Streaming potential and electroosmotic flow in heterogeneous circular microchannels with nonuniform zeta potentials: requirements of flow rate and current continuities

Real surfaces are typically heterogeneous, and microchannels with heterogeneous surfaces are commonly found due to fabrication defects, material impurities, and chemical adsorption from solution. Such surface heterogeneity causes a nonuniform surface potential along the microchannel. Other than surface heterogeneity, one could also pattern the various surface potentials along the microchannels. To understand how such variations affect electrokinetic flow, we proposed a model to describe its behavior in circular microchannels with nonuniform surface potentials. Unlike other models, we considered the continuities of flow rate and electric current simultaneously. These requirements cause a nonuniform electric field distribution and pressure gradient along the channel for both pressure-driven flow (streaming potential) and electric-field-driven flow (electroosmosis). The induced nonuniform pressure and electric field influence the electrokinetic flow in terms of the velocity profile, the flow rate, and the streaming potential.     

On the surface conductance, flow rate, and current continuities of microfluidics with nonuniform surface potentials

The characteristics of electrokinetic flow in a microchannel depend on both the nature of surface potentials, that is, whether it is uniform or nonuniform, and the electrical potential distribution along the channel. In this paper, the nonlinear Poisson-Boltzmann equation is used to model the electrical double layer and the lattice Boltzmann model coupled with the constraint of current continuity is used to simulate the microfluidic flow field in a rectangular microchannel with a step variation of surface potentials. This current continuity, including surface conduction, convection, and bulk conduction currents, has often been neglected in the literature for electroosmotic flow with nonuniform (heterogeneous) microchannels. Results show that step variation of ion distribution caused by step variation surface potential will influence significantly the electrical potential distribution along the channel and volumetric flow rate. For the system considered, we showed that the volumetric flow rate could have been overestimated by as much as 70% without consideration of the current continuity constraint.     

Electrokinetically-driven flow mixing in microchannels with wavy surface

This paper investigates the mixing characteristics of electrokinetically-driven flow in microchannels with different wavy surface configurations. Numerical simulations are performed to analyze the influence of the wave amplitude and the length of the wavy section on the mixing efficiency within the microchannel. Typically, straight channels have a poor mixing performance because the fluid flow is restricted to the low Reynolds number regime, and hence mixing takes place primarily as a result of diffusion effects. However, the wavy surfaces employed in the current microchannels increase the interfacial contact area between the two species in the microchannel and therefore improve the mixing efficiency. The mixing performance is further enhanced by the application of a heterogeneous charge pattern on the wavy surfaces. The numerical results show that the heterogeneous charge pattern generates flow circulations near the microchannel walls. These circulations are shown to provide an effective enhancement in the mixing performance. Overall, the present results show that the mixing performance is improved by increasing the magnitude of the heterogeneous surface zeta potential upon the wavy surface or by increasing the wave amplitude or the length of the wavy section in the microchannel.     

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.     

Influence of the three-dimensional heterogeneous roughness on electrokinetic transport in microchannels

Surface roughness has been considered as a passive means of enhancing species mixing in electroosmotic flow through microfluidic systems. It is highly desirable to understand the synergetic effect of three-dimensional (3D) roughness and surface heterogeneity on the electrokinetic flow through microchannels. In this study, we developed a three-dimensional finite-volume-based numerical model to simulate electroosmotic transport in a slit microchannel (formed between two parallel plates) with numerous heterogeneous prismatic roughness elements arranged symmetrically and asymmetrically on the microchannel walls. We consider that all 3D prismatic rough elements have the same surface charge or zeta potential, the substrate (the microchannel wall) surface has a different zeta potential. The results showed that the rough channel's geometry and the electroosmotic mobility ratio of the roughness elements' surface to that of the substrate, epsilon(mu), have a dramatic influence on the induced-pressure field, the electroosmotic flow patterns, and the electroosmotic flow rate in the heterogeneous rough microchannels. The associated sample-species transport presents a tidal-wave-like concentration field at the intersection between four neighboring rough elements under low epsilon(mu) values and has a concentration field similar to that of the smooth channels under high epsilon(mu) values.     

Electroosmotic flow in a microcavity with nonuniform surface charges

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

Unsteady electroosmosis in a microchannel with Poisson-Boltzmann charge distribution

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

Electrokinetic transport through nanochannels

This article presents a numerical study of the electrokinetic transport phenomena (electroosmosis and electrophoresis) in a three-dimensional nanochannel with a circular cross-section. Due to the nanometer dimensions, the Boltzmann distribution of the ions is not valid in the nanochannels. Therefore, the conventional theories of electrokinetic flow through the microchannels such as Poisson-Boltzmann equation and Helmholtz-Smoluchowski slip velocity approach are no longer applicable. In the current study, a set of coupled partial differential equations including Poisson-Nernst-Plank equation, Navier-Stokes, and continuity equations is solved to find the electric potential field, ionic concentration field, and the velocity field in the three-dimensional nanochannel. The effects of surface electric charge and the radius of nanochannel on the electric potential, liquid flow, and ionic transport are investigated. Unlike the microchannels, the electric potential field, ionic concentration field, and velocity field are strongly size-dependent in nanochannels. The electric potential gradient along the nanochannel also depends on the surface electric charge of the nanochannel. More counter ions than the coions are transported through the nanochannel. The ionic concentration enrichment at the entrance and the exit of the nanochannel is completely evident from the simulation results. The study also shows that the flow velocity in the nanochannel is higher when the surface electric charge is stronger or the radius of the nanochannel is larger.     

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

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

Numerical analysis of electroosmotic flow in dense regular and random arrays of impermeable, nonconducting spheres

We present a numerical scheme for analyzing steady-state isothermal electroosmotic flow (EOF) in three-dimensional random porous media, involving solution of the coupled Poisson, Nernst-Planck, and Navier-Stokes equations. While traditional finite-difference methods were used to resolve the Poisson-Nernst-Planck problem, the (electro)hydrodynamics has been addressed with high efficiency using the lattice-Boltzmann method. The developed model allows simulation of electrokinetic transport under most general conditions, including arbitrary value and distribution of electrokinetic potential at the solid-liquid interface, electrolyte composition, and pore space morphology. The approach provides quantitative information on a spatial distribution of simulated velocities. This feature was utilized to characterize EOF fields in regular and random, confined and bulk packings of hard (i.e., impermeable, nonconducting) spheres. Important aspects of pore space morphology (sphere size distribution), surface heterogeneity (mismatch in electrokinetic potentials at confining wall and sphere surface), and fluid phase properties (electrical double layer thickness) were investigated with respect to their influence on the EOF dynamics over microscopic and macroscopic spatial domains. Most important is the observation of a generally nonuniform pore-level EOF velocity profile in the sphere packings (even in the thin double layer limit) which is caused by pore space morphology and which is in contrast to the pluglike velocity distribution in a single, straight capillary under the same conditions.     

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.     

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.     

Numerical analysis of the thermal effect on electroosmotic flow and electrokinetic mass transport in microchannels

Joule heating is present in electrokinetically driven flow and mass transport in microfluidic systems. Nowadays, there is a trend of replacing costly glass-based microfluidic systems by the disposable, cheap polymer-based microfluidic systems. Due to poor thermal conductivity of polymer materials, the thermal management of the polymer-based microfluidic systems may become a problem. In this study, numerical analysis is presented for transient temperature development due to Joule heating and its effect on the electroosmotic flow (EOF) and mass species transport in microchannels. The proposed model includes the coupling Poisson-Boltzmann (P-B) equation, the modified Navier-Stokes (N-S) equations, the conjugate energy equation, and the mass species transport equation. The results show that the time development for both the electroosmotic flow field and the Joule heating induced temperature field are less than 1 s. The Joule heating induced temperature field is strongly dependent on channel size, electrolyte concentration, and applied electric field strength. The simulations reveal that the presence of the Joule heating can result in significantly different characteristics of the electroosmotic flow and electrokinetic mass transport in microchannels.     

Performance characterization of an insulator-based dielectrophoretic microdevice

Dielectrophoresis (DEP), the motion of particles in nonuniform electric fields, is a nondestructive electrokinetic (EK) transport mechanism can be used to concentrate and separate bioparticles. Traditionally, DEP has been performed employing microelectrodes, an approach that is expensive due to the cost of microelectrode fabrication. An alternative is insulator-based DEP (iDEP), an inexpensive method where nonuniform electric fields are created with arrays of insulating structures. This study presents the effects of operating conditions on the dielectrophoretic behavior of polystyrene microparticles under iDEP. Experiments were performed employing microchannels containing insulating structures that worked as insulators. The parameters varied were pH (8-9) and conductivity (25-100 microS/cm) of the bulk medium, and the magnitude of the applied field (200-850 V/cm). Optimal operating conditions in terms of pH and conductivity were obtained, and the microdevice performance was characterized in terms of concentration factor and minimum electric field required (minimum energy consumption). This is the first report on improving iDEP processes when EOF is present. DEP and EOF have been studied extensively, however, this study integrates the effect of suspending medium characteristics on both EK phenomena. These findings will allow improving the performance of iDEP microdevices achieving the highest concentration fold with the lowest energy consumption.     

Control of electroosmotic flow in laser-ablated and chemically modified hot imprinted poly(ethylene terephthalate glycol) microchannels

The fabrication of microchannels in poly(ethylene terephthalate glycol) (PETG) by laser ablation and the hot imprinting method is described. In addition, hot imprinted microchannels were hydrolyzed to yield additional charged organic functional groups on the imprinted surface. The charged groups are carboxylate moieties that were also used as a means for the further reaction of different chemical species on the surface of the PETG microchannels. The microchannels were characterized by fluorescence mapping and electroosmotic flow (EOF) measurements. Experimental results demonstrated that different fabrication and channel treatment protocols resulted in different EOF rates. Laser-ablated channels had similar EOF rates (5.3+/-0.3 x 10(-4) cm(2)/Vs and 5.6+/-0.4 x 10(-4) cm(2)/Vs) to hydrolyzed imprinted channels (5.1+/-0.4 x 10(-4) cm(2)/Vs), which in turn demonstrated a somewhat higher flow rate than imprinted PETG channels that were not hydrolyzed (3.5+/-0.3 x 10(-4) cm(2)/Vs). Laser-ablated channels that had been chemically modified to yield amines displayed an EOF rate of 3.38+/- 0.1 x 10(-4) cm(2)/Vs and hydrolyzed imprinted channels that had been chemically derivatized to yield amines showed an EOF rate of 2.67+/-0.6 cm(2)/Vs. These data demonstrate that surface-bound carboxylate species can be used as a template for further chemical reactions in addition to changing the EOF mobility within microchannels.     

Induced electrokinetic transport in micro-nanofluidic interconnect devices

Hybrid micro-nanofluidic interconnect devices can be used to control analyte transfer from one microchannel to the other through a nanochannel under rest, injection, and recovery stages of operation by varying the applied potential bias. Using numerical simulations based on coupled transient Poisson-Nernst-Planck and Stokes equations, we examine the electrokinetic transport in a gateable device consisting of two 100 microm long, 1 microm wide negatively charged microchannels connected by a 1 microm long, 10 nm wide positively charged nanochannel under both positive and negative bias potentials. During injection, accumulation of ions is observed at the micro-nano interface region with the positive potential and depletion of ions is observed at the other micro-nano junction region. Net space charge in the depletion region gives rise to nonlinear electrokinetic transport during the recovery stage due to induced pressure, induced electroosmotic flow of the second kind, and complex flow circulations. Ionic currents are computed as a function of time for both positive and negative bias potentials for the three stages. Analytical expressions derived for ion current variation are in agreement with the simulated results. In the presence of multiple accumulation or depletion regions, we show that a hybrid micro-nano device can be designed to function as a logic gate.     

Electroosmotic flow in poly(dimethylsiloxane) microchannels

This paper reports on the study of electroosmotic flow (EOF) in poly(dimethylsiloxane) (PDMS) microchannels on the basis of indirect amperometric detection method. Gradual increase of EOF rate in freshly prepared PDMS microchannels was observed with the running buffer of phosphate buffer solution (PBS). With the same concentration (10 mM) of PBS containing different cations and the same pH value (7.0) and, the time of the stable EOF in PDMS microchannels under the applied separation voltage of 1000 V was 49.8 s (Li+ -PBS), 57.1 s (Na+ -PBS), 91 s (K+ -PBS), respectively. Meanwhile, the different adsorption of cations (Li+, Na+ and K+) on hydrophobic PDMS wall was observed through their separation in PDMS microchannels. Such experimental results demonstrated that the EOF in PDMS microchannels came from the cations and anions adsorbed on PDMS wall. This study would not only help us understand the surface state of PDMS, but also provide a useful guidance for establishing the effective surface modification methods in PDMS microchip CE.     

Electrokinetic transport of red blood cells in microcapillaries

Electrokinetic flow of a suspension of erythrocytes (red blood cells, RBCs) in 20 num cylindrical fused-silica capillaries is examined in the present work. Flow direction anomalies are observed experimentally and tentatively explained by the development of a pH gradient between the cathode well and the anode well due to electrolysis reactions at the electrodes. This pH gradient alters the local zeta potentials of both the capillary and the RBC and thus the local electroendosmotic liquid flow (EOF) velocities and RBC electrophoretic (EP) velocities. The two velocities are opposite in direction but with EOF dominating such that the RBC moves toward the cathode, opposite to the anode migration observed in bulk conditions. The opposing zeta potentials also lead to RBC aggregation at the anode end for low fields less than 25 V/cm. As the electroendosmotic velocity decreases at the anode end due to decreasing pH, pressure-driven back flow develops to oppose the original EOF at the remaining portions of the capillary ensuring constant fluid flux. When the anode EOF velocity is smaller in magnitude than the EP velocity, reversal of blood cell transport is observed after a short transient time in which a pH gradient forms. RBC velocities and pH dependencies on electric field and MgCl(2) concentration are presented along with data showing the accumulation of charge separation across the capillary. Also, a short-term solution to the pH gradient formation is presented that could help thwart development of pH gradients in micro-devices at lower voltages.     

Studies of electroosmotic flow and the effects of protein adsorption in plasma‐polymerized microchannel surfaces

This paper presents a study of EOF properties of plasma‐polymerized microchannel surfaces and the effects of protein (fibrinogen and lysozyme) adsorption on the EOF behavior of the surface‐modified microchannels. Three plasma polymer surfaces, i.e. tetraglyme, acrylic acid and allylamine, are tested. Results indicate EOF suppression in all plasma‐coated channels compared with the uncoated glass microchannel surfaces. The EOF behaviors of the modified microchannels after exposure to protein solutions are also investigated and show that even low levels of protein adsorption can significantly influence EOF behavior, and in some cases, result in the reversal of flow. The results also highlight that EOF measurement can be used as a method for detecting the presence of proteins within microchannels at low surface coverage (<1 ng/cm² on glass). Critically, the results illustrate that the non‐fouling tetraglyme plasma polymer is able to sustain EOF. Comparison of the plasma‐polymerized surfaces with conventionally grafted polyelectrolyte surfaces demonstrates the stabilities of the plasma polymer films, enabling multiple EOF runs over 3 days without deterioration in performance. The results of this study clearly demonstrate that plasma polymers enable the surface chemistry of microfluidic devices to be tailored for specific applications. Critically, the deposition of the non‐fouling tetraglyme coating enables stable EOF to be induced in the presence of protein.     

Analytical treatment of electrokinetic microfluidics in hydrophobic microchannels

Microfluidics in microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) devices is complex due to the large surface area to volume ratio. Thus, surface properties play an important role in flow behavior. In this paper, we summarize the effects of electric double layer and surface hydrophobicity of rectangular microchannels on time-dependent electrokinetic flow. Theoretically, we have shown that flow resistance can, in principal, be significantly reduced so that a larger flow rate can be obtained for pressure-driven flow or electric-field-driven flow. This relies on the ability to change surface charges and surface hydrophobicity independently. Our theoretical results provide guidelines for the design and operation of microfluidic flow in rectangular microchannels. Because of liquid slippage, zeta potential determination by traditional method could be overestimated. Taking into account the effect of hydrophobicity, a modified method is proposed to determine the zeta potential and slip coefficient for parallel-plate microchannels with hydrophobic surfaces.