electrokinetic widths. On the other hand, the solution for the oscillatory flow is shown to have important physical implications on EOF in mixing electrolytes in terms of the amplitude and phase of the resulting time-harmonic EOF rate, which depends on the applied frequency and the electrokinetic width of the microchannel as well as on the parameter λ.     

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.     

Influence of the Modifier Type and its Concentration on Electroosmotic Flow of the Mobile Phase in Pressurized Planar Electrochromatography

The aim of this work was to find a relationship between electroosmotic flow (EOF) velocity of the mobile phase in pressurized planar electrochromatography (PPEC) and physicochemical properties like zeta potential, dielectric constant, and viscosity of the mobile phase as well as its composition. The study included different types of organic modifiers (acetonitrile, methanol, ethanol, acetone, formamide, N-methylformamide and N,N-dimethylformamide) in the full concentration range. In all experiments, chromatographic glass plates HPTLC RP-18 W from Merck (Darmstadt) were used as a stationary phase. During the study we found that there is no linear correlation between EOF velocity of the mobile phase and single variables such as zeta potential or dielectric constant or viscosity. However, there is quite strong linear correlation between EOF velocity of the mobile phase and variable obtained by multiplying zeta potential of the stationary phase–mobile phase interface, by dielectric constant of the mobile phase solution and dividing by viscosity of the mobile phase. Therefore, it could be concluded that the PPEC system fulfilled the Helmholtz–Smoluchowski equation.     

Generation of directional EOF by interactive oscillatory zeta potential

A steady directional EOF due to a nonlinear interaction between oscillatory axial electrical fields and oscillatory wall potentials (zeta potentials) is presented. This is a new mechanism to produce such a mean flow. It is found that the flow velocity depends not on the external driving frequency but on the phase angle difference between the electric fields and the zeta potentials. The formulation can also be reduced to the static EOF straightforwardly. For the purpose of theoretical demonstration, we use the Debye-Huckel approximation for the zeta potential. Results of planar and cylindrical capillaries are given.     

Effects of surface heterogeneity on flow circulation in electroosmotic flow in microchannels

The characteristics of electroosmotic flow in a cylindrical microchannel with non-uniform zeta potential distribution are investigated in this paper. Two-dimensional full Navier–Stokes equation is used to model the flow field and the pressure field. The numerical results show the distorted electroosmotic velocity profiles and various kinds of flow circulation resulting from the axial variation of the zeta potential. The influences of heterogeneous patterns of zeta potential on the velocity profile, the induced pressure distribution and the volumetric flow rate are discussed in this paper. This work shows that using either heterogeneous patterns of zeta potential or a combination of a heterogeneous zeta potential distribution and an applied pressure difference over the channel can generate local flow circulations and hence provide effective means to improve the mixing between different solutions in microchannels.     

A velocity program using the Kanade–Lucas–Tomasi feature-tracking algorithm with demonstration for pressure and electroosmosis conditions

Investigating microfluidic flow profiles is of interest in the microfluidics field for the determination of various characteristics of a lab-on-a-chip system. Microparticle tracking velocimetry uses computational methods upon recording video footage of microfluidic flow to ultimately visualize motion within a microfluidic system across all frames of a video. Current methods are computationally expensive or require extensive instrumentation. A computational method suited to microparticle tracking applications is the robust Kanade–Lucas–Tomasi (KLT) feature-tracking algorithm. This work explores a microparticle tracking velocimetry program using the KLT feature-tracking algorithm. The developed program is demonstrated using pressure-driven and EOF and compared with the respective mathematical fluid flow models. An electrostatics analysis of EOF conditions is performed in the development of the mathematical using a Poisson's Equation solver. This analysis is used to quantify the zeta potential of the electroosmotic system. Overall, the KLT feature-tracking algorithm presented in this work proved to be highly reliable and computationally efficient for investigations of pressure-driven and EOF in a microfluidic system.     

Electroosmotic flow in template-prepared carbon nanotube membranes.

Carbon nanotube membranes (CNMs) were prepared by doing chemical vapor deposition of carbon within the pores of a microporous alumina template. Electroosmotic flow (EOF) was driven across the CNMs by allowing the membrane to separate two electrolyte solutions and using an electrode in each solution to pass a constant ionic current through the nanotubes. EOF was investigated by measuring the flux of a probe molecule (phenol) across the CNM. The as-synthesized CNMs have anionic surface charge, and EOF is in the direction of cation migration across the membrane. Measurements of the rate of EOF as a function of applied transmembrane current provided the zeta potential. The effect of pH on zeta provided the pK(a) for the surface acidic sites responsible for this anionic charge; the acidic-site density was also determined. An electrochemical derivatization method was used to attach carboxylate groups to the nanotube walls; this enhances the anionic surface charge density, resulting in a corresponding increase in the EOF rate. Electrochemical derivatization was also used to attach cationic ammonium sites to the nanotube walls to yield CNMs that show EOF in the opposite direction of the as-synthesized or carboxylated membranes.     

Modeling the zeta potential of silica capillaries in relation to the background electrolyte composition

A theoretical relation between the zeta potential of silica capillaries and the composition of the background electrolyte (BGE) is presented in order to be used in capillary zone electrophoresis (CZE). This relation is derived on the basis of the Poisson-Boltzmann equation and considering the equilibrium dissociation of silanol groups at the capillary wall as the mechanism of charge generation. The resulting model involves the relevant physicochemical parameters of the BGE-capillary interface. Special attention is paid to the characterization of the BGE, which can be either salt or/and buffer solutions. The model is successfully applied to electroosmotic flow (EOF) experimental data of different aqueous solutions, covering a wide range of pH and ionic strength. Numerical predictions are also presented showing the capability of the model to quantify the EOF, the control of which is relevant to improve analyte separation performance in CZE.     

Towards the ultimate minimum particle diameter of silica packings in capillary electrochromatography

Porous silica beads with an average particle diameter between 0.2 and 3 microm have been applied as packing material in capillary electrochromatography (CEC). The experiments were directed to investigate whether it is really feasible and as promising as expected to use such small particles. In CEC, plate heights of H approximately/= 1-2 d(p) can be achieved which is smaller than the plate heights usually attained in high-performance liquid chromatography. Using a capillary packed with 0.5 microm silica beads we achieved a plate height of H = 3 d(p) indicating the presence of dispersive effects like Joule heating. Calculations demonstrate that at a field strength of about 800 V cm(-1) one third of the plate height can be lost by Joule heating effects if the heat is not removed by a cooling system. Additionally, the H(u) curve is still descending at the maximum electroosmotic flow (EOF) velocity we generated with the modified capillary electrophoresis instrument. To fully exploit the potential of submicron size silicas higher field strengths, i.e., higher EOF velocities, must be attained. To study the influence of the kind of packing on the EOF porous as well as nonporous silicas have been applied. The experiments clearly indicate that the EOF of porous and nonporous silicas is the same. Since the EOF is more or less exclusively generated by the packing material the zeta potential of n-octyl bonded 0.5 microm silica has been determined. The dependence of the zeta potential on the pH is identical to the dependence of the EOF on the pH in a packed capillary. The point of zero charge of the silica is at pH 2-3.     

In situ particle zeta potential evaluation in electroosmotic flows from time-resolved microPIV measurements

A time-resolved microPIV method is presented to measure in an EOF the particles zeta potential in situ during the transient start-up of a microdevice. The method resolves the electrophoretic velocity of fluoro-spheres used as tracer particles in microPIV. This approach exploits the short transient regime of the EOF generated after a potential drop is imposed across a microchannel and before reaching quasisteady state. During the starting of the transient regime, the electrophoretic effect is dominant in the center of the channel and the EOF is negligible. By measuring the velocity of the tracer particles with a microPIV system during that starting period, their electrophoretic velocity is obtained. The technique also resolves the temporal evolution of the EOF with three regions identified. The first region occurs before the electroosmotic effect reaches the center of the channel, the second region extends until the EOF reaches steady state, and thereafter is the third region. The two time constants separating these regions are also obtained and compared to the theory. The zeta potential of 860 nm diameter polystyrene particles is calculated for different solutions including borate buffer, sodium chloride, and deionized water. Results show that the magnitudes of the electrophoretic and electroosmotic velocities are in the range of |300| to |700| μm/s for these measurements. The zeta potential values are compared to the well-established closed cell technique showing improved accuracy. The method also resolves the characteristic response time of the EOF, showing small but important deviations from current analytical predictions. Additionally, the measurements can be performed in situ in microfluidic devices under actual working EOF conditions and without the need for calibrations.     

Enhancement of electroosmotic flow in capillary electrochromatography.

A major impediment to enhancing the speed of separation in capillary electrochromatography (CEC) is the upper limit on the electroosmotic flow (EOF) velocity by the maximal zeta potential of the chromatographic surface. Here, a new approach to speeding up EOF, suggested by Yang and El Rassi (Electrophoresis 1999, 20,18-23), is examined critically. It entails the use of a tandem arrangement of a separating column and an auxiliary column, the sole function of which is to boost EOF velocity in the separating column and thus facilitate faster analysis by CEC. Based on the principle of conservation of mass and current and using experimental data obtained in a wide range of conditions, the flow velocities in the separating and auxiliary columns were evaluated. The results show that an equidiameter open tubular auxiliary column offers a greater enhancement of EOF velocity than a packed column. Nevertheless, within the scope of the experiments the enhancement of EOF velocity by as much as 50% by using open tubular auxiliary columns has been obtained.     

Electroosmotic flow in a microcavity with nonuniform surface charges

In this work, we theoretically explore the characteristics of electroosmostic flow (EOF) in a microcavity with nonuniform surface charges. It is well known that a uniformly charged EOF does not give rise to flow separation because of its irrotational nature, as opposed to the classical problem of viscous flow past a cavity. However, if the cavity walls bear nonuniform surface charges, then the similitude between electric and flow fields breaks down, leading to the generation of vorticity in the cavity. Because this vorticity must necessarily diffuse into the exterior region that possesses a zero vorticity set by a uniform EOF, a new flow structure emerges. Assuming Stokes flow, we employ a boundary element method to explore how a nonuniform charge distribution along the cavity surface affects the flow structure. The results show that the stream can be susceptible to flow separation and exhibits a variety of flow structures, depending on the distributions of zeta potentials and the aspect ratio of the cavity. The interactions between patterned EOF vortices and Moffatt eddies are further demonstrated for deep cavities. This work not only has implications for electrokinetic flow induced by surface imperfections but also provides optimal strategies for achieving effective mixing in microgrooves.     

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.     

Electrical currents and liquid flow rates in micro-reactors

For micro-reactor devices in which liquids are pumped by electro-osmotic flow (EOF), in situ monitoring of the electrical currents in the channel networks provides a valuable diagnostic tool. We demonstrate here that the voltage-current characteristics of a micro-reactor channel network can be accurately modelled using measurements of the full 3-D geometry of the channel network, the liquid conductivity and the channel wall-liquid surface conductivity. It is shown that surface conductivity provides a significant contribution to the overall measured electrical currents in channel networks for which the ratio of surface area to volume is high. Following correction for surface conductivity, the electrical currents are proportional to the liquid volumetric flow rates measured in the different branches of the channel network. The constant of proportionality is related to the zeta potential of the channel wall-liquid surface. Measurements of the variation of electrical currents and volumetric flow rates as a function of the applied voltages allows the determination of the surface conductivity and zeta potential within the micro-reactor which enables the prediction of the voltages required to produce the desired flow rates in any channel section. In situ logging of the electrical currents, incorporated within the control system, allows continuous monitoring of the liquid flow rates during micro-reactor operation.     

Water-vapor plasma-based surface activation for trichlorosilane modification of PMMA

Separation rates and resolutions within capillary electrophoretic (CE) systems can be enhanced when surface zeta potentials are uniform with minimum deviations from ideal pluglike flow. Microfluidic CE devices based on poly(methyl methacrylate) (PMMA) are being developed due to the optical clarity, availability, stability, and reproducible electroosmotic flow (EOF) rates displayed by this polymer. Control of EOF in polymer-based CE systems can be achieved by surface zeta potential alteration through chemical modification. Herein, a method will be presented for the surface functionalization of PMMA with chemistry analogous to formation of trichlorosilane self-assembled monolayers on SiO2. The current method involves two separate steps. First, surface activation with water-vapor plasma introduces surface hydroxylation. Second, treatment of the plasma-treated PMMA with a substituted trichlorosilane solution forms the functional surface layer. The modified surfaces were characterized using several analytical techniques, including water contact angle, X-ray photoelectron spectroscopy, Fourier transform infrared-attenuated total reflection, secondary ion mass spectroscopy, and measurement of EOF velocities within PMMA microchannels.     

Field-effect flow control in a polydimethylsiloxane-based microfluidic system.

The application of the field-effect for direct control of electroosmosis in a polydimethylsiloxane (PDMS)-based microfluidic system, constructed on a silicon wafer with a 2.0 microm electrically insulating layer of silicon dioxide, is demonstrated. This microfluidic system consists of a 2.0 cm open microchannel fabricated on a PDMS slab, which can reversibly adhere to the silicon wafer to form a hybrid microfluidic device. Aside from mechanically serving as a robust bottom substrate to seal the channel and support the microfluidic system, the silicon wafer is exploited to achieve field-effect flow control by grounding the semiconductive silicon medium. When an electric field is applied through the channel, a radial electric potential gradient is created across the silicon dioxide layer that allows for direct control of the zeta potential and the resulting electroosmotic flow (EOF). By configuring this microfluidic system with two power supplies at both ends of the microchannel, the applied electric potentials can be varied for manipulating the polarity and the magnitude of the radial electric potential gradient across the silicon dioxide layer. At the same time, the longitudinal potential gradient through the microchannel, which is used to induce EOF, is held constant. The results of EOF control in this hybrid microfluidic system are presented for phosphate buffer at pH 3 and pH 5. It is also demonstrated that EOF control can be performed at higher solution pH of 6 and 7.4 by modifying the silicon wafer surface with cetyltrimethylammonium bromide (CTAB) prior to assembly of the hybrid microfluidic system. Results of EOF control from this study are compared with those reported in the literature involving the use of other microfluidic devices under comparable solution conditions.     

十二烷基硫酸钠微乳色谱体系中pH值对其电渗流行为与微结构的影响

以十二烷基硫酸钠(SDS)/正己烷/正丁醇/硼砂微乳液为毛细管电色谱运行研究体系,以甲醇峰为微乳体系电渗流峰(EOF),考察不同pH值条件下微乳体系电渗流出峰时间(tEOF)和变化趋势.以微乳液滴粒径和ξ电位考察pH值对SDS缓冲溶液微乳体系微结构的影响,用微乳体系的电导值分析pH值条件下微乳液滴与氢氧根离子之间的相互...     

Lattice Poisson-Boltzmann simulations of electro-osmotic flows in microchannels

This paper presents the numerical results of electro-osmotic flows in micro- and nanofluidics using a lattice Poisson-Boltzmann method (LPBM) which combines a potential evolution method on discrete lattices to solve the nonlinear Poisson equation (lattice Poisson method) with a density evolution method on discrete lattices to solve the Boltzmann-BGK equation (lattice Boltzmann method). In an electrically driven osmotic flow field, the flow velocity increases with both the external electrical field strength and the surface zeta potential for flows in a homogeneous channel. However, for a given electrical field strength and zeta potential, electrically driven flows have an optimal ionic concentration and an optimum width that maximize the flow velocity. For pressure-driven flows, the electro-viscosity effect increases with the surface zeta potential, but has an ionic concentration that yields the largest electro-viscosity effect. The zeta potential arrangement has little effect on the electro-viscosity for heterogeneous channels. For flows driven by both an electrical force and a pressure gradient, various zeta potential arrangements were considered for maximize the mixing enhancement with a less energy dissipation.     

Theoretical analysis of electrokinetic flow and heat transfer in a microchannel under asymmetric boundary conditions

The main theme of the present work is to investigate the electrokinetic effects on liquid flow and heat transfer in a flat microchannel of two parallel plates under asymmetric boundary conditions including wall-sliding motion, unequal zeta potentials, and unequal heat fluxes on two walls. Based on the Debye-Huckel approximation, an electrical potential solution to the linearized Poisson-Boltzmann equation is obtained and employed in the analysis. The analytic solutions of the electrical potential, velocity distributions, streaming potential, friction coefficient, temperature distribution, and heat transfer rate are obtained, and thereby the effects of electrokinetic separation distance (K), zeta-potential level (zeta;(1)), ratio of two zeta potentials (r(zeta) identical with zeta;(2)/zeta;(1)), wall-sliding velocity (u(w)), and heat flux ratio (r(q) identical with q"(2)/q"(1)) are investigated. The present results reveal the effects of wall-sliding and zeta-potential ratio on the hydrodynamic nature of microchannel flow, and they are used to provide physical interpretations for the resultant electrokinetic effects and the underlying electro-hydrodynamic interaction mechanisms. In the final part the results of potential and velocity fields are applied in solving the energy equation. The temperature distributions and heat transfer characteristics under the asymmetrical kinematic, electric, and thermal boundary conditions considered presently are dealt with.     

Influence of the Dukhin and Reynolds numbers on the apparent zeta potential of granular porous media

The Helmholtz-Smoluchowski (HS) equation is widely used to determine the apparent zeta potential of porous materials using the streaming potential method. We present a model able to correct this apparent zeta potential of granular media of the influence of the Dukhin and Reynolds numbers. The Dukhin number represents the ratio between the surface conductivity (mainly occurring in the Stern layer) and the pore water conductivity. The Reynolds number represents the ratio between inertial and viscous forces in the Navier-Stokes equation. We show here that the HS equation can lead to serious errors if it is used to predict the dependence of zeta potential on flow in the inertial laminar flow regime without taking into account these corrections. For indifferent 1:1 electrolytes (such as sodium chloride), we derived two simple scaling laws for the dependence of the streaming potential coupling coefficient (or the apparent zeta potential) on the Dukhin and Reynolds numbers. Our model is compared with a new set of experimental data obtained on glass bead packs saturated with NaCl solutions at different salinities and pH. We find fairly good agreement between the model and these experimental data.