A linear analysis of the effect of Faradaic currents on traveling-wave electroosmosis

Induced-charge electrophoresis of a tilted metal nanowire near an insulating wall

Electric fields are commonly used to control the orientation and motion of microscopic metal particles in aqueous suspensions. For example, metallodielectric Janus spheres are propelled by the induced-charge electro-osmotic flow occurring on their metallic side, the most common case in electrokinetics of exploiting symmetry breaking of surface properties for achieving net particle motion. In this work, we demonstrate that a homogeneous metal rod can translate parallel to a dielectric wall as a result of the hydrodynamic wall-particle interaction arising from the induced-charge electro-osmosis on the rod surface. The applied electric field could be either dc or low-frequency ac. The only requirement for a nonvanishing particle velocity is that the axis of the rod be inclined with respect to the wall, i.e., it cannot be neither parallel nor perpendicular. We show numerical results of the rod velocity as a function of rod orientation and distance to the wall. The maximum particle velocity is found for an orientation of between ∼30^{∘} and ∼50^{∘}, depending on the position and aspect ratio of the cylinder. Particle velocities of up to tens of µm/s are predicted for typical conditions in electrokinetic experiments.

Insulating traveling-wave electrophoresis

Traveling-wave electrophoresis (TWE) is a method for transporting charged colloidal particles used in many microfluidic techniques for particle manipulation and fractionation. This method exploits the traveling-wave components of the electric field generated by an array of electrodes subjected to ac voltages with a phase delay between neighboring electrodes. In this article, we propose an alternative way of generating traveling-wave electric fields in microchannels. We apply a rotating electric field around a cylindrical insulating micropillar and the resulting traveling-wave modes induce particle drift around the cylinder. We term this phenomenon insulating traveling-wave electrophoresis (i-TWE) to distinguish it from standard TWE performed with arrays of microelectrodes. We characterized the particle drift experimentally and show a quantitative comparison of the particle velocity with theoretical predictions. Excellent agreement is found when the influence of electro-osmosis on the channel walls is also considered.

Travelling-Wave Dipolophoresis: Levitation and Electrorotation of Janus Nanoparticles

We present a theoretical study of the hydrodynamic and electrokinetic response of both metallic spherical polarized colloids as well as metallodielectic Janus particles, which are subjected to an arbitrary non-uniform ambient electric field (DC or AC forcing). The analysis is based on employing the linearized ‘standard’ model (Poisson–Nernst–Planck formulation) and on the assumptions of a ‘weak’ field and small Debye scale. In particular, we consider cases of linear and helical time-harmonic travelling-wave excitations and provide explicit expressions for the resulting dielectrophoretic and induced-charge electrophoretic forces and moments, exerted on freely suspended particles. The new analytic expressions thus derived for the linear and angular velocities of the initially uncharged polarizable particle are compared against some available solutions. We also analyze the levitation problem (including stability) of metallic and Janus particles placed in a cylindrical (insulating or conducting) pore near a powered electrode.

Multifrequency Induced-Charge Electroosmosis

We present herein a unique concept of multifrequency induced-charge electroosmosis (MICEO) actuated directly on driving electrode arrays, for highly-efficient simultaneous transport and convective mixing of fluidic samples in microscale ducts. MICEO delicately combines transversal AC electroosmotic vortex flow, and axial traveling-wave electroosmotic pump motion under external dual-Fourier-mode AC electric fields. The synthetic flow field associated with MICEO is mathematically analyzed under thin layer limit, and the particle tracing experiment with a special powering technique validates the effectiveness of this physical phenomenon. Meanwhile, the simulation results with a full-scale 3D computation model demonstrate its robust dual-functionality in inducing fully-automated analyte transport and chaotic stirring in a straight fluidic channel embedding double-sided quarter-phase discrete electrode arrays. Our physical demonstration with multifrequency signal control on nonlinear electroosmosis provides invaluable references for innovative designs of multifunctional on-chip analytical platforms in modern microfluidic systems.

Modeling the AC Electrokinetic Behavior of Semiconducting Spheres

We study theoretically the dielectrophoresis and electrorotation of a semiconducting microsphere immersed in an aqueous electrolyte. To this end, the particle polarizability is calculated from first principles for arbitrary thickness of the Debye layers in liquid and semiconductor. We show that the polarizability dispersion arises from the combination of two relaxation interfacial phenomena: charging of the electrical double layer and the Maxwell⁻Wagner relaxation. We also calculate the particle polarizability in the limit of thin electrical double layers, which greatly simplifies the analytical calculations. Finally, we show the model predictions for two relevant materials (ZnO and doped silicon) and discuss the limits of validity of the thin double layer approximation.

Pumping of electrolytes by electrical forces induced on the diffusion layer: A weakly nonlinear analysis

Pumping of electrolytes in microchannels can be achieved with the use of microelectrodes subjected to AC potentials. Experiments have shown an influence of Faradaic currents in the pumping performance, and theoretical studies for asymmetric electrolytes suggest that induced charges in the diffusion layer play an important role. In this work we consider the case of a diffusion layer induced by an array of electrodes subjected to a traveling wave potential and we include Faradaic currents. Previous theoretical studies considered the case of very small applied voltages, which allowed for two major simplifications: (i) Butler-Volmer (B-V) equation was linearized, and (ii) the presence of gradients in ion concentration was neglected. We extend previous results and used the full nonlinear B-V equation. A comparison with the linear limit shows that the flow rate in both cases coincides for voltages around and below ≈0.25 V. For voltages larger than this, the nonlinear equations show that gradients in ion concentration appear and have an important influence, therefore, the predictions deviate from the linear model. We show that the electrical force in the diffusion layer can induce pumping either in the same or the opposite direction of the applied traveling-wave potential and it could be responsible for the reversal of the flow as observed in experiments.

Kinetic mechanism for modeling of electrochemical reactions

We propose a kinetic mechanism of electrochemical interactions. We assume fast formation and recombination of electron donors D- and acceptors A+ on electrode surfaces. These mediators are continuously formed in the electrode matter by thermal fluctuations. The mediators D- and A+, chemically equivalent to the electrode metal, enter electrochemical interactions on the electrode surfaces. Electrochemical dynamics and current-voltage characteristics of a selected electrochemical system are studied. Our results are in good qualitative agreement with those given by the classical Butler-Volmer kinetics. The proposed model can be used to study fast electrochemical processes in microsystems and nanosystems that are often out of the thermal equilibrium. Moreover, the kinetic mechanism operates only with the surface concentrations of chemical reactants and local electric potentials, which facilitates the study of electrochemical systems with indefinable bulk.

Zig-zag arrangement of four electrodes for ac electro-osmotic micropumps

This paper deals with the mathematical modeling of traveling-wave ac electro-osmotic micropumps with a zig-zag arrangement of microelectrodes. A mathematical model based on the Poisson-Nernst-Planck-Navier-Stokes description is used in this study within the physically relevant ranges of the model parameters. We present an extensive set of parametrical studies concerning the dependence of the net velocity on a variety of parameters. We also demonstrate limits of the validity of the commonly used Capacitor-Resistor-Capacitor model. In order to achieve high net velocities, we found that there are the optimal values of the electrode length, the shift between the top and bottom electrode arrays, and the signal frequency. Performance of the zig-zag micropumps is evaluated by the means of back-pressure loads. The suggested zig-zag design brings two main benefits: (i) it allows an easier construction of four-phase traveling-wave micropumps without the need of spatially complicated electrode connections, and (ii) the zig-zag pumps can provide higher flow rates than those with single-sided coplanar arrangements. Another robust feature of the proposed zig-zag system is that a single flow reversal is observed at the ac frequency approximately six times higher than the reciprocal resistor-capacitor time even in low-amplitude regimes.

ac Electrokinetic phenomena over semiconductive surfaces: effective electric boundary conditions and their applications

Electrokinetic boundary conditions are derived for ac electrokinetic phenomena over leaky dielectric (i.e., semiconducting) surfaces. Such boundary conditions correlate the electric potentials across a semiconductor-electrolyte interface (consisting of an electric double layer inside the electrolyte solution and a space charge layer inside the semiconductor) in an ac electric field with arbitrary wave forms. The presented electrokinetic boundary conditions allow for evaluation of the induced ζ potential contributed by both bond charges (due to electric polarization) and free charges (due to electric conduction) from the leaky dielectric materials. Two well-known limiting cases, (i) the conventional insulating boundary condition and (ii) the perfectly polarizable boundary condition, can be recovered from the generalized electrokinetic boundary conditions derived in the present paper. Subsequently, we demonstrate the implementation of the derived boundary conditions for analyzing the ac induced-charge electrokinetic flow around a semiconducting cylinder. The results show that the flow circulations exist around the semiconducting cylinder and become stronger in the ac field with a lower frequency and around the semiconducting cylinder with a higher conductivity.

Analysis of traveling-wave electro-osmotic pumping with double-sided electrode arrays

In this paper, a series of numerical simulations was performed to investigate the pumping performance of electro-osmotic micropumps containing electrode arrays patterned on the upper and lower sides of a microchannel. The simulations have been analyzed with a linear electro-osmotic model based upon the Debye-Hückel theory of the double layer. The potential drop across the diffuse layer is assumed to be less than 25 mV (k(B)T/e), and there is a linear response between the surface charge and the voltage drop across the double layer. The double layer is not resolved but is lumped into effective parameters that are imported from the Debye-Hückel and Stern layers. We examined the effects of the relative positioning of the electrodes in the opposing arrays (i.e., symmetrical or staggered), and the phase lag and the angular frequency of the alternating current (ac) signals applied to the electrodes within the two arrays. A critical height of the microchannel was observed, below which the interactions of the applied electrical potentials on the walls became significant. The optimum pumping effect was obtained when the electrode arrays were symmetrical to one another around the centerline of the channel and were activated by ac potentials with a 0° phase shift. The corresponding angular frequency of the maximum pumping velocity for different phase shifts of the applied ac signals was also determined. Overall, the simulation results presented in this paper provide a useful insight into the optimal design parameters and operating conditions for micropumps containing two arrays of microelectrodes on the microchannel walls.

Effect of the combined action of Faradaic currents and mobility differences in ac electro-osmosis

In this work, we extend previous analyses of ac electro-osmosis to account for the combined action of two experimentally relevant effects: (i) Faradaic currents from electrochemical reactions at the electrodes and (ii) differences in ion mobilities of the electrolyte. In previous works, the ac electro-osmotic motion has been analyzed theoretically under the assumption that only forces in the diffuse (Debye) layer are relevant. Here, we first show that if the ion mobilities of a 1-1 aqueous solution are different, the charged zone expands from the Debye layer to include the diffusion layer. We later include the Faradaic currents and, as an attempt to explore both factors simultaneously, we perform a thin-layer, low-frequency, linear analysis of the system. Finally, the model is applied to the case of an electrolyte actuated by a traveling-wave signal. A steady liquid motion in opposite direction to the applied signal is predicted for some ranges of the parameters. This could serve as a partial explanation for the observed flow reversal in some experiments.

Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions

The venerable theory of electrokinetic phenomena rests on the hypothesis of a dilute solution of point-like ions in quasi-equilibrium with a weakly charged surface, whose potential relative to the bulk is of order the thermal voltage (kT/e approximately 25 mV at room temperature). In nonlinear electrokinetic phenomena, such as AC or induced-charge electro-osmosis (ACEO, ICEO) and induced-charge electrophoresis (ICEP), several V approximately 100 kT/e are applied to polarizable surfaces in microscopic geometries, and the resulting electric fields and induced surface charges are large enough to violate the assumptions of the classical theory. In this article, we review the experimental and theoretical literatures, highlight discrepancies between theory and experiment, introduce possible modifications of the theory, and analyze their consequences. We argue that, in response to a large applied voltage, the "compact layer" and "shear plane" effectively advance into the liquid, due to the crowding of counterions. Using simple continuum models, we predict two general trends at large voltages: (i) ionic crowding against a blocking surface expands the diffuse double layer and thus decreases its differential capacitance, and (ii) a charge-induced viscosity increase near the surface reduces the electro-osmotic mobility; each trend is enhanced by dielectric saturation. The first effect is able to predict high-frequency flow reversal in ACEO pumps, while the second may explain the decay of ICEO flow with increasing salt concentration. Through several colloidal examples, such as ICEP of an uncharged metal sphere in an asymmetric electrolyte, we show that nonlinear electrokinetic phenomena are generally ion-specific. Similar theoretical issues arise in nanofluidics (due to confinement) and ionic liquids (due to the lack of solvent), so the paper concludes with a general framework of modified electrokinetic equations for finite-sized ions.

Flow reversal in traveling-wave electrokinetics: an analysis of forces due to ionic concentration gradients

Pumping of electrolytes using ac electric fields from arrays of microelectrodes is a subject of current research. The behavior of fluids at low signal amplitudes (<2-3 V(pp)) is in qualitative agreement with the prediction of the ac electroosmosis theory. At higher voltages, this theory cannot account for the experimental observations. In some cases, net pumping is generated in the direction opposite to that predicted by the theory (flow reversal). In this work, we use fluorescent dyes to study the effect of ionic concentration gradients generated by Faradaic currents. We also evaluate the influence of factors such as the channel height and microelectrode array shape in the pumping of electrolytes with traveling-wave potentials. Induced charge beyond the Debye length is postulated to be responsible for the forces generating the observed flows at higher voltages. Numerical calculations are performed in order to illustrate the mechanisms that might be responsible for generating the flow.

Experimental verification of Faradaic charging in ac electrokinetics

This paper investigates the phenomenon of Faradaic charging in ac electrokinetics. Faradaic reactions were suggested as a key effect responsible for the reversal of pumping direction in ac micropumps. However, this hypothesis has yet to be proven convincingly and directly. Here we present an ion detection strategy to determine the production of ions through Faradaic hydrolytic reactions originating from direct application of voltage to electrolytic solutions during ac electrokinetics. Experiments were performed with symmetrical planar electrodes aligned along a microfluidic channel. Fluorescein, a pH-dependent dye, was employed as the pH indicator for the detection of ion production. Images were captured for analysis at various voltage levels. From analyzing the fluorescence intensity and its distribution, it can be concluded that the production of ions from hydrolytic reactions takes place and increases with the ac voltage. The coefficient of deviation indicates a significant enhancement at ac voltage above 11 V(pp). Lastly, we demonstrate a strategy using dc-biased ac electrokinetics to achieve controllability in direction and magnitude of the net fluid flow in pumping application.

DC-biased AC-electroosmotic and AC-electrothermal flow mixing in microchannels

This paper presents a novel approach of mixing two laminar flowing streams in microchannels. The mixer consists of a pair of electrodes disposed along a fluidic channel. By energizing the electrodes with a DC-biased (2.5 V) AC voltage (20 Vpp), an electrokinetic flow is induced with a flow profile perpendicular to that of the incoming laminar streams of liquids to be mixed. As a result, the flow lines of the incoming streams and the induced flow are forced to crossover and very efficient stirring and mixing at short mixing length can be achieved. The mixer can be operated from the AC-electroosmotic (ACEO) (sigma=1 mS/m, f=100 kHz) to the AC-electrothermal (ACET) (sigma=500 mS/m, f=500 kHz) flow regimes. The mixing efficiency in the ACEO regime was 92%, with a mixing length of 600 microm (Q=2 microL/min), an estimated mixing time of 69 ms and an induced ACEO flow velocity of approximately 725 microm/s. The mixing efficiency in the ACET regime was 65% for a mixing length of approximately 1200 microm. The mixer is efficient and suitable for mixing reagents in a fluid media from low to high conductivity as required in diverse microfluidic applications.

Traveling-wave electrokinetic micropumps: velocity, electrical current, and impedance measurements

An array of microelectrodes covered in an electrolyte and energized by a traveling-wave potential produces net movement of the fluid. Arrays of platinum microelectrodes of two different characteristic sizes have been studied. For both sizes of arrays, at low voltages (<2 V pp) the electrolyte flow is in qualitative agreement with the linear theory of ac electroosmosis. At voltages above a threshold, the direction of fluid flow is reversed. The electrical impedance of the electrode-electrolyte system was measured after the experiments, and changes in the electrical properties of the electrolyte were observed. Measurements of the electrical current during pumping of the electrolyte are also reported. Transient behaviors in both electrical current and fluid velocity were observed. The Faradaic currents probably generate conductivity gradients in the liquid bulk, which in turn give rise to electrical forces. These effects are discussed in relation to the fluid flow observations.