Electroosmotic transport through rectangular channels with small zeta potentials

In this article, we analyze the electroosmotic transport of neutral samples through rectangular channels having a small zeta potential at their walls. Exact analytical expressions have been derived for quantifying the solute velocity in such conduits and the Taylor-Aris dispersivity in large-aspect-ratio rectangular geometries. In addition, a semianalytical theory has been presented for estimating the solutal spreading rate in rectangular profiles of all aspect ratios by decoupling the effects of vertical and horizontal velocity gradients in the system. Finally, the predictions made by this theory have been compared with the results from numerical simulations in which all assumptions were relaxed. Our analysis shows that while the sidewalls in a rectangular conduit modify the fluid velocity only to a moderate extent, they can increase the hydrodynamic dispersion of sample slugs as much as by a factor of 8 under strong Debye-layer overlap conditions. In the opposite limit of thin Debye layers, however, the increase in dispersion due to the side regions is only by a factor of 2 and remains nearly unaffected by the aspect ratio of the channel, in agreement with the prediction by [E.K. Zholkovskij, J.H. Masliyah, J. Czarnecki, Anal. Chem. 75 (2003) 901].     

Electroosmotic flow in channels with step changes in zeta potential and cross section

We consider the effects that step changes in zeta potential and cross section have on electroosmosis in long-and-narrow channels with arbitrary cross-sectional shapes. The Stokes equation of flow is solved analytically utilizing the thin Debye layer approximation to provide effective slip velocities on the channel walls. The effects of channel dimensions, surface potentials, applied pressure drop, and applied voltage are discussed. One anecdotal case, a two-region rectangular channel, is presented to illustrate the solution. The flow in each region is a combination of a uniform electroosmotic flow and a nonuniform pressure-driven flow. The electroosmotic pumping causes the pressure gradient in each region to adjust so that the flow rate is the same in each region and the overall applied pressure drop is met, resulting in convex velocity profiles in some regions and concave velocity profiles in other regions. By appropriate choice of the applied pressure drop, flat velocity profiles may be achieved in one or more regions.     

Electroosmotic flows with random zeta potential

The hydrodynamic problem of electroosmotic flow in a cylindrical capillary with random zeta potential is solved in the limit of small Deybe length and low Reynolds number. Averages are defined over multiple experiments and the mean axial velocity is found to be a plug flow. The variance of the velocity exhibits parabolic-like variation across the capillary. Average concentrations of samples transported by the flow are approximated by defining an effective diffusivity coefficient. Theoretical formulas for the average concentration are supported by numerical experiments.     

Electroosmotic flow controllable coating on a capillary surface by a sol-gel process for capillary electrophoresis

A simple coating procedure employing a sol-gel process to modify the inner surface of a bare fused-silica capillary with a positively charged quaternary ammonium group is established. Scanning electron microscopic studies reveal that a smooth coating with 1 to approximately 2 microm thickness can be obtained at optimized coating conditions. With 40 mM citrate as a running electrolyte, the plot of electroosmotic flow (EOF) versus pH shows a unique three-stage EOF pattern from negative to zero and then to positive over a pH range of 2.5 to 7.0. At pH above 5.5, the direction of the EOF is from the anode to the cathode, as is the case in a bare fused-silica capillary, and the electroosmotic mobility increases as the pH increases. However, the direction of the EOF is reversed at pH below 4.0. Over the pH range of 4.0 to 5.5, zero electroosmotic mobility is obtained. Such a three-stage EOF pattern has been used to separate six aromatic acids under suppressed EOF and to separate nitrate and nitrite with the anions migrating in the same direction as the EOF. The positively charged quaternary ammonium group on the coating was also utilized to minimize the adsorption problem during the separation of five basic drugs under suppressed EOF and during the separation of four basic proteins with the cations migrate in the opposite direction as the EOF. Also, the stability and reproducibility of this column are good.     

Electroosmosis in porous solids for high zeta potentials

When surface potentials (or the surface charges) are high, the exponential term on the right-hand side of the Poisson-Boltzmann equation cannot be linearized. This nonlinear regime is systematically studied for various porous media and various physicochemical conditions. As in the linear regime, the numerical data for the electroosmotic coefficient when made dimensionless are shown to follow the semianalytical solution derived for a plane Poiseuille flow. Therefore, this coefficient can be deduced either from the specific surface or from the permeability and the formation factor.     

Numerical study of electroosmotic slip flow of fractional Oldroyd-B fluids at high zeta potentials

In this paper, an investigation of the electroosmotic flow of fractional Oldroyd-B fluids in a narrow circular tube with high zeta potential is presented. The Navier linear slip law at the walls is considered. The potential field is applied along the walls described by the nonlinear Poisson–Boltzmann equation. It's worth noting here that the linear Debye–Hückel approximation can't be used at the condition of high zeta potential and the exact solution of potential in cylindrical coordinates can't be obtained. Therefore, the Matlab bvp4c solver method and the finite difference method are employed to numerically solve the nonlinear Poisson–Boltzmann equation and the governing equations of the velocity distribution, respectively. To verify the validity of our numerical approach, a comparison has been made with the previous work in the case of low zeta potential and the excellent agreement between the solutions is clear. Then, in view of the obtained numerical solution for the velocity distribution, the numerical solutions of the flow rate and the shear stress are derived. Furthermore, based on numerical analysis, the influence of pertinent parameters on the potential distribution and the generation of flow is presented graphically.     

Ionic transport in porous media for high zeta potentials

Ionic transport coefficients are numerically calculated in various porous media for high zeta potentials zeta by solving the Poisson-Boltzmann, the Stokes, and the convection-diffusion equations on the pore scale. Theoretical formulae for the simple case of a plane Poiseuille flow are derived in this limit. These formulae, when expressed in terms of the characteristic length Lambda, provide an excellent estimate of the ionic transport coefficients whatever the porous medium and whatever the value of zeta.     

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.     

Electroosmotic flow modulation in capillary electrophoresis by organic cations from ionic liquids

This paper describes the ability of several ionic liquids cations for electroosmotic flow modulation in capillary electrophoresis. Organic salts based on phosphonium, sulfonium, cysteinium, ammonium, and guanidinium cations were selected to study this property. In addition, the synergistic effect of these compounds in cyclodextrin chiral separation was also evaluated. In comparison with most studied imidazolium-based ionic liquids, several of the cations studied, are stronger modifiers in terms of electroosmotic flow (EOF) modulation. Phosphonium-based compounds and tri-octyl methylammonium chloride ([Aliquat]Cl) had the strongest ability to reverse EOF both in acidic and in basic conditions and had the lowest EOF reversal concentrations in the presence of hydroxypropyl-β-cyclodextrin. EOF modulation ability of phosphonium cations also contributed to the improvement of chiral separation of DL-propranolol by hydroxypropyl-β-cyclodextrin at lower concentrations in comparison with most commonly used EOF modulators such as tetrabutylammonium phosphate.     

Electroosmotic flow suppression in capillary electrophoresis: chemisorption of trimethoxy silane-modified polydimethylacrylamide

Adsorbed polymers are widely used to suppress electroosmotic flow (EOF) in capillary electrophoresis (CE). Polymeric coatings, physisorbed onto the surface of the capillary wall, are often unstable under harsh conditions. This can be attributed to the reversible nature of the coating which becomes apparent when the adsorbed layer competes with a second species in the electrophoresis buffer solution for attachment/interaction with the capillary surface. In an effort to overcome the problem of coating instability, trimethoxysilane-modified polydimethylacrylamide was synthesized. This copolymer rapidly adsorbs on the wall from ultradilute aqueous solutions. After incubation at a temperature of 60 degrees C silyl groups, which extend from the polymer backbone, form condensation bonds with the silanols on the capillary surface. This enables subsequent formation of strong covalent bonds between the copolymer and the capillary wall. In this research, we establish that physisorption of polymer chains to the surface is essential for close alignment of surface and polymer silane groups which facilitates the formation of covalent bonds.     

Electroosmotic flow with Joule heating effects

Electroosmotic flow with Joule heating effects was examined numerically and experimentally in this work. We used a fluorescence-based thermometry technique to measure the liquid temperature variation caused by Joule heating along a micro capillary. We used a caged-fluorescent dye-based microfluidic visualization technique to measure the electroosmotic velocity profile along the capillary. Sharp temperature drops close to the two ends and a high-temperature plateau in the middle of the capillary were observed. Correspondingly, concave-convex-concave velocity profiles were observed in the inlet-middle-outlet regions of a homogeneous capillary. These velocity perturbations were due to the induced pressure gradients resulting from axial variations of temperature. The measured liquid temperature distribution and the electroosmotic velocity profile along the capillary agree well with the predictions of a theoretical model developed in this paper.     

Electroosmotic flow reversal for the determination of inorganic anions by capillary electrophoresis with methanol-water buffers

Manipulation of the electroosmotic flow (EOF) is essential for achieving optimized separations of small anions by capillary electrophoresis (CE). In this work, efficient suppression or reversal of EOF is achieved upon addition of small amounts of the cationic surfactants, cetyltrimethylammonium bromide (CTAB) or didodecyldimethylammonium bromide (DDAB) to the electrophoretic buffer. Highly stable and reversed EOF are achieved using the surfactants in the presence of up to 50% MeOH. In aqueous and low methanol containing solutions (up to 30%, v/v) surface aggregation of the surfactants at the capillary wall occurs at a concentration below the critical micelle concentration (CMC). The impact of MeOH on reversed EOF is predominantly a function of the diminished zeta potential of the silica, and to a lesser extent on the CMC in the bulk solution of the surfactant. Fast baseline separation and selectivity changes for small inorganic anions are observed when mixed aqueous-organic buffers are employed. Changes in EOF, micellar properties of the surfactant and selectivity for inorganic anions upon addition of various percent of methanol are also discussed.     

Electroosmotic flow velocity measurements in a square microchannel

Experiments were performed using a microparticle image velocimetry (MPIV) for 2D velocity distributions of electroosmotically driven flows in a 40-mm-long microchannel with a square cross section of 200×200 μm. Electroosmotic flow (EOF) bulk fluid velocity measurements were made in a range of streamwise electric field strengths from 5 to 25 kV/m. A series of seed particle calibration tests can be made in a 200×120×24,000-μm untreated polydimethyl siloxane (PDMS channel incorporating MPIV to determine the electrophoretic mobilities in aqueous buffer solutions of 1× TAE, 1× TBE, 10 mM NaCl, and 10 mM borate. A linear/nonlinear (due to Joule heating) flow rate increase with applied field was obtained and compared with those of previous studies. A parametric study, with extensive measurements, was performed with different electric field strength and buffer solution concentration under a constant zeta potential at wall for each buffer. The characteristics of EOF in square microchannels were thus investigated. Finally, a composite correlation of the relevant parameters was developed in the form of within ±1% accuracy for 99% of the experimental data.     

Electrophoresis in a Carreau fluid at arbitrary zeta potentials

The electrophoresis of colloidal particles has been studied extensively in the past. Relevant analyses, however, are focused mainly on the electrophoretic behavior of a particle in a Newtonian fluid. Recent advances in science and technology suggest that the electrophoresis conducted in a non-Newtonian fluid can play a role in practice. Here, the electrophoresis of a concentrated colloidal dispersion in a Carreau fluid is investigated under the conditions of arbitrary electrical potential where the effect of double-layer polarization may be significant. A pseudo-spectral method coupled with a Newton-Raphson iteration scheme is used to solve the governing equations, which describe the electric, the flow, and the concentration fields. The results of numerical simulation reveal that, due to the effect of shear thinning, the electrophoretic mobility for the case of a Carreau fluid is greater than for that of a Newtonian fluid. Also, the higher the surface potential of a particle, the more significant the non-Newtonian nature of a Carreau fluid on its electrophoretic mobility.     

Electroosmotic flow mixing in zigzag microchannels

In this study we performed numerical and experimental investigations into the mixing of EOFs in zigzag microchannels with two different corner geometries, namely sharp corners and flat corners. In the zigzag microchannel with sharp corners, the flow travels more rapidly near the inner wall of the corner than near the outer wall as a result of the higher electric potential drop. The resulting velocity gradient induces a racetrack effect, which enhances diffusion within the fluid and hence improves the mixing performance. The simulation results reveal that the mixing index is approximately 88.83%. However, the sharp-corner geometry causes residual liquid or bubbles to become trapped in the channel at the point where the flow is almost stationary, when the channel is in the process of cleaning. Accordingly, a zigzag microchannel with flat-corner geometry is developed. The flat-corner geometry forms a convergent-divergent type nozzle which not only enhances the mixing performance in the channel, but also prevents the accumulation of residual liquid or bubbles. Scaling analysis reveals that this corner geometry leads to an effective increase in the mixing length. The experimental results reveal that the mixing index is increased to 94.30% in the flat-corner zigzag channel. Hence, the results demonstrate that the mixing index of the flat-corner zigzag channel is better than that of the conventional sharp-corner microchannel. Finally, the results of Taguchi analysis indicate that the attainable mixing index is determined primarily by the number of corners in the microchannel and by the flow passing height at each corner.     

Electroosmotic flow changes due to interactions of background electrolyte counter-ions with polyethyleneimine coating in capillary zone electrophoresis of proteins

The properties and behavior of polyethyleneimine (PEI) covalently coated capillaries with respect to different background electrolytes used in capillary zone electrophoresis (CZE) are described. The coating stability and changes of inner surface charge in the capillary were followed by measurement of electroosmotic flow (EOF). Interest was focused mainly on conjugate bases of carboxylic acids as anionic background electrolyte components (acetate, citrate, malate, malonate, tartrate, and succinate). An interesting phenomenon was observed in PEI-coated capillaries: The direction (and the magnitude) of EOF depends on the composition of the background electrolyte and at a certain pH it can undergo reversible change. Ionic complex formation was suggested as a hypothesis to explain this behavior. With this knowledge, the PEI-coated capillary was used for the separation of basic proteins in the above-mentioned background electrolytes. A standard protein mixture of cytochrome c, ribonuclease A, and lysozyme at a concentration of 0.25 mg/mL each was chosen as model sample.     

Electrokinetic-vortex formation near a two-part cylinder with same-sign zeta potentials in a straight microchannel

Vortex formation near a two-part cylinder with zeta potentials of different values but the same sign under an external DC electric field is numerically investigated in this paper. The cylinder, inserted in a straight microchannel filled with an aqueous solution, is composed of an upstream part and a downstream part. When a DC electric field is applied in the channel, under certain conditions, the vortex will form near the cylinder due to the different velocities of electroosmotic flow generated on the cylinder surface. The numerical results reveal that the larger the velocity difference of electroosmotic flow generated on the two-part cylinder and the smaller the channel width, the more conducive to vortex formation in the channel. In addition, if the zeta potential ratios of cylinder downstream part to upstream part and channel wall to cylinder upstream part are unchanged, the DC electric field strength and the zeta potential value do not affect the pattern of vortices formed in the channel. This study provides a way for vortex formation in microchannels and has the potential application in microfluidic devices.     

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.