Oscillatory electrokinetic flow is numerically examined in a rectangular annulus microtube under the influence of various wave forms. When the inner and outer walls of the capillary are oppositely charged, an instantaneous two-direction flow field is produced and consequently the resultant flow rate is relatively reduced. A zero or negative flow rate may be achieved by appropriate design of the channel geometrical characteristics (e.g., hydraulic diameter) as well as the walls charges. In the case of sufficiently low kinematic viscosity and/or high excitation frequency, a relatively thin transient frictional layer is established close to the walls while the bulk fluid lags behind the liquid motion in the electric double layer by a phase shift. If different waveforms are combined together, fascinating outcomes can be obtained depending on the frequency of each individual wave. Applied electric fields with equal- and unequal-frequency combined waves may have the advantages of a double velocity field and a net mass flow rate, respectively. Interestingly, a direct flow pattern may be achieved by appropriately combining various waveforms with unequal frequencies. The mass flow rate decreases, with the constancy of the electrokinetic diameter, with approximately the square of hydraulic diameter. The Poiseuille number exhibits various characteristics depending on the excitation frequency as well as the type of wave especially in combination.

Mixing in a microfluidic device is a major challenge due to creeping flow, which is a significant roadblock for development of lab-on-a-chip device. In this study, an analytical model is presented to study the fluid flow behavior in a microfluidic mixer using time-periodic electro-osmotic flow. To facilitate mixing through microvortices, nonuniform surface charge condition is considered. A generalized analytical solution is obtained for the time-periodic electro-osmotic flow using a stream function technique. The electro-osmotic body force term is accounted as a slip boundary condition on the channel wall, which is a function of time and space. To demonstrate the applicability of the analytical model, two different surface conditions are considered: sinusoidal and step change in zeta potential along the channel surface. Depending on the zeta potential distribution, we obtained diverse flow patterns and vortices. The flow circulation and its structures depend on channel size, charge distribution, and the applied electric field frequency. Our results indicate that the sinusoidal zeta potential distribution provides elliptical shaped vortices, whereas the step change zeta potential provides rectangular shaped vortices. This analytical model is expected to aid in the effective micromixer design.

In this paper, we have analyzed an enhanced electroosmotic flow (EOF) by geometric modulation of the surface of a charged nanochannel. Otherwise, flat walls of the channel are modulated by embedding rectangular grooves placed perpendicular to the direction of the applied electric field in a periodic manner. The modulated channel is filled with a single electrolyte. The EOF within the modulated channel is determined by computing the Navier–Stokes–Nernst–Planck–Poisson equations for a wide range of Debye length. The objective of the present study is to achieve an enhanced EOF in the surface modulated channel. A significant enhancement in average EOF is found for a particular arrangement of grooves with the width of the grooves much higher than its depth and the Debye length is in the order of the channel height. However, the formation of vortex inside the narrow grooves can reduce the EOF when the groove depth is in the order of its width. Results are compared with the cases in which the grooves are replaced by superhydrophobic patches along which a zero shear stress condition is imposed.

Adopting the Navier slip conditions, we analyze the fully developed electroosmotic flow in hydrophobic microducts of general cross section under the Debye–Hückel approximation. The method of analysis includes series solutions which their coefficients are obtained by applying the wall boundary conditions using the least-squares matching method. Although the procedure is general enough to be applied to almost any arbitrary cross section, eight microgeometries including trapezoidal, double-trapezoidal, isosceles triangular, rhombic, elliptical, semi-elliptical, rectangular, and isotropically etched profiles are selected for presentation. We find that the flow rate is a linear increasing function of the slip length with thinner electric double layers (EDLs) providing higher slip effects. We also discover that, unlike the no-slip conditions, there is not a limit for the electroosmotic velocity when EDL extent is reduced. In fact, utilizing an analysis valid for very thin EDLs, it is shown that the maximum electroosmotic velocity in the presence of surface hydrophobicity is by a factor of slip length to Debye length higher than the Helmholtz–Smoluchowski velocity. This approximate procedure also provides an expression for the flow rate which is almost exact when the ratio of the channel hydraulic diameter to the Debye length is equal to or higher than 50.

In this study, the form of the analytes distribution in isotachophoresis (ITP) in the presence of a convective flow is analyzed in a wide rectangular microchannel. The imposed convection is considered due to a mismatch of electroosmotic (EO) slip velocity of electrolytes of different electrophoretic mobilities. We compute the two-dimensional (2D) Nernst–Planck equations coupled with the Navier–Stokes equations for fluid flow and an equation for electric field. We use a control volume method along with a higher-order upwind scheme to capture the sharp variation of variables in the transition zones. The convection of electrolytes produces a smearing effect on the steepness of the electric field and ion distribution in the interface between two adjacent electrolytes in the ITP process. The dispersion of the interface in plateau-mode and the sample in peak-mode is analyzed through the second- and third-order moments. The dispersion due to nonuniform EO flow (EOF) of electrolytes is found to be different from the case when the dispersion is considered only due to an external pressure driven Poiseuille flow. The nonuniform EOF of electrolytes produces less dispersion and skewness in the sample distribution when the molecular diffusivity of the sample ionic species is close to the harmonic mean of the diffusivity of adjacent electrolytes. We find that the EOF may become advantageous in separating two analytes of close diffusivity. Our results show that the one-dimensional (1D) Taylor–Aris model is suitable to predict the dispersed ITP when the average convection speed of electrolytes is in the order of the ITP speed.

An analytical study is presented in this paper on hydrodynamic dispersion due to steady electro-osmotic flow (EOF) in a slit microchannel with longitudinal step changes of ζ potential. The channel wall is periodically patterned with alternating stripes of distinct ζ potentials. Existing studies in the literature have considered dispersion in EOF with axial nonuniformity of ζ potential only in the limiting case where the length scale for longitudinal variation is much longer than the cross-sectional dimension of the channel. Hence, the existing theories on EOF dispersion subject to nonuniform charge distributions are all based on the lubrication approximation, by which cross-sectional mixing is ignored. In the present study, the general case where the length of one periodic unit of wall pattern (which involves a step change of ζ potential) is comparable with the channel height, as well as the long-wave limiting case, are investigated. The problem for the hydrodynamic dispersion coefficient is solved numerically in the general case, and analytically in the long-wave lubrication limit. The dispersion coefficient and the plate height are found to have strong, or even nonmonotonic, dependence on the controlling parameters, including the period length of the wall pattern, the area fraction of the EOF-suppressing region, the Debye parameter, the Péclet number, and the ratio of the two ζ potentials.

The time-periodic electro-osmotic flow in a microannulus is investigated based on the linearized Poisson–Boltzmann equation. An exact solution of the velocity distribution is obtained by using the Green's function approach. The influences of the geometric radius ratio, the wall ζ potential ratio, the electrokinetic radius, and the dimensionless frequency on velocity profiles are presented. Variations of the geometric radius ratio (between zero and one) can lead to quite different flow behaviors. The wall ζ potential ratio affects the magnitude and direction of the velocity profiles within the electric double layer near the two walls of a microannulus. Depending on the frequency and the geometric radius ratio, the walls identically and/or oppositely charged, both may result in the two-opposite-direction flow in the annulus. For high frequency, the electro-osmotic velocity variations are restricted mainly within a thin layer near the two cylindrical walls. Increasing the electrokinetic radius leads to decrease the electric double layer thickness as well as the maximum velocity near the walls.

Induced-charge electroosmosis (ICEO) around multiple gold-coated stainless steel rods under different ac electric fields is analyzed using microparticle image velocimetry (micro-PIV) and numerical simulations. In the present investigation, the induced electric double layer (EDL) is in weakly nonlinear limit. The ICEO flow around multiple touching rods exhibits geometry dependent quadrupolar flow structures with four vortices. The velocity magnitude is proportional to the square of the electric field. The ICEO flow velocity also depends on the cylinder orientation. The velocity increases with increased radial distance from the rod’s surface, attains a maximum, and then decays to zero. Experimental and numerical velocity distributions have the same trend beyond 0.2 mm of the rod’s surface.

A numerical investigation is performed into the flow characteristics of the electroosmotic flow induced within a microchannel with a complex-wavy surface by a time-varying periodic electric field. The simulations focus specifically on the effects of the Strouhal number of the periodic electric potential, the amplitude of the periodic electric potential, the amplitude of the complex-wavy surface, and the waveform geometry. The results show that under steady-time periodic conditions, the flow pattern induced within the microchannel varies over the course of the oscillation period. In particular, it is shown that a flow recirculation structure is generated in the trough region of the wavy surface as the applied electric field falls to zero if the amplitude of the wavy surface exceeds a certain threshold value. In addition, it is shown that the phases of the electric field and electroosmotic velocity near the wall surface are almost identical. However, a phase shift exists between the electric field and the bulk flow velocity in the central region of the channel; particularly at larger values of the Strouhal number. Finally, it is shown that the velocity profile near the wavy surface is more sensitive to changes in the waveform geometry than that in the center of the channel. Overall, the simulation results presented in the study provide a useful source of reference for the development of new microfluidic systems incorporating microchannels with complex-wavy surfaces.

In this paper, we have studied the electrokinetics and mixing driven by an imposed pressure gradient and electric field in a charged modulated microchannel. By performing detailed numerical simulations based on the coupled Poisson, Nernst–Planck, and incompressible Navier–Stokes equations, we discussed electrokinetic transport and other hydrodynamic effects under the application of combined pressure and dc electric fields for different values of electric double layer thickness and channel patch potential. A numerical method based on the pressure correction iterative algorithm is adopted to compute the flow field and mole fraction of the ions. Since electroosmotic flow depends on the magnitude and sign of wall potential, a vortex can be generated through adjusting the patch potential. The dependence of the vortical flow on imposed pressure gradient is investigated. Formation of vortex in electroosmotic flow has importance in producing solute dispersion. The circulation of vortex grows with the rise of patch potential, whereas the pressure-assisted electroosmotic flow produces a reduction in vortex size. However, the flow rate is substantially increased in pressure-assisted electroosmotic flow. Flow reversal and suppression of fluid transport is possible through an adverse pressure gradient. The ion distribution and electric field above the potential patch are distorted by the imposed pressure gradient. At higher values of the pressure gradient, the combined pressure electroosmotic-driven flow resembles the fully developed Poiseuille flow. Current density is found to increase with the rise of imposed pressure gradient.

This is an analytical study on electrohydrodynamic flows through a circular tube, of which the wall is micropatterned with a periodic array of longitudinal or transverse slip-stick stripes. One unit of the wall pattern comprises two stripes, one slipping and the other nonslipping, and each with a distinct ζ potential. Using the methods of eigenfunction expansion and point collocation, the electric potential and velocity fields are determined by solving the linearized Poisson–Boltzmann equation and the Stokes equation subject to the mixed electrohydrodynamic boundary conditions. The effective equations for the fluid and current fluxes are deduced as functions of the slipping area fraction of the wall, the intrinsic hydrodynamic slip length, the Debye parameter, and the ζ potentials. The theoretical limits for some particular wall patterns, which are available in the literature only for plane channels, are extended in this paper to the case of a circular channel. We confirm that some remarks made earlier for electroosmotic flow over a plane surface are also applicable to the present problem involving patterns on a circular surface. We pay particular attention to the effects of the pattern pitch on the flow in both the longitudinal and transverse configurations. When the wall is uniformly charged, the adverse effect on the electroosmotic flow enhancement due to a small fraction of area being covered by no-slip slots can be amplified if the pitch decreases. Reducing the pitch will also lead to a greater deviation from the Helmholtz–Smoluchowski limit when the slipping regions are uncharged. With oppositely charged slipping regions, local recirculation or a net reversed flow is possible, even when the wall is on the average electropositive or neutral. The flow morphology is found to be subject to the combined influence of the geometry of the tube and the electrohydrodynamic properties of the wall.

Flow dynamics in nano-scaled structures such as nanochannels and nanopores have recently become important in developing next-generation high-speed DNA sequencers. In the present paper, we report the electrokinetic flow dynamics of λDNA confined in nanochannels having heights that are smaller than the molecular radius of gyration. Nanochannels of varying heights of from 330 to 650 nm were used in the experiments in order to systematically investigate the effect of confinement. Weakly aggregated λDNA flowed in a direction opposite to an applied electric field as a result of the competition of electrophoresis and electroosmotic flows. The terminal velocity of λDNA was proportional to the strength of the electric field, and the mobility was found to decrease with the channel height. A simple theoretical model explaining the decrease in the mobility was developed taking into account the shear stress due to small clearances between λDNA and the walls of nanochannels. The validity of the model was confirmed by reasonable agreement between the theoretical and experimental results. The theoretical model and the transport properties under confinement provide basic design data for the development of next-generation DNA sequencers.

The development of microfluidics platforms in recent years has led to an increase in the number of applications involving the flow of multiple immiscible layers of viscous electrolyte fluids. In this study, numerical results as well as analytic equations for velocity and shear stress profiles were derived for N layers with known viscosities, assuming steady laminar flow in a microchannel driven by pressure and/or electro-static (Coulomb) forces. Numerical simulation results, using a commercial software package, match analytical results for fully-developed flow. Entrance flow effects with centered fluid-layer shrinking were studied as well. Specifically, cases with larger viscosities in the inner layers show a very good agreement with experimental correlations for the dimensionless entrance length as a function of inlet Reynolds number. However, significant deviations may occur for multilayer flows with smaller viscosities in the inner layers. A correlation was deduced for the two-layer electroosmotic flow and the pressure driven flow, both being more complex when compared with single-layer flows. The impact of using power-law fluids on resulting velocity profiles has also been explored and compared to Newtonian fluid flows. The present model readily allows for an exploration of the impact of design choices on velocity profiles, shear stress, and channel distribution in multilayer microchannel flows as a function of layered viscosity distribution and type of driving force.

The motivation of the present study is to generate vortical flow by introducing channel wall roughness in the form of a wall mounted block that has a step-jump in ζ -potential on the upper face. The characteristics for the electrokinetic flow are obtained by numerically solving the Poisson equation, the Nernst–Planck equation, and the Navier–Stokes equations, simultaneously. A numerical method based on the pressure correction iterative algorithm ( SIMPLE ) is adopted to compute the flow field and mole fraction of the ions. The potential patch induces a strong recirculation vortex, which in turn generates a strong pressure gradient. The strength of the vortex, which appears adjacent to the potential patch, increases almost linearly with the increase in ζ -potential. The streamlines follow a tortuous path near the wall roughness. The average axial flow rate over the block is enhanced significantly. We found that the ionic distribution follow the equilibrium Boltzmann distribution away from the wall roughness. The solutions based on the Poisson–Boltzmann distribution and the Nernst–Planck model are different when the inertial effect is significant. The combined effects due to geometrical modulation of the channel wall and heterogeneity in ζ -potential is found to produce a stronger vortex, and hence a stronger mixing, compared with either of these. Increase in ζ -potential increases both the transport rate and mixing efficiency. A novelty of the present configuration is that the vortex forms above the obstacle even when the patch potential is negative.

The effects of non-uniform zeta potentials on electro-osmotic flows in flat microchannels have been investigated with particular attention to reservoir effects. The governing equations, which consist of a Laplace equation for the distribution of external electric potential, a Poisson equation for the distribution of electric double layer potential, the Nernst-Planck equation for the distribution of charge density, and modified Navier-Stokes equations for the flow field are solved numerically for an incompressible steady flow of a Newtonian fluid using the finite-volume method. For the validation of the numerical scheme, the key features of an ideal electro-osmotic flow with uniform zeta potential have been compared with analytical solutions for the ionic concentration, electric potential, pressure, and velocity fields. When reservoirs are included in the analysis, an adverse pressure gradient is induced in the channel due to entrance and exit effects even when the reservoirs are at the same pressure. Non-uniform zeta potentials lead to complex flow fields, which are examined in detail.