Liquid transport in rectangular microchannels by electroosmotic pumping

The characteristics of electroosmotic flow in rectangular microchannels were investigated in this paper. A 2D Poisson–Boltzmann equation and the 2D momentum equation were used to model the electric double layer field and the flow field. The numerical solutions show significant influences of the channel cross-section geometry (i.e. the aspect ratio) on the velocity field and the volumetric flow rate. Also, the numerical simulation of the electroosmotic flow reveals how the velocity field and the volumetric flow rate depend on the ionic concentration, zeta potential, channel size and the applied electrical field strength.     

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.     

Transient electroosmotic flow induced by DC or AC electric fields in a curved microtube

This study investigates transient electroosmotic flow in a rectangular curved microtube in which the fluid is driven by the application of an external DC or AC electric field. The resultant flow-field evolutions within the microtube are simulated using the backwards-Euler time-stepping numerical method to clarify the relationship between the changes in the axial-flow velocity and the intensity of the applied electric field. When the electric field is initially applied or varies, the fluid within the double layer responds virtually immediately, and the axial velocity within the double layer tends to follow the varying intensity of the applied electric field. The greatest net charge density exists at the corners of the microtube as a result of the overlapping electrical double layers of the two walls. It results in local maximum or minimum axial velocities in the corners during increasing or decreasing applied electric field intensity in either the positive or negative direction. As the fluid within the double layer starts to move, the bulk fluid is gradually dragged into motion through the diffusion of momentum from the double layer. A finite time is required for the full momentum of the double layer to diffuse to the bulk fluid; hence, a certain phase shift between the applied electric field and the flow response is inevitable. The patterns of the axial velocity contours during the transient evolution are investigated in this study. It is found that these patterns are determined by the efficiency of momentum diffusion from the double layer to the central region of the microtube.     

Passive solute separation in AC electroosmosis including surface charge-coupled hydrodynamic slip effects

Separation of electrically neutral, mutually noninteracting passive solutes via AC electroosmotic slit channel flows is investigated for general asymmetric wall surface zeta potentials and apparent hydrodynamic slip lengths. We consider the nontrivial coupling between the surface potentials (or charge densities) and the apparent slip lengths, and focus our attention on the occurrence of a so called “crossover phenomenon” for separating out the slow diffusers when both slow and fast diffusers are present. Results show that regardless of the potential-slip coupling, wider bandwidths become available for crossover phenomenon to occur when the electroosmotic velocity gradient (magnitude) is greater. Contrarily, plug-like velocity profiles inhibit crossover phenomenon, and the potential-slip parametric combinations leading to such profiles can be easily identified by the conditions for minimal transport enhancement reported in recent literature. When separating out the slow diffuser or crossover phenomenon is desired, we recommend incorporating significant asymmetry in the surface potential and apparent slip boundary conditions such that the operating frequency and flow oscillation amplitude may be lowered to more practical values. Our results also agree with and strengthen the physical picture for explaining crossover phenomenon in macroscopic pressure-driven oscillatory flows.     

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.     

Simultaneous estimation of zeta potential and slip coefficient in hydrophobic microchannels

Electroosmotic flows through hydrophobic microchannels experience velocity slip at the channel wall, which increases the volumetric flow rate at a given electric potential gradient. The conventional method of zeta potential estimation using the volumetric flow rate may yield quite inaccurate zeta potential unless the velocity slip is appropriately taken care of. In the present investigation we develop a method for simultaneous estimation of zeta potential and velocity slip coefficient in the electroosmotic flow through a hydrophobic microchannel using velocity measurements. The relevant inverse problem is solved through the minimization of a performance function utilizing a conjugate gradient method. The present method is found to estimate the zeta potential and slip coefficient accurately even with noisy velocity measurements.     

Flow behavior of periodical electroosmosis in microchannel for biochips

This paper presents an analytical solution for periodical electroosmotic flows in two-dimensional uniform microchannel based on Poisson-Boltzmann equations for electric double layer (EDL) and Navier-Stokes equation for incompressible viscous fluid. Analytical results indicate that the velocity of periodical electroosmosis strongly depends on Reynolds number Re=omegah(2)/nu, as well as on EDL properties and applied electric field. Slip velocity of EDL decreases as the Reynolds number increases. Electroosmotic velocity outside the EDL decreases, and lag phase angle of velocity increases as distance away from the channel wall increases. A wavelike velocity profile across the channel is found. An asymptotic solution for low Reynolds number is given in this paper. Periodical electroosmosis with low Reynolds has same velocity amplitude and a pluglike velocity profile as that of steady electroosmosis. Based on Debye-Hückel approximation, this paper also obtains a solution of periodical electroosmosis applicable to cases where the thickness of EDL is of the same order as half of channel width.     

Electrokinetic-vortex formation near a two-part cylinder with same-sign zeta potentials in a straight microchannel

Vortex formation near a two-part cylinder with zeta potentials of different values but the same sign under an external DC electric field is numerically investigated in this paper. The cylinder, inserted in a straight microchannel filled with an aqueous solution, is composed of an upstream part and a downstream part. When a DC electric field is applied in the channel, under certain conditions, the vortex will form near the cylinder due to the different velocities of electroosmotic flow generated on the cylinder surface. The numerical results reveal that the larger the velocity difference of electroosmotic flow generated on the two-part cylinder and the smaller the channel width, the more conducive to vortex formation in the channel. In addition, if the zeta potential ratios of cylinder downstream part to upstream part and channel wall to cylinder upstream part are unchanged, the DC electric field strength and the zeta potential value do not affect the pattern of vortices formed in the channel. This study provides a way for vortex formation in microchannels and has the potential application in microfluidic devices.     

Electrokinetic mixing vortices due to electrolyte depletion at microchannel junctions

Due to electric field leakage across sharp corners, the irrotational character of Ohmic electroosmotic flow is violated. Instead, we demonstrate experimentally and theoretically evidence of electrolyte depletion and vortex separation in electroosmotic flow around a junction between wide and narrow channels. When the penetration length of the electric field exceeds the width of the narrow channel and if the electric field is directed from the narrow to the wide channel, the electromigration of ions diminishes significantly at the junction end of the narrow channel due to this leakage. Concentration depletion then develops at that location to maintain current balance but it also increases the corner zeta potential and the local electroosmotic slip velocity. A back pressure gradient hence appears to maintain flow balance and, at a sufficient magnitude, generates a pair of vortices.     

Eddies in a bottleneck: an arbitrary Debye length theory for capillary electroosmosis

Using an applied electrical field to drive fluid flows becomes desirable as channels become smaller. Although most discussions of electroosmosis treat the case of thin Debye layers, here electroosmotic flow (EOF) through a constricted cylinder is presented for arbitrary Debye lengths (kappa(-1)) using a long wavelength perturbation of the cylinder radius. The analysis uses the approximation of small potentials. The varying diameter of the cylinder produces radially and axially varying effective electric fields, as well as an induced pressure gradient. We predict the existence of eddies for certain constricted geometries and propose the possibility of electrokinetic trapping in these regions. We also present a leading-order criterion which predicts central eddies in very narrow constrictions at the scale of the Debye length. Eddies can be found both in the center of the channel and along the perimeter, and the presence of the eddies is a consequence of the induced pressure gradient that accompanies electrically driven flow into a narrow constriction.     

Expressions for evaluating the possibility of slip at the liquid-solid interface in open tube capillary electrochromatography

In this work, expressions are constructed and solved that describe the velocity field of electroosmotic flow (EOF) in open tube capillary electrochromatography (CEC) systems when the possibility of having unequal tangential velocities at the liquid-solid interface is considered and a slip condition is employed as a boundary condition for the velocity of the EOF at the capillary wall. The coupled equations of hydrodynamics (momentum balance equation) and electrostatics (Poisson equation) are solved numerically in order to obtain the distribution of the velocity field as well as the value of the volumetric flow rate in the open tube. Also, expressions for the velocity field and the volumetric flow rate of the EOF are presented that are valid for certain electrolytic systems and for certain parameter values for which analytical solutions to the momentum balance and Poisson equations could be obtained. The results presented in this work indicate that having slip in the velocity of the EOF at the wall of the capillary could (i) substantially increase the electroosmotic velocity in the plug-flow region of the radial domain of the open capillary tube and (ii) increase the portion of the radial domain of the open capillary tube where the velocity of the EOF has a plug-flow profile, which in turn could increase the average velocity and volumetric flow rate of the EOF in the open capillary tube. Furthermore, the modeling approach and the results presented in this work indicate a method for experimentally evaluating the possibility of having slip in the velocity of the EOF at the capillary wall.     

Start‐up of electrophoresis of an arbitrarily oriented dielectric cylinder

An analytical study is presented for the transient electrophoretic response of a circular cylindrical particle to the step application of an electric field. The electric double layer adjacent to the particle surface is thin but finite compared with the radius of the particle. The time‐evolving electroosmotic velocity at the outer boundary of the double layer is utilized as a slip condition so that the transient momentum conservation equation for the bulk fluid flow is solved. Explicit formulas for the unsteady electrophoretic velocity of the particle are obtained for both axially and transversely applied electric fields, and can be linearly superimposed for an arbitrarily‐oriented applied field. If the cylindrical particle is neutrally buoyant in the suspending fluid, the transient electrophoretic velocity is independent of the orientation of the particle relative to the applied electric field and will be in the direction of the applied field. If the particle is different in density from the fluid, then the direction of electrophoresis will not coincide with that of the applied field until the steady state is attained. The growth of the electrophoretic mobility with the elapsed time for a cylindrical particle is substantially slower than for a spherical particle.     

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.     

Transient electroosmotic flow induced by AC electric field in micro-channel with patchwise surface heterogeneities

This paper investigates two-dimensional, time-dependent electroosmotic flow driven by an AC electric field via patchwise surface heterogeneities distributed along the micro-channel walls. The time-dependent flow fields through the micro-channel are simulated for various patchwise heterogeneous surface patterns using the backwards-Euler time stepping numerical method. Different heterogeneous surface patterns are found to create significantly different electrokinetic transport phenomena. The transient behavior characteristics of the generated electroosmotic flow are then discussed in terms of the influence of the patchwise surface heterogeneities, the direction of the applied AC electric field, and the velocity of the bulk flow. It is shown that the presence of oppositely charged surface heterogeneities on the micro-channel walls results in the formation of localized flow circulations within the bulk flow. These circulation regions grow and decay periodically in phase with the applied periodic AC electric field intensity. The location and rotational direction of the induced circulations are determined by the directions of the bulk flow velocity and the applied electric field.     

Continuous-Flow Nanoparticle Trapping Driven by Hybrid Electrokinetics in Microfluidics

We introduce herein an efficient microfluidic approach for continuous transport and localized collection of nanoparticles via hybrid electrokinetics, which delicately combines linear and nonlinear electrokinetics driven by a composite DC-biased AC voltage signal. The proposed technique utilizes a simple geometrical structure, in which one or a series of metal strips serving as floating electrode (FE) are attached to the substrate surface and arranged in parallel between a pair of coplanar driving electrodes (DE) in a straight microchannel. On application of a DC-biased AC electric field across the channel, nanoparticles can be transported continuously by DC bulk electroosmotic flow, and then trapped selectively onto the metal strips due to AC-field induced-charge electrokinetic (ICEK) phenomenon, which behaves as counter-rotating micro-vortices around the ideally polarizable surfaces of FE. Finite-element simulation is carried out by coupling the dual-frequency electric field, flow field and sample mass transfer in sequence, for guiding a practical design of the microfluidic nanoparticle concentrator. With the optimal device geometry, the actual performance of the technique is investigated with respect to DC bias, AC voltage amplitude, and field frequency by using both latex nanospheres (∼500 nm) and BSA molecules (∼10 nm). Our experimental observation indicates nanoparticles are always enriched into a narrow bright band on the surface of each FE, and a horizontal concentration gradient even emerges in the presence of multiple metal strips, which therefore permits localized analyte enrichment. The proposed trapping method is supposed to guide an elaborate design of flexible electrokinetic frameworks embedding FE for continuous-flow analyte manipulation in modern microfluidic systems.     

Diffusioosmosis of electrolyte solutions in a fine capillary slit

The steady diffusioosmotic flows of an electrolyte solution along a charged plane wall and in a capillary channel between two identical parallel charged plates generated by an imposed tangential concentration gradient are theoretically investigated. The plane walls may have either a constant surface potential or a constant surface charge density. The electrical double layers adjacent to the charged walls may have an arbitrary thickness and their electrostatic potential distributions are determined by the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the tangential direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as a function of the lateral position in a self-consistent way. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the wall, the properties of the electrolyte solution, and other relevant factors. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field and the relaxation effect in the double layer on the diffusioosmotic flow are found to be very significant.     

Electrophoresis of a colloidal sphere in a spherical cavity with arbitrary zeta potential distributions

An analytical study is presented for the quasi-steady electrophoretic motion of a dielectric sphere situated at the center of a spherical cavity when the surface potentials are arbitrarily nonuniform. The applied electric field is constant, and the electric double layers adjacent to the solid surfaces are assumed to be much thinner than the particle radius and the gap width between the surfaces. The presence of the cavity wall causes three basic effects on the particle velocity: (1) the local electric field on the particle surface is enhanced or reduced by the wall; (2) the wall increases the viscous retardation of the moving particle; and (3) a circulating electroosmotic flow of the suspending fluid exists because of the interaction between the electric field and the charged wall. The Laplace and Stokes equations are solved analytically for the electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the electrophoretic and angular velocities of the particle are obtained. To apply these formulas, one has to calculate only the monopole, dipole, and quadrupole moments of the zeta-potential distributions at the particle and cavity surfaces. It is found that the contribution from the electroosmotic flow developing from the interaction of the imposed electric field with the thin double layer adjacent to the cavity wall and the contribution from the wall-corrected electrophoretic driving force to the particle velocities can be superimposed as a result of the linearity of the problem.     

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.     

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

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

Analysis of electroosmotic flow of power-law fluids in a slit microchannel

Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity, and velocity distribution. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Calculations are performed to examine the effects of kappaH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.