Broadening of neutral analyte band in electroosmotic flow through slit channel with different zeta potentials of the walls

The study is concerned with addressing hydrodynamic dispersion of an electroneutral non-adsorbed solute being transported by electroosmotic flow through a slit channel formed by walls with different zeta potentials. The analysis is conducted in terms of the plate height which, using the Van Deemter equation, can be expressed through the cross-sectional mean flow velocity, the solute molecular diffusion coefficient and a length scale parameter having meaning of the minimum achievable plate height and depending on the velocity distribution within the channel cross-section. The minimum plate height is determined by substituting distribution of electroosmotic velocity into the preliminary derived integral expression that is valid for any given velocity distribution within a slit channel cross-section. The electroosmotic velocity distribution within the slit channel cross-section is obtained by solving one-dimensional version of the Stokes equation accounting for electric force exerted on the local equilibrium electric space charge. The major obtained result is an analytical expression which represents the minimum plate height normalized by half of channel width as a function of two dimensionless parameters, namely, half of channel width normalized by the Debye length, and the ratio of the wall zeta potentials. The obtained result reveals a substantial increase in the minimum plate height compared with the case of equal wall zeta potentials. Different limiting cases of the obtained relationships are analyzed and possible applications are discussed.     

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.     

Solute dispersion in oscillating electro-osmotic flow with boundary mass exchange

Mass transfer in an oscillatory electro-osmotic flow (EOF) is theoretically studied, for the case of a cylindrical tube with a reactive wall. An expression for the dispersion coefficient, reflecting the time-averaged mass flux of an electrically neutral solute, is derived analytically. Under the influence of a reversible solute-wall mass exchange, the dispersion coefficient exhibits a complex dependence on the various parameters representing the effects of the electric double-layer thickness, oscillation frequency, solution transport properties, solute partitioning, and reaction kinetics. Our results suggest that, in the presence of a reversible mass exchange at the wall, an oscillatory EOF may be used for separation of species. It is found that optimal conditions for separation are achieved for a thin double-layer, where an inert solute, or one with slow exchange kinetics, experiences virtually no dispersion while the dispersion is maximized for the reactive solute exhibiting fast kinetics.     

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.     

Bubble-free electrokinetic pumping

Bubble-free electroosmotic flow (fr-EOF) of aqueous electrolytes in microfluidic channels with integrated electrodes is demonstrated. Undesirable electrolytic bubble formation is avoided by applying a periodic, zero net charge current to generate a nonzero average potential between the electrodes. Electrokinetic pressure generated in this active segment of the microchannel drives now upstream and downstream where electric field is absent. Flow rates commensurate with theoretical predictions for EOF driven by a dc voltage equivalent to the average net potential have been measured. By significantly reducing driving potentials and liquid exposure time to strong electric fields, fr-EOF opens the way for fully integrated, versatile micro total analysis systems (/spl mu/TAS).     

Induced mixing electrokinetics in a charged corrugated nano-channel: towards a controlled ionic transport

To perform a fluid analysis for electroosmotic flows in micro- and nano-channels, it is necessary to mix various fluid contents in micro- and nano-scales. It is observed that fluids in electroosmotic flow exhibits Reynolds number effect as the flow exerts very weak inertial force and it requires long channel for mixing of different layers and species through diffusion process. Hence, if the desired length scale of mixing is large, an enormous time is needed for the molecules to be thoroughly mixed by diffusion. The theory of dynamic equations on time scale is used to study the stability of these systems. It is found that such a system may exhibits an unstable nature for overlapping electric double layer field with fluctuating velocities and stability is preserved for zero linear growth coefficient. To obtain an improved understanding of mixing performance, a numerical study is performed with the variation of channel height when more than one ionic species with channels patterned with heterogeneity is considered. The wall heterogeneity may be created by placing some blocks of unequal size (with or without charged) close to the channel wall or some external potential patches. The analytical results for the transport characteristics of electroosmotic flow obtained are compared with the direct numerical simulation of the Navier–Stokes equation, Nernst–Plank equation, and Poisson equation, simultaneously. It is shown that heterogeneous potential could generate complex flow structures and the increment of species layers at different levels of the channel cross section from inlet to outlet significantly improve the mixing rate.     

Dynamic aspects of electroosmotic flow

This article presents an analysis of the frequency and time dependent electroosmotic flow in open-end and closed-end microchannels of arbitrary cross-section shape. In the numerical model, the modified Navier–Stokes equation governing the AC electroosmotic flow is solved using the control volume method. The iterative approach is used to determine the induced backpressure gradient. The potential distribution of the EDL in the channel is obtained by solving the non-linear 2D Poisson–Blotzmann equation. The comparison between the control volume formulation and the Green’s function method for the case of a rectangular microchannel shows a good agreement. The time evolution of the electroosmotic flow and the effect of a frequency-dependent AC electric field on the oscillating electroosmotic flow are also examined. The effect of the induced backpressure gradient with the frequency of the applied electric field is also shown.     

Molecular dynamics simulations of oscillatory Couette flows with slip boundary conditions

The effect of interfacial slip on steady-state and time-periodic flows of monatomic liquids is investigated using non-equilibrium molecular dynamics simulations. The fluid phase is confined between atomically smooth rigid walls, and the fluid flows are induced by moving one of the walls. In steady shear flows, the slip length increases almost linearly with shear rate. We found that the velocity profiles in oscillatory flows are well described by the Stokes flow solution with the slip length that depends on the local shear rate. Interestingly, the rate dependence of the slip length obtained in steady shear flows is recovered when the slip length in oscillatory flows is plotted as a function of the local shear rate magnitude. For both types of flows, the friction coefficient at the liquid–solid interface correlates well with the structure of the first fluid layer near the solid wall.     

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.     

Electroosmotic flow control in complex microgeometries

Numerical simulation results for pure electroosmotic and combined electroosmotic/pressure driven Stokes flows are presented in the cross-flow and Y-split junctions. The numerical algorithm is based on a mixed structured/unstructured spectral element formulation, which results in high-order accurate resolution of thin electric double layers with discretization flexibility for complex engineering geometries. The results for pure electroosmotic flows in cross-flow junctions under multiple electric fields show similarities between the electric and velocity fields. The combined electroosmotic/pressure driven flows are also simulated by regulating the flowrate in different branches of the cross-flow junctions. Flow control in the Stokes flow regime is shown to have linear dependence on the magnitude of the externally applied electric field, both for pure electroosmotic and combined flows. This linear behavior enables utilization of electroosmotic forces as nonmechanical means of flow control for microfluidic applications     

Electroosmotic control of width and position of liquid streams in hydrodynamic focusing

This paper presents theoretical and experimental investigations on electroosmotic control of stream width in hydrodynamic focusing. In the experiments, three liquids (aqueous NaCl, aqueous glycerol and aqueous NaCl) are introduced by syringe pumps to flow side by side in a straight rectangular microchannel. External electric fields are applied on the two aqueous NaCl streams. Under the same inlet volumetric flow rates, the applied electric fields are varied to control the interface positions and consequently the width of the focused aqueous glycerol stream. The electroosmotic effect on the width of the aqueous glycerol is measured using fluorescence imaging technique. The electroosmotic effect under different flow rates, different viscosity, and aspect ratio are investigated. The results indicate that the electroosmotic effect on the pressure-driven flow becomes weaker with the increase in flow rates, viscosity ratio or aspect ratio of the channel. The measured results of the focused width of the non-conducting fluid agree well with the analytical model.     

Hydrodynamic dispersion in long microchannels under conditions of electroosmotic circulation: II. Electrolytes

This work describes the steady-state transport of an electrolyte due to a stationary concentration difference in straight long channels under conditions of electroosmotic circulation. The electroosmotic flow is induced due to the slip produced at the charged channel walls. This flow is assumed to be compensated by a pressure-driven counterflow so that the net volume flow through the channel is exactly zero. Owing to the concentration dependence of electroosmotic slip, there is an involved coupling between the solute transfer, hydrodynamic flow and charge conservation. Nevertheless, for such a system the Taylor–Aris dispersion (TAD) theory is shown to be approximately applicable locally within an inner part of the channel for a wide range of Péclet numbers (Pe) irrespective of the concentration difference. Numerical simulations reveal only small deviations from analytical solutions for the inner part of the channel. The breakdown of TAD theory occurs within boundary regions near the channel ends and is related to the variation of the dispersion mechanism from the purely molecular diffusion at the channel ends to the hydrodynamic dispersion within the inner part of the channel. This boundary region is larger at the lower-concentration channel edge and its size increases nearly linearly with Pe number. It is possible to derive a simple analytical approximation for the inner profile of cross-section-averaged electrolyte concentration in terms of only few parameters, determined numerically. Such analytical approximations can be useful for experimental studies of concentration polarization phenomena in long microchannels.     

Approach to analytic solutions for electroosmotic flow in micro-ducts by eigenfunctions of the Helmholtz equation

In the literature, a limited number of analytical solutions for electroosmotic (EO) flow in micro-ducts were obtained. In this study, we present a general formulation using eigenfunctions of the Helmholtz equation to obtain analytic solutions for steady and unsteady EO flow in micro-ducts under Debye–Hückel approximation. The key observation is that the differential operator associated with the equation for the EO flow is strictly positive definite. Examples that add to analytic solutions for EO flow include exact series and closed-form solutions to the steady flow, and the starting flow and the oscillatory flow in three triangular ducts are found. It is easy to deduce some salient features of flow physics, such as the flow rate, transient time and phase lag as well as the velocity profile from the general solution, and they are given quantitative values in the individual examples.     

Modeling oscillatory flows in the transition regime using a high-order moment method

We present results using three different continuum-based models to study oscillatory flow in the transition regime. Data obtained from numerical solutions of the Boltzmann equation and the direct simulation Monte Carlo method, are used to assess the ability of the continuum models to capture important rarefaction effects. We further highlight the need to consider two Knudsen numbers: one based upon the length scale and the other upon the time scale. It is found that the regularized 26 moment model can follow kinetic theory in the early transition regime in terms of both Knudsen numbers but the regularized 13 moment equations can only be used up to the upper limit of the hydrodynamic regime. However, the subtle interplay of the length and time scales on oscillatory non-equilibrium flow causes the Navier–Stokes equations to fail even in the hydrodynamic regime. In addition, the effect of modifying the accommodation coefficient is also considered. It is found that reducing the accommodation coefficient on the stationary wall alone will increase the motion of the gas. However, gaseous movement will be reduced by changing both walls from diffusive to specular reflection.     

Manipulation of microfluidic flow pattern by optically controlled electroosmosis

Light is used to dynamically control the pattern of electroosmotic flow in a microfluidic channel. One wall of the channel is formed by a photoconductor film in a specific geometry. Illumination of this surface results in an increase of the conductivity that modifies the structure of the electric field inside the channel. A dramatic change of the electroosmotic flow pattern can be achieved. This approach provides useful capabilities for the manipulation of fluids in microfluidic systems like directing flow and mixing.     

A clip-on electroosmotic pump for oscillating flow in microfluidic cell culture devices

Recent advances in microfluidic devices put a high demand on small, robust and reliable pumps suitable for high-throughput applications. Here we demonstrate a compact, low-cost, directly attachable (clip-on) electroosmotic pump that couples with standard Luer connectors on a microfluidic device. The pump is easy to make and consists of a porous polycarbonate membrane and poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) electrodes. The soft electrode and membrane materials make it possible to incorporate the pump into a standard syringe filter holder, which in turn can be attached to commercial chips. The pump is less than half the size of the microscope slide used for many commercial lab-on-a-chip devices, meaning that these pumps can be used to control fluid flow in individual reactors in highly parallelized chemistry and biology experiments. Flow rates at various electric current and device dimensions are reported. We demonstrate the feasibility and safety of the pump for biological experiments by exposing endothelial cells to oscillating shear stress (up to 5 dyn/cm²) and by controlling the movement of both micro- and macroparticles, generating steady or oscillatory flow rates up to ± 400 μL/min.     

Hydrodynamic dispersion of neutral solutes in nanochannels: the effect of streaming potential

An analytical model is developed to account for the effect of streaming potential on the hydrodynamic dispersion of neutral solutes in pressure-driven flow. The pressure-driven flow and the resulting electroosmotic backflow exhibit coupled dispersion effects in nanoscale channels where the hydraulic diameter is on the order of the electrical double layer thickness. An effective diffusion coefficient for this regime is derived. The influence of streaming potential on hydrodynamic dispersion is found to be mainly dependent on an electrokinetic parameter, previously termed the “figure of merit”. Results indicate that streaming potential decreases the effective diffusion coefficient of the solute, while increasing the dispersion coefficient as traditionally defined. This discrepancy arises from the additional effect of streaming potential on average solute velocity, and discussed herein.     

Lattice Boltzmann method simulation of electroosmotic stirring in a microscale cavity

The suitable surface modification of microfluidic channels can enable a neutral electrolyte solution to develop an electric double layer (EDL). The ions contained within the EDL can be moved by applying an external electric field, inducing electroosmotic flows (EOFs) that results in associated stirring. This provides a solution for the rapid mixing required for many microfluidic applications. We have investigated EOFs generated by applying a steady electric field across a square cavity that has homogenous electric potentials along its walls. The flowfield is simulated using the lattice Boltzmann method. The extent of mixing is characterized for different electrode configurations and electric field strengths. We find that rapid mixing can be achieved by using this simple configuration which increases with increasing electric field strength. The mixing time for water-soluble organic molecules can be decreased by four orders of magnitude by suitable choice of wall zeta potential and electric field. We dedicate this paper to the memory of our colleagues Professors Kevin Granata and Liviu Librescu who fell tragically on April 16, 2007 while answering their call to serve higher education. They continue to inspire us. AM gratefully acknowledges support from Jadavpur University under the World Bank funded Technical Education Quality Improvement Programme of the Government of India and the hospitality of the Virginia Tech ESM Department where he conducted a portion of this work.     

Numerical study of the viscous flow in oscillatory spherical annuli

The method of fractional steps is applied for investigating the viscous flow field in the oscillatory spherical annuli. The numerical solution obtained enlarges the intervals of the frequency parameter M and amplitude of the torsional oscillations ε in comparison with known solutions. Typical flow fields are shown graphically.     

Experiment and simulation of mixed flows in a trapezoidal microchannel

This paper presents experimental and numerical results of mixed electroosmotic and pressure driven flows in a trapezoidal shaped microchannel. A micro particle image velocimetry (μPIV) technique is utilized to acquire velocity profiles across the microchannel for pressure, electroosmotic and mixed electroosmotic-pressure driven flows. In mixed flow studies, both favorable and adverse pressure gradient cases are considered. Flow results obtained from the μPIV technique are compared with 3D numerical predictions, and an excellent agreement is obtained between them. In the numerical technique, the electric double layer is not resolved to avoid expensive computation, rather a slip velocity is assigned at the channel surface based on the electric field and electroosmotic mobility. This study shows that a trapezoidal microchannel provides a tapered-cosine velocity profile if there is any pressure gradient in the flow direction. This result is significantly different from that observed in rectangular microchannels. Our experimental results verify that velocity distribution in mixed flow can be decomposed into pressure and electroosmotic driven components.