Particle handling in straight microfluidic channels via opposing electroosmotic and pressure-driven flows

The current study presents a method for producing recirculation zones in a straight microchannel using opposing pressure-driven and electrokinetically driven flows. The interaction of these two flow streams causes flow recirculation structures, which restricts the flow passage within the microchannel and causes a nozzle-like effect, thereby increasing the separation distance between particles in the fluid stream. Theoretical and experimental investigations are performed to investigate the effects of the applied electrical field intensity on the flow recirculation size, and the nozzle-like effect, respectively. In general, the results confirm that the proposed approach provides an effective means of achieving particle acceleration and separation distance within straight microchannels, and therefore provides a viable technique for improving particle manipulation and optical detection in conventional microfluidic devices. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Effect of finite reservoir size on electroosmotic flow in microchannels

In electrokinetically driven microfluidic applications, reservoirs are indispensable and have finite sizes. During operation processes, as the liquid level in reservoirs keeps changing as time elapses, a backpressure is generated. Thus, the flow in microfluidic channels actually exhibits a combination of the electroosmotic flow and the time-dependent induced backpressure-driven flow. In this paper, a model is presented to describe the effect of the finite reservoir size on electroosmotic flow in a rectangular microchannel. Important parameters that describe the effect of finite reservoir size on flow characteristics are discussed. A new concept termed as “effective pumping period” is introduced to characterize the reservoir size effect. The proposed model identifies the mechanisms of the finite-reservoir size effects and is verified by experiment using the micro-PIV technique. The results reported in this study can be used for facilitating the design of microfluidic devices.     

Effects of molecular level surface roughness on electroosmotic flow

Electroosmotic flow is widely used to transport and mix fluids in micro- and nanofluidic systems. Though essentially all surfaces exhibit certain degrees of roughness, the effects of surface roughness on electroosmotic flow is not well-understood. In this paper, we investigate how the electrical double layer and electroosmotic flow are affected by molecular level surface roughness by using molecular dynamics simulations. The simulation results indicate that, when the thickness of the electrical double layer is comparable to the height of surface roughness, presence of sub-nanometer deep concave regions on a rough surface can alter the electrical double layer near the surface, and reduce the electroosmotic flow significantly.     

Electrokinetically driven flow mixing utilizing chaotic electric fields

This paper presents a novel microfluidic mixing scheme in which the species streams are mixed via the application of chaotic electric fields to four electrodes mounted on the upper and lower surfaces of the mixing chamber. Numerical simulations are performed to analyze the effects of the resulting chaotic electrokinetic driving forces on the fluid flow characteristics within the micromixer and the corresponding mixing performance. During simulation, chaotic oscillating electric potentials are derived using a Duffing–Holmes chaos system. Simulation results indicate that the chaotic electrokinetic driving forces induce a complex flow behavior within the micromixer which results in efficient mixing of the two species streams. It is shown that mixing efficiencies up to 95% can be obtained in the novel micromixer.     

Experimental characterization of the temperature dependence of zeta potential and its effect on electroosmotic flow velocity in microchannels

This study attempts to characterize the influence of temperature on zeta potential for a number of commonly used buffers in both poly(dimethylsiloxane) (PDMS):glass and PDMS:PDMS microchannels. The study is motivated by the apparent inability of the Smoluchowski equation for electroosmotic flow (EOF) velocity, U = [ε ₀ ε _r ζ/μ]E _z , to accurately predict EOF velocities at elevated temperatures. Error can result if zeta potential (ζ) is taken to be constant, even if permittivity (ε) and viscosity (μ) are treated as temperature-dependent variables. In some cases, velocity may be underestimated by more than 30%. In this study, the time-interval current-monitoring method was used to measure zeta potential. A hotplate maintained precise channel temperatures and applied electric field strengths were selected so that Joule heating was negligible. Results show that in some solutions (e.g., KCl, TBE), the zeta potential can exhibit a strong dependence on temperature, changing by as much as 50% over a span of 60°C. This influence was found to increase with solution concentration. Other buffers (e.g., TE, Na₂CO₃/NaHCO₃) were stable over all measured temperatures.     

Fabrication and electroosmotic flow measurements in micro- and nanofluidic channels

An easy method for fabricating micro- and nanofluidic channels, entirely made of a thermally grown silicon dioxide is presented. The nanochannels are up to 1-mm long and have widths and heights down to 200 nm, whereas the microfluidic channels are 20-μm wide and 4.8-μm high. The nanochannels are created at the interface of two silicon wafers. Their fabrication is based on the expansion of growing silicon dioxide and the corresponding reduction in channel cross-section. The embedded silicon dioxide channels were released and are partially freestanding. The transparent and hydrophilic silicon dioxide channel system could be spontaneously filled with aqueous, fluorescent solution. The electrical resistances of the micro- and nanofluidic channel segments were calculated and the found values were confirmed by current measurements. Electrical field strengths up to 600 V/cm were reached within the nanochannels when applying a potential of only 10 V. Electroosmotic flow (EOF) measurements through micro- and nanofluidic channel systems resulted in electroosmotic mobilities in the same order of those encountered in regular, fused silica capillaries.     

Numerical simulation of flow through microchannels with designed roughness

A three-dimensional numerical simulation of flow through serpentine microchannels with designed roughness in form of obstructions placed along the channels walls is conducted here. CFD-ACE+ is used for the numerical simulations. The effect of the roughness height (surface roughness), geometry, Reynolds number on the friction factor is investigated. It is found that the friction factor increases in a nonlinear fashion with the increase in obstruction height. The friction factor is more for rectangular and triangular obstructions and it decreases as the obstruction geometry is changed to trapezoidal. It is observed that the obstruction geometry, i.e., aspect ratio plays an important role in prediction of friction factor in rough channels. It is also found that the pressure drop decreases with the increase in the roughness pitch. Hence, the roughness pitch is an important design parameter for microchannels.     

Analysis of electroosmotic flow in a microchannel packed with microspheres

The electroosmotic flow in a microchannel packed with microspheres under both direct and alternating electric fields is analyzed. In the case of the steady DC electroosmosis in a packed microchannel, the so-called capillary model is used, in which it is assumed that a porous medium is equivalent to a series of intertwined tubules. The interstitial tubular velocity is obtained by analytically solving the Navier–Stokes equation and the complete Poisson–Boltzmann equation. Then, using the volume-averaging method, the solution for the electroosmotic flow in a single charged cylindrical tubule is applied to estimate the electroosmosis in the overall porous media by introducing the porosity and tortuosity. Assuming uniform porosity, an exact solution accounting for the electrokinetic wall effect is obtained by solving the modified Brinkman momentum equation. For the electroosmotic flow under alternating electric fields in a cylindrical microchannel packed with microspheres of uniform size, two different conditions regarding the openness of the channel ends are considered. Based on the capillary model, the time-periodic oscillating electroosmotic flow in an open-ended microchannel in response to the application of an alternating electric field is obtained using the Greens function approach to the Navier–Stokes equation. When the two ends of the channel are closed, a backpressure is induced to generate a counter flow, resulting in a new zero flow rate. Such induced backpressure associated with the counter flow in a closed-end microchannel is obtained analytically by solving the transient modified Brinkman momentum equation.     

Mesoscopic simulations of electroosmotic flow and electrophoresis in nanochannels

We review recent dissipative particle dynamics (DPD) simulations of electrolyte flow in nanochannels. A method is presented by which the slip length δB at the channel boundaries can be tuned systematically from negative to infinity by introducing suitably adjusted wall-fluid friction forces. Using this method, we study electroosmotic flow (EOF) in nanochannels for varying surface slip conditions and fluids of different ionic strength. Analytic expressions for the flow profiles are derived from the Stokes equation, which are in good agreement with the numerical results. Finally, we investigate the influence of EOF on the effective mobility of polyelectrolytes in nanochannels. The relevant quantity characterizing the effect of slippage is found to be the dimensionless quantity κδB, where 1/κ is an effective electrostatic screening length at the channel boundaries.     

Effects of applied electric field and microchannel wetted perimeter on electroosmotic velocity

Parameters which affect electroosmotic flow (EOF) behavior need to be determined for characterizing flow in miniature biological and chemical experimental processes. Several parameters like buffer pH, ionic concentration, applied electric field and channel dimensions influence the magnitude of the electroosmotic flow. We conducted numerical and experimental investigations to determine the impact of electric field strength and wetted microchannel perimeter on EOF in straight microchannels of rectangular cross-section. Deviation from theoretical behavior was also investigated. In the numerical model, we solved the continuity and Navier–Stokes equations for the fluid flow and the Gauss law equation for the electric field. Computational results were validated against experimental data for PDMS-glass channels of different wetted perimeters over a range of applied electric fields. Results show that increasing the applied electric field at constant wetted perimeter caused the electroosmotic mobility, the ratio of electroosmotic velocity to applied electric field, to increase nonlinearly. It was also found that increasing the wetted perimeter at constant applied electric field decreased the electroosmotic flow. These findings will be useful in determining the optimum value of the electric field required to produce a desired electroosmotic flow rate in a channel of a particular dimension. Alternately, these will also be useful in determining the optimum channel dimensions to provide a desired electroosmotic flow rate at a specified value of the electric field.     

Liquid flow through microchannels with grooved walls under wetting and superhydrophobic conditions

Recent developments in superhydrophobic surfaces have enabled significant reduction in the frictional drag for liquid flow through microchannels. There is an apparent risk when using such surfaces, however, that under some conditions the liquid meniscus may destabilize and, consequently, the liquid will wet the entire patterned surface. This paper presents analytical and experimental results that compare the laminar flow dynamics through microchannels with superhydrophobic walls featuring ribs and cavities oriented both parallel and transverse to the direction of flow under both wetting and non-wetting conditions. The results show the reduction in the total frictional resistance is much greater in channels when the liquid phase does not enter the cavity regions. Further, it is demonstrated that the wetting and non-wetting cavity results represent limiting cases between which the experimental data lie. Generalized expressions enabling prediction of the classical friction factor-Reynolds number product as a function of the relevant governing dimensionless parameters are also presented for both the superhydrophobic and wetting states. Experimental results are presented for a range of parameters in the laminar flow regime.     

Comprehensive model of electrokinetic flow and migration in microchannels with conductivity gradients

A comprehensive model of electrokinetic flow and transport of electrolytes in microchannels with conductivity gradients is developed. The electrical potential is modeled by a combination of an electrostatic and an electrodynamic approach. The fluid dynamics are described by the Navier–Stokes equations, extended by an electrical force term. The chemistry of the system is represented by source terms in the mass transport equations, derived from an equilibrium approach. Moreover, the interaction between ionic species concentration and physicochemical properties of the microchannel substrate (i.e. zeta-potential) is taken into consideration by an empirical approach. Approximate analytical solutions for all variables are found which are valid within the electrical double layer. By using the method of matched asymptotic expansions, these solutions provide boundary conditions for the numerical simulation of the bulk liquid. The models are implemented in a Finite-Element-Code. As an example, simulations of an electrophoretic injection/separation process in a micro-electrophoresis device are performed. The results of the simulations show the strong coupling between the involved physicochemical phenomena. Simulations with a constant and a concentration-depend zeta-potential clarify the importance of a proper modeling of the physicochemical substrate characteristics.     

A reduced-order model of the low-voltage cascade electroosmotic micropump

In the present investigation, we have derived an efficient reduced-order model of the low-voltage cascade electroosmotic micropump. This model can be combined with the equivalent circuit model of straight microchannels to construct a complete model for a microfluidic device, which can be employed to implement modern control schemes. To demonstrate the efficiency of the reduced-order model we employ it to estimate the zeta potentials of many subchannels in the micropump cascade using velocity measurements, which is a preliminary step to the implementation of modern control schemes. It is found that a conjugate gradient procedure employing the reduced-order model estimates accurately the zeta potential variation in the subchannels, which may be caused by adhesion of biomolecules, even with noisy velocity measurements.     

Dissipative particle dynamics simulations of electroosmotic flow in nano-fluidic devices

When modeling the hydrodynamics of nanofluidic systems, it is often essential to include molecular-level information such as molecular fluctuations. To this effect, we present a mesoscopic approach which combines a fluctuating hydrodynamics formulation with an efficient implementation of Electroosmotic flow (EOF) in the small Debye length limit. The resulting approach, whose major ingredient is Dissipative Particle Dynamics, is sufficiently coarse-grained to allow efficient simulation of the hydrodynamics of micro/nanofluidic devices of sizes that are too large to be simulated by ab initio methods such as Molecular Dynamics. Within our formulation, EOF is efficiently generated using the recently proven similitude between velocity and electric field under appropriate conditions. More specifically, EOF is generated using an effective boundary condition, akin to a moving wall, thus avoiding evaluation of the computationally expensive electrostatic forces. Our method is used for simulating EOFs and DNA molecular sieving in simple and complex two-dimensional (2D) and 3D geometries frequently used in nano-fluidic devices. The numerical data obtained from our model are in very good agreement with theoretical results.     

One-dimensional axial simulation of electric double layer overlap effects in devices combining micro- and nanochannels

This paper presents a numerical steady-state model of ion transport in micro- and nanofluidic devices with widely varying geometric scale, such as transitions between micro- and nanochannels. Finite element or finite volume simulation of such problems is challenging, due to the number of elements needed to produce a satisfactory mesh. Here, only the lengthwise channel dimension is meshed; standard analytical approximations are used to incorporate cross-channel properties. Singularly perturbed cases are built up by continuation. The method is shown to reproduce our previously reported measurements of electric double-layer effects on conductivity, ion concentration, and ion enhancement and depletion. Comparison with 2-D simulations reported in the literature shows that effects on accuracy due to the 1-D approximation are small. The model incorporates analytical models of surface charge density taken from the literature. This enables predictive simulation with reasonable accuracy using published parameter values, or these values may be tuned based on experiment to give improved results. Use of the model for iterative design and parameter estimation is demonstrated.     

Electrohydrodynamics around single ion-permselective glass beads fixed in a microfluidic device

This work demonstrates by direct visualization using confocal laser scanning microscopy that the application of electrical fields to a single-fixed, ion-permselective glass bead produces a remarkable complexity in both the coupled mass and charge transport through the bead and the coupled electrokinetics and hydrodynamics in the adjoining bulk electrolyte. The visualization approach enables the acquisition of a wealth of information, forming the basis for a detailed analysis of the underlying effects (e.g., ion-permselectivity, concentration polarization, nonequilibrium electroosmotic slip) and an understanding of electrohydrodynamic phenomena at charge-selective interfaces under more general conditions. The device used for fixing single beads in a microfluidic channel is flexible and allows to investigate the electrohydrodynamics in both transient and stationary regimes under the influence of bead shape, pore size and surface charge density, mobile phase composition, and applied volume forces. This insight is relevant for the design of microfluidic/nanofluidic interconnections and addresses the ionic conductance of discrete nanochannels, as well as nanoporous separation and preconcentration units contained as hybrid configurations, membranes, packed beds, or monoliths in lab-on-a-chip devices.     

Numerical analysis on electroosmotic flows in a microchannel with rectangle-waved surface roughness using the Poisson–Nernst–Planck model

The present study has numerically investigated two-dimensional electroosmotic flows in a microchannel with dielectric walls of rectangle-waved surface roughness to understand the roughness effect. For the study, numerical simulations are performed by employing the Nernst–Planck equation for the ionic species and the Poisson equation for the electric potential, together with the traditional Navier–Stokes equation. Results show that the steady electroosmotic flow and ionic-species transport in a microscale channel are well predicted by the Poisson–Nernst–Planck model and depend significantly on the shape of surface roughness such as the amplitude and periodic length of wall wave. It is found that the fluid flows along the surface of waved wall without involving any flow separation because of the very strong normal component of EDL (electric double layer) electric field. The flow rate decreases exponentially with the amplitude of wall wave, whereas it increases linearly with the periodic length. It is mainly due to the fact that the external electric-potential distribution plays a crucial role in driving the electroosmotic flow through a microscale channel with surface roughness. Finally, the present results using the Poisson–Nernst–Planck model are compared with those using the traditional Poisson–Boltzmann model which may be valid in these scales.     

Application of continuum mechanics to fluid flow in nanochannels

A fundamental understanding of the transport phenomena in nanofluidic channels is critical for systematic design and precise control of such miniaturized devices towards the integration and automation of Lab-on-a-chip devices. The goal of this study is to develop a theoretical model of electroosmotic flow in nano channels to gain a better understanding of transport phenomena in nanofluidic channels. Instead of using the Boltzmann distribution, the conservation condition of ion number and the Nernst equation are used in this new model to find the ionic concentration field of an electrolyte solution in nano channels. Correct boundary conditions for the potential field at the center of the nanochannel and the concentration field at the wall of the channel are developed and applied to this model. It is found that the traditional plug-like velocity profile is distorted in the center of the channel due to the presence of net charges in this region opposite to that in the electrical double layer region. The developed model predicted a trend similar to that observed in experiments reported in the literature for the area-average velocity versus the ratio of Debye length to the channel height.     

Electroosmotic flows in an electric double layer overlapped channel with rectangle-waved surface roughness

To further understand the wall-roughness effect, the present study has performed numerical simulations, by employing the Poisson–Nernst–Planck model, on the two-dimensional electroosmotic flow in a plane channel with dielectric walls of rectangle-waved surface roughness where the two electric double layers (EDLs) are overlapped. Results show that the steady electroosmotic flow and ionic-species transport depend significantly on the shape of the surface roughness such as the amplitude and periodic length of wall wave, but their characteristics are basically different from those in the case where the EDLs are not overlapped at all (Kang and Suh in Microfluid Nanofluid, doi:, 2008). It is found that the fluid flows over the waved wall (or wall roughness) with involving a separation or recirculation of flow in the cavity, which resembles much the traditional pressure-driven flow. In addition, the flow characteristics are determined chiefly by the level of the electric-charge density in the bulk region above the waved wall. As a result, with increasing wall-wave amplitude (0.01 ≤ h/H ≤ 0.2), the flow rate increases due to the enhanced amount of electric charges released from the enlarged wet surface at low amplitudes and then decreases due to the reduced flow-passage area at high amplitudes above a certain critical value. With increasing periodic length (0.2 ≤ L/H ≤ 1.2), on the other hand, the flow rate decreases in a hyperbolic fashion due to the reduced amount of electric charges.     

Rheometry of non-Newtonian electrokinetic flow in a microchannel T-junction

Two-dimensional finite element simulations of electrokinetic flow in a microchannel T-junction of a fluid with a Carreau-type nonlinear viscosity are presented. The motion of the electrical double layer at the channel walls is approximated by velocity wall slip boundary conditions. The fluid experiences a range of shear rates as it turns the corner, and the flow field is shown to be sensitive to the non-Newtonian characteristics of the Carreau model. A one-to-one mapping between the Carreau parameters and the end wall pressure is demonstrated through statistical analysis of the pressure profile for a broad range of physical and operating parameters. Such a mapping allows the determination of the Carreau parameters of an unknown fluid if the end wall pressure profile is known; thus a highly efficient viscometric device may be constructed. A graphical technique to show that the inverse problem is well posed is shown, and a method for solving the inverse problem is presented. The challenges that must be overcome before a practical device can be constructed are discussed.