Modeling of combined electroosmotic and capillary flow in microchannels

In the present study, theoretical model for the transient response of a capillary flow under the combined effects of electroosmotic and capillary forces at low Reynolds number is presented. The governing equation is derived based on the balance among the electrokinetic, surface, viscous and gravity forces. A non-dimensional transient governing equation for the penetration depth as a function of time is obtained by normalizing the viscous, gravity and electroosmotic forces with surface tension force. A new non-dimensional group for the electroosmotic force, E_o, is obtained through the non-dimensional analysis. This new non-dimensional group is a representation of combined electroosmosis and surface tension, i.e., capillarity. The numerical solution of governing equation is obtained to study the effect of different operating parameters on the flow front transport. In a combined flow, it is observed that the flow with positive and low negative magnitude E_o numbers, the attainment of equilibrium penetration depth is similar to a capillary flow. In case of high negative magnitude E_o numbers, complete filling of the channel is observed. The electrolyte with lower permittivity delays the progress of the flow front whereas a large EDL transports the electrolyte quickly. Higher viscous and gravity forces also delay the transport process in the combined flow. This model suggests that in combined flow the electrokinetic parameters also play an important role on the capillary flow and experiments are required to confirm this electrokinetic effect on capillary transport.     

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.     

The influence of surface treatments on the electroosmotic flow in micellar electrokinetic capillary chromatography

Summary An investigation was carried out to study the electroosmotic flow (EOF) in micellar electrokinetic capillary chromatography (MECC). Fused silica capillaries were treated with various reagents to investigate the parameters influencing the magnitude and reproducibility of the EOF. The results for untreated and treated columns were collected and compared under the same experimental conditions. Furthermore, experiments with and without sodium dodecylsulfate (SDS) addition to the buffer were carried out to elucidate the influence of this surfactant on the EOF. The mechanisms behind the effects of these modifications on the EOF and the stability of the coatings on the column wall are discussed.     

Two-fluid electroosmotic flow in microchannels

This paper presents a mathematical model to describe a two-fluid electroosmotic pumping technique, in which an electrically non-conducting fluid is delivered by the interfacial viscous force of a conducting fluid; the latter is driven by electroosmosis. The electrical potential in the conducting fluid and the analytical solution of the steady two-fluid electroosmotic stratified flow in a rectangular microchannel was presented by assuming a planar interface between the two immiscible fluids. The effects of viscosity ratio, hold-up, concentration, and interfacial zeta potential are analyzed to show the potential feasibility of this technique.     

Surfactant-induced electroosmotic flow in microfluidic capillaries

Control of EOF in microfluidic devices is essential in applications such as protein/DNA sizing and high‐throughput drug screening. With the growing popularity of poly(methyl methacrylate) (PMMA) as the substrate for polymeric‐based microfludics, it is important to understand the effect of surfactants on EOF in these devices. In this article, we present an extensive investigation exploring changes in EOF rate induced by SDS, polyoxyethylene lauryl ether (Brij35) and CTAB in PMMA microfluidic capillaries. In a standard protein buffer (Tris‐Glycine), PMMA capillaries exhibited a cathodic EOF with measured mobility of 1.54 ± 0.1 (× 10^?4 cm²/V.s). In the presence of surfactant below a critical concentration, EOF was independent of surfactant concentration. At high concentrations of surfactants, the electroosmotic mobility was found to linearly increase/decrease as the logarithm of concentration before reaching a constant value. With SDS, the EOF increased by 257% (compared to buffer), while it was decreased by 238% with CTAB. In the case of Brij35, the electroosmotic mobility was reduced by 70%. In a binary surfactant system of SDS/CTAB and SDS/Brij35, addition of oppositely charged CTAB reduced the SDS‐induced EOF more effectively compared to nonionic Brij35. We propose possible mechanisms that explain the observed changes in EOF and zeta potential values. Use of neutral polymer coatings in combination with SDS resulted in 50% reduction in the electroosmotic mobility with 0.1% hydroxypropyl methyl cellulose (HPMC), while including 2% poly (N,N‐dimethylacrylamide) (PDMA) had no effect. These results will potentially contribute to the development of PMMA‐based microfluidic devices.     

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.     

Metal cation control of electroosmotic flow magnitude in phospholipid‐coated capillaries

CZE has become widespread for the separation and analysis of biomolecules such as proteins and peptides, due to factors such as, the speed of the separations, low sample volume, and high resolution associated with the technique. However, the separation of biomolecules by CZE does present a significant challenge due to the electrostatic attraction and adsorption of cationic, or cation containing, biomolecules to the capillary surface. To that end numerous methods have been developed to passivate, or protect the surface, in order to prevent the adsorption of analytes. Yet, in the process of protecting the capillary surface, the potential for further modification of the EOF, a factor crucial to effective analyte resolution, is greatly diminished. In seeking to overcome this limitation we have explored the potential of incorporating a range of metal cations into a phospholipid bilayer capillary coating. It has previously been established that the inclusion of calcium into the separation buffer with a phospholipid coating will reverse the EOF in the capillary. Here, we present our investigation of a broader range of metal cations included in the separation buffer (Ca²⁺, Mg²⁺, Co²⁺, Ni²⁺, Sr²⁺, Ba²⁺, and Ce³⁺) revealing that the choice of metal cation can drastically influence the EOF, with observed values between ?3.80 × 10^?4 and ?5.74 × 10^?5 cm²/V·s.     

Theoretical study on potential distribution and electroosmotic flow velocity in microscale channel

A developed mathematical model for calculating potential distribution inside the electrical double layer is explored in this paper based on the Poisson-Boltzmann equation. By modifying the ion concentration, we numerically simulated the potential profile inside the actual electrical double layer according to the zeta potential. Then a theoretical analysis on the streamwise electroosmotic velocity in microscale channel is presented. Furthermore, the expression of the electroosmotic velocity is significantly suppressed after considering the Helmboltz-Smolucbowski equation boundary conditions. The results show that the calculated electroosmotic values basically agree with the experimental ones. Therefore, this provides the data for micro- and nano-channels’ electrophoretic transport, as well as separation of neutral and charged electrolyte.     

Mobilization of electroosmotic flow markers in capillary zone electrophoresis

UV-absorbing neutral substances are commonly used as markers of mean electroosmotic flow in capillary electrophoresis for their zero electrophoretic mobility in an electric field. However, some of these markers can interact with background electrolyte components and migrate at a different velocity than the electroosmotic flow. Thus, we tested 11 markers primarily varying in their degree of methylation and type of central atom in combination with five background electrolyte cations differing in their ionic radii and surface charge density, measuring the relative electrophoretic mobility using thiourea as a reference marker. Our results from this set of experiments showed some general trends in the mobilization of the markers based on the effects of marker structure and type of background electrolyte cation on the relative electrophoretic mobility. As an example, the effects of an inadequate choice of marker on analyte identification were illustrated in the electrophoretic separation of glucosinolates. Therefore, our findings may help electrophoretists appropriately select electroosmotic flow markers for various electrophoretic systems.     

Mobility-based selective on-line preconcentration of proteins in capillary electrophoresis by controlling electroosmotic flow

A simple method to perform selective on-line preconcentration of protein samples in capillary electrophoresis (CE) is described. The selectivity, based on protein electrophoretic mobility, was achieved by controlling electroosmotic flow (EOF). A short section of dialysis hollow fiber, serving as a porous joint, was connected between two lengths of fused silica capillary. High voltage was applied separately to each capillary, and the EOF in the system was controlled independently of the local electric field intensity by controlling the total voltage drop. An equation relating the EOF with the total voltage drop was derived and evaluated experimentally. On-line preconcentration of both positively charged and negatively charged model proteins was demonstrated without using discontinuous background electrolytes, and protein analytes were concentrated by approximately 60-200-fold under various conditions. For positively charged proteins, positive voltages of the same magnitude were applied at the free ends of the connected capillaries while the porous joint was grounded. This provided a zero EOF in the system and a non-zero local electric field in each capillary to drive the positively charged analytes to the porous joint. CE separation was then initiated by switching the polarity of the high voltage over the second capillary. For negatively charged proteins, the procedure was the same except negative voltages were applied at the free ends of the capillaries. Mobility-based selective on-line preconcentration was also demonstrated with two negatively charged proteins, i.e. beta-lactoglobulin B and myoglobin. In this case, negative voltages of different values were applied at the free ends of the capillaries with different values, which provided a non-zero EOF in the system. The direction of EOF was the same as that of the electrophoretic migration velocities of the protein analytes in the first capillary and opposite in the second capillary. By controlling the EOF, beta-lactoglobulin B, which has a higher mobility, could be concentrated over 150-fold with a 15 min injection while myoglobin, which has a lower mobility, was eliminated from the system.     

Numerical study of the vortex-induced electroosmotic mixing of non-Newtonian biofluids in a nonuniformly charged wavy microchannel: Effect of finite ion size

We propose a micromixer for obtaining better efficiency of vortex induced electroosmotic mixing of non-Newtonian bio-fluids at a relatively higher flow rate, which finds relevance in many biomedical and biological applications. To represent the rheology of non-Newtonian fluid, we consider the Carreau model in this study, while the applied electric field drives the constituent components in the micromixer. We show that the spatial variation of the applied field, triggered by the topological change of the bounding surfaces, upon interacting with the non-uniform surface potential gives rise to efficient mixing as realized by the formation of vortices in the proposed micromixer. Also, we show that the phase-lag between surface potential leads to the formation of asymmetric vortices. This behavior offers better mixing performance following the appearance of undulation on the flow pattern. Finally, we establish that the assumption of a point charge in the paradigm of electroosmotic mixing, which is not realistic as well, under-predicts the mixing efficiency at higher amplitude of the non-uniform zeta potential. The inferences of the present analysis may guide as a design tool for micromixer where rheological properties of the fluid and flow actuation parameters can be simultaneously tuned to obtain phenomenal enhancement in mixing efficiency.     

Direct and indirect electroosmotic flow velocity measurements in microchannels

As microfluidic technologies mature, increasingly complex solutions are employed, and accurate methods for the measurement of electroosmotic flow rates are becoming increasingly important. The methodologies of both a direct method and an indirect method of flow rate measurement are presented here. The direct method involves flow visualization using trace amounts of a caged fluorescent dye. The indirect method is based on the change in current that occurs when one solution in the microchannel is replaced by another. The results of concurrent and independent measurements of electroosmotic velocities of Tris-acetate with EDTA (TAE) and Tris-borate with EDTA (TBE) at 1x concentration in fused silica capillaries are presented. Although these buffers are commonly used in biological chemistry, these mobilities have not previously been reported. Strong agreement among data collected with both methods establishes confidence in the electroosmotic mobility values obtained and indicates that the current-based method, which requires less infrastructure than the direct method, can provide accurate flow rate measurements under these conditions. Constant electroosmotic mobilities of 4.90 x 10(-8) m(2) V(-1) s(-1) for TAE and 3.10 x 10(-8) m(2) V(-1) s(-1) for TBE were determined by tests in a range of electrical field strengths from 5 to 20 kV/m. A linear flow rate increase with applied field strength indicated that constant mobility and negligible Joule heating effects were present. Applicability and limitations of both the measurement methods and these buffers are discussed in the context of microfluidic applications.     

Tradeoff between mixing and transport for electroosmotic flow in heterogeneous microchannels with nonuniform surface potentials

Electroosmotic flow (EOF) is a phenomenon associated with the movement of an aqueous solution induced by the application of an electric field in microchannels. The characteristics of EOF depend on the nature of the surface potential, i.e., whether it is uniform or nonuniform. In this paper, a lattice Boltzmann model (LBM) combined with the Poisson-Boltzmann equation is used to simulate flow field in a rectangular microchannel with nonuniform (step change) surface potentials. The simulation results indicate that local circulations can occur near a heterogeneous region with nonuniform surface potentials, in agreement with those by other authors. Largest circulations, which imply a highest mixing efficiency due to convection and short-range diffusion, were found when the average surface potential is zero, regardless of whether the distribution of the heterogeneous patches is symmetric or asymmetric. In this work, we have illustrated that there is a trade-off between the mixing and liquid transport in EOF microfluidics. One should not simply focus on mixing and neglect liquid transport, as performed in the literature. Excellent mixing could lead to a poor transport of electroosmotic flow in microchannels.     

Cationic polymer coatings for design of electroosmotic flow and control of DNA adsorption

A difficulty with the design and operation of an electrokinetically operated DNA hybridization microfluidic chip is the opposite direction of the electroosmotic flow and electrophoretic mobility of the oligonucleotides. This makes it difficult to simultaneously deliver targets and an appropriate hybridization buffer simultaneously to the probe sites. In this work we investigate the possibility of coating the inner walls of the microfluidic system with hexadimentrine bromide (polybrene, PB) and other cationic polymers in order to reverse the direction of electroosmotic flow so that it acts in the same direction as the electrophoretic transport of the oligonucleotides. The results indicated that the electroosmotic flow (EOF) in channels that were coated with the polymer could be reversed in 1× TBE buffer or 1× SSC buffer. Under these conditions, the DNA and EOF move in the same direction, and the flow can be used to deliver DNA to an area for selective hybridization within the channel. The effects of coating the surface of a nucleic acid microarray with polybrene were also studied to assess non-selective adsorption and stability. The polybrene coating significantly reduced the extent of non-selective adsorption of oligonucleotides in comparison to adsorption onto a glass surface, and the coating did not alter the extent of hybridization. The results suggest that use of the coating makes it possible to achieve semi-quantitative manipulation of nucleic acid oligomers for delivery to an integrated microarray or biosensor.     

Effect of magnetic field on electroosmotic flow of viscoelastic fluids in a microchannel

Electroosmotic flow is an efficient transportation technology driven by applying an external electric field across the microchannel, which has a great potential for future application. This work is presented to study the unsteady electroosmotic flow of viscoelastic fluids combined with a constant pressure gradient and a vertical magnetic field through a parallel plate microchannel. For the reason that the upper and bottom walls of the parallel plate microchannel in microfluidic devices can be made of different materials, this leads to different hydrophobic properties, asymmetric zeta wall potentials, and different slip boundary conditions. The Navier slip model with different slip coefficients at walls is considered. The generalized Maxwell fluid with fractional derivative is adopted for the constitutive equation of the fluid. The analytical and numerical solutions of velocity are derived by employing the integral transform method and finite difference method, respectively. Excellent agreement is found between the numerical solutions and analytical solutions. Finally, the effects of fractional parameter , relaxation time , slip coefficients and , the ratio of wall zeta potentials , Hartmann number , and electrical field strength parameter on velocity profiles are interpreted graphically in detail.     

Influence of varying electroosmotic flow on the effective diffusion in electric field gradient separations

Recently the use electric field gradient focusing (EFGF) to enhance focusing of proteins has been proposed and explored to provide significant improvement in separation resolution. The objective of EFGF is to focus proteins of specific electrophoretic mobilities at distinct stationary locations in a column or channel. This can be accomplished in a capillary by allowing the electric potential to vary in the streamwise direction. Because the electric field is varying, so also is the electrokinetic force exerted on the proteins and the electroosmotic velocity of the buffer solution. Due to the varying electric field, the Taylor diffusion characteristics will also vary along the column, causing a degradation of peak widths of some proteins, dependent on their equilibrium positions and local velocity distributions. The focus of this paper is an analysis that allows characterization of the local Taylor diffusion and resulting protein band peak width as a function of the local magnitude of the EOF relative to the average fluid velocity for both cylindrical and rectangular channels. In general the analysis shows that as the ratio of the local electroosmotic velocity to the average velocity deviates from unity, the effective diffusion increases significantly. The effectiveness of EFGF devices over a range of protein diffusivities, capillary diameters, flow velocities, and electric field gradient is discussed.     

Characterization of the SDS-induced electroosmotic flow in micellar electrokinetic chromatography with cationic polyelectrolyte-coated capillaries

Manipulation of the EOF is essential for achieving optimal separations by MEKC. In this paper, we present an extensive investigation of the effect of common experimental conditions on the EOF observed in a capillary coated with poly(diallyldimethylammonium chloride) (PDADMA) polyelectrolyte under MEKC conditions. It was found that highly reproducible cathodal EOF is achieved approximately at or just below the conditional CMC value of SDS in the electrolytes used. At concentrations of SDS greater than the CMC the EOF is independent of pH. The impact of common organic modifiers (ACN, methanol, urea, beta-CD and nonionic surfactant) on the EOF behavior in both a PDADMA-coated capillary and a bare silica capillary is compared. The suppressing effect of organic modifiers on the EOF is much stronger for coated capillary indicating that these compounds additionally reduce the negative charge density on the capillary surface due to alteration of the surfactant coating.     

Continuous and precise particle separation by electroosmotic flow control in microfluidic devices

A new scheme has been described for continuous particle separation using EOF in microfluidic devices. We have previously reported a method for particle separation, called "pinched flow fractionation (PFF)", in which size-dependent and continuous particle separation can be achieved by introducing pressure-driven flows with and without particles into a pinched microchannel. In this study, EOF was employed to transport fluid flows inside a microchannel. By controlling the applied voltage to electrodes inserted in each inlet/outlet port, the flow rates from both inlets, and flow rates distributed to each outlet could be accurately tuned, thus enabling more effective separation compared to the pressure-driven scheme. In the experiment, the particle behaviors were compared between EOF and pressure-driven flow schemes. In addition, micrometer- and submicrometer-sized particles were accurately separated and individually collected using a microchannel with multiple outlet branch channels, demonstrating the high efficiency of the presented scheme.     

Adsorption of buffer ion pairs can alter long‐term electroosmotic flow stability

Dynamic capillary coatings have become widespread due to their efficacy in modifying the EOF in capillary electrophoretic separations and ability to limit unwanted analyte‐surface interactions. However, our understanding of exactly what types of interactions are taking place at the surface of a capillary when these dynamic additives are present is limited. In this work, we have chosen a simple, small molecule additive, tetramethylammonium to examine its influence on the EOF under typical separation conditions. What we have revealed is that this simple compound does not interact with the capillary surface in a very simple manner. Our initial hypothesis of a direct ionic interaction with the silanol surface has evolved with evidence of complex ion pairing between the silanols, the tetramethylammonium, and the buffer ions. This ion pairing can result in drastic changes in the EOF over time, and that the EOF can only be restored to initial levels with harsh rinses containing sodium hydroxide.     

Elastic instabilities in the electroosmotic flow of non-Newtonian fluids through T-shaped microchannels

Electroosmotic flow (EOF) has been widely used to transport fluids and samples in micro- and nanofluidic channels for lab-on-a-chip applications. This essentially surface-driven plug-like flow is, however, sensitive to both the fluid and wall properties, of which any inhomogeneity may draw disturbances to the flow and even instabilities. Existing studies on EOF instabilities have been focused primarily upon Newtonian fluids though many of the chemical and biological solutions are actually non-Newtonian. We carry out a systematic experimental investigation of the fluid rheological effects on the elastic instability in the EOF of phosphate buffer-based polymer solutions through T-shaped microchannels. We find that electro-elastic instabilities can be induced in shear thinning polyacrylamide (PAA) and xanthan gum (XG) solutions if the applied direct current voltage is above a threshold value. However, no instabilities are observed in Newtonian or weakly shear thinning viscoelastic fluids including polyethylene oxide (PEO), polyvinylpyrrolidone (PVP), and hyaluronic acid (HA) solutions. We also perform a quantitative analysis of the wave parameters for the observed elasto-elastic instabilities.