ac electroosmosis in rectangular microchannels

Motivated by the growing interest in ac electroosmosis as a reliable no moving parts strategy to control fluid motion in microfluidic devices for biomedical applications, such as lab-on-a-chip, we study transient and steady-state electrokinetic phenomena (electroosmosis and streaming currents) in infinitely extended rectangular charged microchannels. With the aid of Fourier series and Laplace transforms we provide a general formal solution of the problem, which is used to study the time-dependent response to sudden ac applied voltage differences in case of finite electric double layer. The Debye-Huckel approximation has been adopted to allow for an algebraic solution of the Poisson-Boltzmann problem in Fourier space. We obtain the expressions of flow velocity profiles, flow rates, streaming currents, as well as expressions of the complex hydraulic and electrokinetic conductances. We analyze in detail the dependence of the electrokinetic conductance on the extension of linear dimensions relative to the Debye length, with an eye on finite electric double layer effects.     

Nonlinear electroosmosis in hierarchical monolithic structures

We studied the dependence of electroosmotic flow (EOF) velocity and separation efficiency for neutral analytes in 100 microm ID capillary monoliths on a variation of the mobile phase ionic strength and applied electrical field strength, i.e., we covered a range for the concentration of Tris buffer from 10(-5) to 10(-2) M and applied electrical field strengths up to 10(5) V/m. The silica-based monoliths are hierarchically structured having intraskeleton mesopores and interskeleton macropores. While a linear dependence of the average EOF velocity on applied field strength could be observed with 5 x 10(-3) M Tris (turning slightly nonlinear at a higher concentration due to thermal effects), this dependence becomes systematically nonlinear as the Tris concentration is reduced towards 10(-4) M. Increased velocities by more than 50% compared to those expected from linear behavior are realized at 10(5) V/m. Concomitantly, as the Tris concentration is reduced from 10(-3) to 10(-4) M, we notice an improvement in plate heights by a factor of more than 2 (they approach 2 microm for ethylbenzoate). We complementary analyzed the onset of the nonlinear EOF dynamics in a hierarchical monolith and the significantly reduced axial dispersion in view of nonequilibrium electrokinetic effects which may develop in porous media due to the presence of ion-permselective regions, e.g., the mesoporous monolith skeleton. In this respect, a decreasing mobile phase ionic strength favors the formation of nonequilibrium concentration polarization in strong electrical fields, and a coupling of the electrostatics and hydrodynamics then may explain nonlinear EOF velocities and increasing separation efficiencies depending on the Tris concentration and applied field strength.     

Low-voltage electroosmosis pump for stand-alone microfluidics devices

Two types of low-voltage electroosmosis pumps were developed using microfabrication technology for usage in handy or stand-alone applications of the micrototal analysis systems (micro-TAS) and the lab-on-a-chip. This was done by making a thin (< 1 microm) region in the flow path and by only applying voltages near this thin region using electrodes inserted into the flow path. The inserted electrodes must be free from bubble formation and be gas-tight in order to avoid pressure leakage. For these electrodes, Ag/AgCl or a gel salt bridge was used. For patterning the gel on the chip, a hydrophilic photopolymerization gel and a photolithographic technique were optimized for producing a gel with higher electric conductivity and higher mechanical strength. For high flow rate application, wide (33.2 mm) and thin (400 nm) pumping channels were compacted into a 1 mm x 6 mm area by folding. This pump achieves an 800 Pa static pressure and a flow of 415 nL/min at 10 V. For high-pressure application, a pump was designed with the thin and thick regions in series and positive and negative electrodes were inserted between them alternatively. This pump could increase the pumping pressure without increasing the supply voltage. A pump with 10-stage connections generated a pressure of 25 kPa at 10 V.     

Study on pressurizing electroosmosis pump for chromatographic separation

A porous core electroosmosis pump was studied and improved in accordance with the electroosmosis theory. Hexamethylene tetraamine (HMTA) was used as the additive of pump carrier solution to improve the flow rate stability and delivery efficiency. The influences of the electric field strength, porous core dimension and acetonitrile concentration of carrier solution on the pump flow rate and output pressure were investigated in detail. The improved electroosmosis pump can provide not only steady flow rate and large flow range, but also moderate output pressure. With the pump carrier solution of 0.5 mmol/L HMTA and the working voltage of 4950 V, the pump output pressure, flow rate and delivery efficiency achieved 1.1 MPa, 1.3 mL/min and 3.2 mL/(min mA), respectively. The pump can be employed for mobile phase delivery in the reversed-phase chromatographic separation of monolithic silica columns.     

Preferential glycerol transport by electroosmosis through ionic membranes

This paper describes a process in which glycerol is preferentially sorbed relative to water by an ionic membrane and transported into the product solution by electroosmosis at a significantly higher concentration than that in the feed solution. Direct measurement of the membrane distribution coefficient demonstrated preferential glycerol sorbtion for Neosepta CL-25T and AV-4T membranes. Both DC and AC electric currents significantly increase glycerol transport over that of a concentration difference alone.     

Molecular dynamics simulations of electroosmosis in perfluorosulfonic acid polymer

An atomistic MD simulation method has been developed to study the electroosmotic drag in the hydrated perfluorosulfonic acid polymer. The transport characteristics of the hydroniums and water molecules are evaluated from their velocity distribution functions with an electric field applied. It is shown that the microstructure of the hydrated perfluorosulfonic acid polymer is not perturbed significantly by the electric field up to 2 V/microm, and the velocity distribution functions obey the peak shifted Maxwell velocity distribution functions. The evaluated peak shifting velocities are only about 1% of the average thermal motion. The hydronium flow and water flow are evaluated from the average transport velocities or the peak shifting velocities. The electroosmotic drag coefficients from the MD simulations are in good correspondence with the experimental values. It is also shown that the electroosmotic drag coefficient has no or weak temperature dependence.     

Frequency-dependent linear response of superconducting systems

We present a density functional scheme for calculating the frequency-dependent linear response of superconductors. The central result is a set of integral equations determining the linear response of the normal and anomalous densities to external perturbations. Analytic solutions of these integral equations are obtained for homogeneous systems with separable effective interactions. For inhomogeneous superconductors, the formalism leads to a scheme for calculating the critical temperature without explicitly solving the gap equation. © 1995 John Wiley & Sons, Inc.     

Frequency-dependent polarizability of open-shell atomic systems

The time-dependent variational principle is used to calculate the frequency-dependent dipole polarizabilities of 2p open-shell atomic systems. A general theory is built up to include frequency-dependent perturbations using the Roothaan–Hartree–Fock (HFR) formalism. The excitation energies corresponding to the low-lying excited states of the system are obtained from the poles of the dynamic polarizability values. A fairly accurate knowledge of transition oscillator strengths is also obtained from a knowledge of the polarizability values near the poles. The excitation energies and oscillator strengths are compared with available data.     

Frequency-dependent electrical detection of protein binding events

Frequency-dependent electrochemical impedance spectroscopy has been used to characterize the changes in electrical response that accompany specific binding of a protein to its substrate, using the biotin-avidin system as a model. Our results show that avidin, at concentrations in the nanomolar range, can be detected electrically in a completely label-free manner under conditions of zero average current flow and without the use of any auxiliary redox agents. Impedance measurements performed on biotin-modified surfaces of gold, glassy carbon, and silicon were obtained over a wide frequency range, from 5 mHz to 1 MHz. On each biotin-modified surface, binding of avidin is most easily detected at low frequencies, <1 Hz. Electrical circuit modeling of the interface was used to relate the frequency-dependent electrical response to the physical structure of the interface before and after avidin binding. Electrical measurements were correlated with measurements of protein binding using fluorescently labeled avidin.     

Diffusioosmosis and electroosmosis of electrolyte solutions in fibrous porous media

The steady diffusioosmotic and electroosmotic flows of an electrolyte solution in the fibrous porous medium constructed by a homogeneous array of parallel charged circular cylinders are analyzed under conditions of small Peclet and Reynolds numbers. The imposed electrolyte concentration gradient or electric field is constant and can be oriented arbitrarily with respect to the axes of the cylinders. The thickness of the electric double layers surrounding the cylinders is assumed to be small relative to the radius of the cylinders and to the gap width between two neighboring cylinders, but the polarization effect of the diffuse ions in the double layers is incorporated. Through the use of a unit cell model, the appropriate equations of conservation of the electrochemical potential energies of ionic species and the fluid momentum are solved for each cell, in which a cylinder is envisaged to be surrounded by a coaxial shell of the fluid. Analytical expressions for the diffusioosmotic and electroosmotic velocities of the bulk electrolyte solution as functions of the porosity of the ordered array of cylinders are obtained in closed form for various cases. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. In the limit of maximum porosity, these results can be interpreted as the diffusiophoretic and electrophoretic velocities of an isolated circular cylinder caused by the imposed electrolyte concentration gradient or electric field.     

Frequency-dependent transversal flow control in centrifugal microfluidics

This work presents a novel flow switch for centrifugal microfluidic platforms which is solely controlled by the Coriolis pseudo force. This Coriolis switch consists of an inverse Y-structure with one common upstream channel and two symmetric outlets on a rotating disk. Above a certain threshold frequency, the Coriolis force becomes dominant that the entire flow is diverted into one of the outlets which is selected by the direction of rotation. The threshold frequency has been measured to be 350 rad s(-1)(approximately 55.7 Hz) for a channel width of 360 microm and a depth of 125 microm. The results are supported by extensive CFD simulations.     

The effects of electroosmosis on the structure of isotachophoresis boundaries

The influence of convection on the structure of an isotachophoretic boundary is investigated using an asymptotic method to simplify the conservation equations. To illustrate the methodology it is applied to a simple strong electrolyte system consisting of three ions and the relevant equations solved numerically. The technique, however, is of general applicability and can be useful in exploring the influence of various flow processes on analytical and preparative electrophoretic separation techniques in addition to isotachophoresis.     

Concentration dependence of electroosmosis and streaming potential across charged membranes

Electroosmosis and streaming potential measurements were carried out across charged membranes made of collodion and sulfonated polystyrene. Experiments were confined to the range where linear flux/force relationships hold. Saxén's relationship holds between electroosmosis and streaming potential; for porous charged membranes these exhibit an approximate inverse proportionality to ionic mobility at the limit of low electrolyte concentration. Both tend towards zero at the limit of high electrolyte concentration.     

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.     

Frequency-dependent dielectric permittivity of salt-free charged lamellar systems

We present a new model to analyze dielectric spectroscopy measurements on charged lamellar systems, with the following improvements with respect to the hitherto available models: (i) it does not rely on the hypothesis of local electro-neutrality, and allows to treat the salt-free case; (ii) the chemical exchange governing the partition between free and bound ions is properly taken into account; (iii) a fully analytical solution is provided. The variation of the frequency-dependent dielectric permittivity with both thermodynamic and kinetic characteristics of the free-bound ion equilibrium is presented. In particular, the relative weights of both relaxation modes (exchange and transport), and their characteristic frequencies are discussed. This study opens the way to the analysis of systems for which the usual models are irrelevant, such as salt-free clay gels or membranes.     

Lateral separation of colloids or cells by dielectrophoresis augmented by AC electroosmosis

Colloidal particles and biological cells are patterned and separated laterally adjacent to a micropatterned electrode array by applying AC electric fields that are principally oriented normally to the electrode array. This is demonstrated for yeast cells, red blood cells, and colloidal polystyrene particles of different sizes and zeta-potentials. The separation mechanism is observed experimentally to depend on the applied field frequency and voltage. At high frequencies, particles position themselves in a manner that is consistent with dielectrophoresis, while at low frequencies, the positioning is explained in terms of a strong coupling between gravity, the vertical component of the dielectrophoretic force, and the Stokes drag on particles induced by AC electroosmotic flow. Compared to high frequency dielectrophoretic separations, the low frequency separations are faster and require lower applied voltages. Furthermore, the AC electroosmosis coupling with dielectrophoresis may enable cell separations that are not feasible based on dielectrophoresis alone.     

Frequency-dependent electromechanics of aqueous liquids: electrowetting and dielectrophoresis

Electrowetting on dielectric and dielectrophoretic electromechanical mechanisms dominate microfluidic actuation in the low- and high-frequency limits, respectively. The frequency-dependent relationship between these two mechanisms has been clarified by the Maxwell stress tensor and a simple RC circuit model. In this paper, we report extensive height-of-rise measurements obtained with vertical, parallel, dielectrically coated electrodes to test this relationship using deionized water and solutions containing sugar and salt. For DC and AC (20 Hz to 20 kHz) voltage magnitudes up to approximately 150 V-rms, the data are highly reproducible and, within experimental error, consistent with the square-law predictions of the model. Eventually as voltage is increased, a saturation phenomenon is observed which exhibits a weak dependence on frequency and is probably correlated to contact angle saturation.     

Model based design of a microfluidic mixer driven by induced charge electroosmosis

Mixing chemical or biological samples with reagents for chemical analysis is one of the most time consuming operations on microfluidic platforms. This is primarily due to the low rate of diffusive transport in liquid systems. Additionally, much research has focused on detection, rather than sample preparation. In response, we describe a mixer for microfluidic sample preparation based on the electrokinetic phenomenon of induced-charge-electroosmosis (ICEO). ICEO creates microvortices within a fluidic channel by application of alternating current (AC) electric fields. The microvortices are driven by electrostatic forces acting on the ionic charge induced by the field near polarizable materials. By enabling mixing to be turned on or off within a channel of fixed volume, these electronically controlled mixers prevent sample dilution-a common problem with other strategies. A three-dimensional model based on the finite volume method was developed to calculate the electric field, fluid flow, and mass transport in a multi-species liquid. After preliminary experiments, the model was used to rapidly prototype a wide range of designs. A new microfabrication process was developed for devices with vertical sidewalls having conductive metal coatings and embedded electrodes. Mixing experiments were carried out in the devices and the results were compared to the model.     

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.