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.     

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

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

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.     

Analysis of electroosmotic flow with step change in zeta potential

The term electroosmotic flow refers to the bulk flow of an aqueous solution induced by the application of the electric field to the zeta potential. The characteristics of EOF in a microchannel depend upon the nature of the zeta potential, i.e., whether it is uniform or nonuniform. In this study, the full Navier-Stokes equation and the Nernst-Planck equation are used to model the change in EOF characteristics that occur when a step change in zeta potential is applied. It is found that the thickness of the electrical double layer gradually increases downstream from the location at which the zeta potential is increased. The results indicate that a step change in zeta potential causes a significant variation in the velocity profile and in the pressure distribution.     

Numerical study of the vortex-induced electroosmotic mixing of non-Newtonian biofluids in a nonuniformly charged wavy microchannel: Effect of finite ion size

We propose a micromixer for obtaining better efficiency of vortex induced electroosmotic mixing of non-Newtonian bio-fluids at a relatively higher flow rate, which finds relevance in many biomedical and biological applications. To represent the rheology of non-Newtonian fluid, we consider the Carreau model in this study, while the applied electric field drives the constituent components in the micromixer. We show that the spatial variation of the applied field, triggered by the topological change of the bounding surfaces, upon interacting with the non-uniform surface potential gives rise to efficient mixing as realized by the formation of vortices in the proposed micromixer. Also, we show that the phase-lag between surface potential leads to the formation of asymmetric vortices. This behavior offers better mixing performance following the appearance of undulation on the flow pattern. Finally, we establish that the assumption of a point charge in the paradigm of electroosmotic mixing, which is not realistic as well, under-predicts the mixing efficiency at higher amplitude of the non-uniform zeta potential. The inferences of the present analysis may guide as a design tool for micromixer where rheological properties of the fluid and flow actuation parameters can be simultaneously tuned to obtain phenomenal enhancement in mixing efficiency.     

Modeling electroosmotic and pressure-driven flows in porous microfluidic devices: zeta potential and porosity changes near the channel walls

This work presents analytical solutions for both pressure-driven and electroosmotic flows in microchannels incorporating porous media. Solutions are based on a volume-averaged flow model using a scaling of the Navier-Stokes equations for fluid flow. The general model allows analysis of fluid flow in channels with porous regions bordering open regions and includes viscous forces, permitting consideration of porosity and zeta potential variations near channel walls. To obtain analytical solutions problems are constrained to the linearized Poisson-Boltzmann equation and a variation of Brinkman's equation [Appl. Sci. Res., Sect. A 1, 27 (1947); 1, 81 (1947)]. Cases include one continuous porous medium, two adjacent regions of different porosities, or one open channel adjacent to a porous region, and the porous material may have a different zeta potential than that of the channel walls. Solutions are described for two geometries, including flow between two parallel plates or in a cylinder. The model illustrates the relative importance of porosity and zeta potential in different regions of each channel.     

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.     

Manipulating particles in microfluidics by floating electrodes

Various particle manipulations including enrichment, movement, trapping, separation, and focusing by floating electrodes attached to the bottom wall of a straight microchannel under an imposed DC electric field have been experimentally demonstrated. In contrast to a dielectric microchannel possessing a nearly uniform surface charge (or ζ potential), the metal strip (floating electrode) is polarized under the imposed electric field, resulting in a nonuniform distribution of the induced surface charge with a zero net surface charge along the floating electrode's surface, and accordingly induced-charge electroosmotic flow near the metal strip. The induced induced-charge electroosmotic flow can be regulated by controlling the strength of the imposed electric field and affects both the hydrodynamic field and the particle's motion. By using a single floating electrode, charged particles could be locally concentrated in a section of the channel or in an end-reservoir and move toward either the anode or the cathode by controlling the strength of the imposed electric field. By using double floating electrodes, negatively charged particles could be concentrated between the floating electrodes, subsequently squeezed to a stream flowing in the center region of the microchannel toward the cathodic reservoir, which can be used to focus particles.     

Boundary effects on electrophoresis of a colloidal cylinder with a nonuniform zeta potential distribution

The electrophoretic motion of a long dielectric circular cylinder with a general angular distribution of its surface potential under a transversely imposed electric field in the vicinity of a large plane wall parallel to its axis is analyzed. The thickness of the electric double layers adjacent to the solid surfaces is assumed to be much smaller than the particle radius and the gap width between the surfaces, but the applied electric field can be either perpendicular or parallel to the plane wall. The presence of the confining 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 viscous retardation of the moving particle; (3) an electroosmotic flow of the suspending fluid may exist due to the interaction between the charged wall and the tangentially imposed electric field. Through the use of cylindrical bipolar coordinates, the Laplace and Stokes equations are solved analytically for the two-dimensional electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the quasisteady electrophoretic and angular velocities of the cylindrical particle are obtained. To apply these formulas, one has only to calculate the multipole moments of the zeta potential distribution at the particle surface. It is found that the existence of a plane wall near a nonuniformly charged particle can cause its translation or rotation which does not occur in an unbounded fluid with the same applied electric field.     

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.     

DC-biased AC-electrokinetics: a conductivity gradient driven fluid flow

This paper studies the principles of fluid flow manipulation based on DC-biased AC-electrokinetics. This method makes use of planar parallel electrodes in a microfluidic channel in contact with an electrolyte solution, with a DC biased AC electrical signal applied to the electrode pair. Due to the application of DC bias, incipient Faradaic electrolytic reactions take place resulting in an increase of the ionic content of the bulk solution. The ionic content was found to be dissimilar at the cathodic and anodic sides of the channel and a conductivity difference of approximately 10% was measured for 2 V(DC). Fluid flow is generated by the action of the DC biased AC electric signal acting on the transverse conductivity gradient generated across the microchannel. The induced flow in the form of vortex was characterized experimentally and the results substantiated theoretically. The velocity of the induced flow vortex under the employed experimental conditions was ~600 to 700 μm s(-1) which is faster than those obtained in conventional AC-electroosmosis and AC-electrothermal types of 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.     

Continuous microfluidic DNA and protein trapping and concentration by balancing transverse electrokinetic forces

Sample pre-concentration can be a critical element to improve sensitivity of integrated microchip assays. In this work a converging Y-inlet microfluidic channel with integrated coplanar electrodes was used to investigate transverse DNA and protein migration under uniform direct current (DC) electric fields to assess the ability to concentrate a sample prior to other enzymatic modifications or capillary electrophoretic separations. Employing a pressure-driven flow to perfuse the microchannel, negatively charged samples diluted in low and high ionic strength buffers were co-infused with a receiving buffer of the same ionic strength into a main daughter channel. Experimental results demonstrated that, depending of the buffer selection, different DNA migration and accumulation dynamics were seen. Charged analytes could traverse the channel width and accumulate at the positive bias electrode in a low electroosmotic mobility, high electrophoretic mobility, high ionic strength buffer or migrated towards an equilibrium position within the channel in a high electroosmotic mobility, high electrophoretic mobility, low ionic strength buffer. The various migration behaviours are the result of a balance between the electrophoretic force and a drag force induced by a recirculating electroosmotic flow generated across the channel width due to the bounding walls. Under continuous flow conditions, DNA samples were concentrated several-fold by balancing these transverse electrokinetic forces. The electrokinetic trapping technique presented here is a simple technique which could be expanded to concentrate or separate other analytes as a preconditioning step for downstream processes.     

Electroosmotic flow in a capillary annulus with high zeta potentials

The electroosmotic flow through an annulus is analyzed under the situation when the two cylindrical walls carry high zeta potentials. The analytical solutions for the electric potential profile and the electroosmotic flow field in the annulus are obtained by solving the Poisson-Boltzmann equation and the Stokes equation under an analytical scheme for the hyperbolic sine function. A mathematical expression for the average electroosmotic velocity is derived in a fashion similar to the Smoluchowski equation. Hence, a correction formula is introduced to modify the Smoluchowski equation, taking into account contributions due to the finite thickness of the electric double layer (EDL) and the geometry ratio-dependent correction. Specifically, under a circumstance when the two annular walls are oppositely charged, the flow direction can be determined from the sign of such correction formula, and there exists a zero-velocity plane inside the annulus. With the assumption of large electrokinetic diameters, the location of the zero-velocity plane can be estimated from the analytical expression for the velocity distribution. In addition, the characteristics of the electroosmotic flow through the annulus are discussed under the influences of the EDL parameters and geometric ratio of the inner radius to the outer radius of the annulus.     

Electrophoretic Motion of a Spherical Particle with a Thick Double Layer in Bounded Flows

The electrophoretic mobility of a spherical colloidal particle with low zeta potential near a solid charged boundary is calculated numerically for arbitrary values of the double layer thickness by a generalization of Teubner's method to the case of bounded flow. Three examples are considered: a sphere near a nonconducting planar wall with electric field parallel to the wall, near a perfectly conducting planar wall with electric field perpendicular to the wall, and on the axis of a cylindrical pore with electric field parallel to the axis. The results are compared with recent analytical calculations using the method of reflections. For the case of a charged sphere near a neutral surface, the reflection results are quite good, provided there is no double layer overlap, in which case there can be extra effects for constant potential particles that are entirely missed by the analytical expressions. For a neutral sphere near a charged surface, the reflection results are less successful. The main reason is that the particle feels the profile of the electroosmotic flow, an effect ignored by construction in the method of reflections. The general case is a combination of these, so that the reflections are more reliable when the electrophoretic motion dominates the electroosmotic flow. The effect on particle mobility of particle-wall interactions follows the trend expected on geometric grounds in that sphere-plane interactions are stronger than sphere-sphere interactions and the effect on a sphere in a cylindrical pore is stronger still. In the latter case, particle mobility can fall by more than 50% for thick double layers and a sphere half the diameter of the pore. The agreement between numerical results and analytical results follows the same trend, being worst for the sphere in a pore. Nevertheless, the reflections can be reliable for some geometries if there is no double layer overlap. This is demonstrated for a specific example where reflection results have previously been compared with experiments on protein mobility through a membrane (J. Ennis et al., 1996, J. Membrane Sci. 119, 47). Copyright 1999 Academic Press.     

The Optimal Control of Geometry and Voltage Parameters on Electrokinetic Transport to Avoid Sample Leakage in Microfluidic Chips

Computer simulation is used to investigate sample transport phenomena of cross microfluidic chips. In this study, Kirchhoff circuit theory is employed to calculate the electric field strength and approximate electroosmotic flow. It is apparent from the results that both the simulation and the theoretical data show similar trends in the electroosmosis of cross microchips. The main target in this study is to summarize the optimal controlling parameter values for avoiding sample leakage in the transport process. The effects of the applied voltage ratio, the geometry ratio and the zeta potential were simulated using a computational fluid dynamics and multiphysics solver software package (CFD-ACE+). Under our designed conditions, two major conclusions were reached: (1) for high-voltage ratios, the sample leakage can be avoided as the geometry ratio is large enough at 0.5 or greater, and (2) for small geometries, maintaining a smaller voltage ratio, 0.3 or less, is essential for avoiding sample leakage. The key is to govern the sample velocity in the upstream faster than that in the downstream. Although real experimental conditions can be further fine tuned under microscopy monitoring, these conclusions are helpful to design the proper channel geometry and set up suitable voltage parameters to avoid sample leakages in one cross-channel chip.     

3-D transient electrophoretic motion of a spherical particle in a T-shaped rectangular microchannel

This paper considers the electrophoretic motion of a spherical particle in an aqueous electrolyte solution in a T-shaped rectangular microchannel, where the size of the channel is close to that of the particle. This is a complicated transient process where the electric field, the flow field, and the particle motion are coupled together. A theoretical model was developed to investigate the influences of the applied electric potentials, the zeta potentials of the channel and the particle, and the size of the particle on the particle motion. A direct numerical simulation method using the finite element method is employed. This method employs a generalized Galerkin finite element formulation that incorporates both equations of the fluid flow and equations of the particle motion into a single variational equation where the hydrodynamic interactions are eliminated. The ALE method is used to track the surface of the particle at each time step. The numerical results show that the electric field in the T-shaped microchannel is influenced by the presence of the particle, and that the particle motion is influenced by the applied electric potentials and the zeta potentials of the channel and the particle. The path of the particle motion is dominated by the local electric field and the ratio of the zeta potential of the channel to that of the particle. The particle's velocity is also dependent on its size in a small channel.     

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.     

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.