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.     

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.     

Effects of surface heterogeneity on flow circulation in electroosmotic flow in microchannels

The characteristics of electroosmotic flow in a cylindrical microchannel with non-uniform zeta potential distribution are investigated in this paper. Two-dimensional full Navier–Stokes equation is used to model the flow field and the pressure field. The numerical results show the distorted electroosmotic velocity profiles and various kinds of flow circulation resulting from the axial variation of the zeta potential. The influences of heterogeneous patterns of zeta potential on the velocity profile, the induced pressure distribution and the volumetric flow rate are discussed in this paper. This work shows that using either heterogeneous patterns of zeta potential or a combination of a heterogeneous zeta potential distribution and an applied pressure difference over the channel can generate local flow circulations and hence provide effective means to improve the mixing between different solutions in microchannels.     

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.     

Liquid transport in rectangular microchannels by electroosmotic pumping

The characteristics of electroosmotic flow in rectangular microchannels were investigated in this paper. A 2D Poisson–Boltzmann equation and the 2D momentum equation were used to model the electric double layer field and the flow field. The numerical solutions show significant influences of the channel cross-section geometry (i.e. the aspect ratio) on the velocity field and the volumetric flow rate. Also, the numerical simulation of the electroosmotic flow reveals how the velocity field and the volumetric flow rate depend on the ionic concentration, zeta potential, channel size and the applied electrical field strength.     

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.     

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.     

Dynamic interfacial effect of electroosmotic slip flow with a moving capillary front in hydrophobic circular microchannels

Miniaturization of chemical analysis using microfabrication is an emerging technology. The use of polymeric materials as opposed to conventional glass substrate is also a promising alternative. As most polymeric materials are hydrophobic relative to glass, we describe here the implication for the loading process of electroosmotic flow (EOF) when a three-phase (solid-liquid-vapor) contact line exists. The presence of these interfaces can result in a large Laplace pressure that resists EOF and hence hinders its flow performance. This effect depends on the phenomenological contact angle at the solid-liquid interface. In our model for EOF, we considered simultaneously the presence of an electric double layer, liquid slips via a weaker solid-liquid interaction and Laplace pressure across a liquid-vapor interface.     

Visualizing the transient electroosmotic flow and measuring the zeta potential of microchannels with a micro-PIV technique

We have demonstrated a transient micro particle image velocimetry (micro-PIV) technique to measure the temporal development of electroosmotic flow in microchannels. Synchronization of different trigger signals for the laser, the CCD camera, and the high-voltage switch makes this measurement possible with a conventional micro-PIV setup. Using the transient micro-PIV technique, we have further proposed a method on the basis of inertial decoupling between the particle electrophoretic motion and the fluid electroosmotic flow to determine the electrophoretic component in the particle velocity and the zeta potential of the channel wall. It is shown that using the measured zeta potentials, the theoretical predictions agree well with the transient response of the electroosmotic velocities measured in this work.     

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.     

Control of electroosmotic flow in laser-ablated and chemically modified hot imprinted poly(ethylene terephthalate glycol) microchannels

The fabrication of microchannels in poly(ethylene terephthalate glycol) (PETG) by laser ablation and the hot imprinting method is described. In addition, hot imprinted microchannels were hydrolyzed to yield additional charged organic functional groups on the imprinted surface. The charged groups are carboxylate moieties that were also used as a means for the further reaction of different chemical species on the surface of the PETG microchannels. The microchannels were characterized by fluorescence mapping and electroosmotic flow (EOF) measurements. Experimental results demonstrated that different fabrication and channel treatment protocols resulted in different EOF rates. Laser-ablated channels had similar EOF rates (5.3+/-0.3 x 10(-4) cm(2)/Vs and 5.6+/-0.4 x 10(-4) cm(2)/Vs) to hydrolyzed imprinted channels (5.1+/-0.4 x 10(-4) cm(2)/Vs), which in turn demonstrated a somewhat higher flow rate than imprinted PETG channels that were not hydrolyzed (3.5+/-0.3 x 10(-4) cm(2)/Vs). Laser-ablated channels that had been chemically modified to yield amines displayed an EOF rate of 3.38+/- 0.1 x 10(-4) cm(2)/Vs and hydrolyzed imprinted channels that had been chemically derivatized to yield amines showed an EOF rate of 2.67+/-0.6 cm(2)/Vs. These data demonstrate that surface-bound carboxylate species can be used as a template for further chemical reactions in addition to changing the EOF mobility within microchannels.     

An analysis of induced pressure fields in electroosmotic flows through microchannels

Induced pressure gradients are found to cause band-broadening effects which are important to the performance of microfluidic devices, such as capillary electrophoresis and capillary chromatography. An improved understanding of the underlying mechanisms causing an induced pressure gradient in electroosmotic flows is presented. The analysis shows that the induced pressure distribution is the key to understanding the experimentally observed phenomena of leakage flows. A novel way of determining the static pressures at the inlet and outlet of microchannels is also presented that takes account of the pressure losses due to flow contraction and expansion. These commonly neglected pressure losses at the channel entrance and outlet are shown to be important in accurately describing the flow. The important parameters that define the effect of induced pressure on the flows are discussed, which may facilitate the design of improved microfluidic devices. The present model clearly identifies the mechanism behind the experimentally observed leakage flows, which is further confirmed by numerical simulations. Not only can the leakage flow occur from the electric-field-free side channel to the main channel, but also the fluid in the main channel can be attracted into the side channel by the induced pressure gradient.     

Hydrodynamic flow and electroosmotic flow in zirconia-packed capillaries

Fused-silica capillaries were packed with Zirchrom-PBD stationary phase for application in CEC, nanoLC and pseudoelectrochromatography (PEC). Acido-basic properties of zirconia can be used to control the EOF even if the zirconia particles were coated by polybutadiene. As for native zirconia, the EOF is pH-dependent and the pI is close to pH 5. The mixed-mode pressure-voltage technique induced a modulation of the mobile-phase velocity as well as an electrophoretic migration of the solutes in order to improve the resolution of the separation. A significant increase of the flow appeared when both hydrodynamic and EOFs were in the same direction. But an important reduction of the electroosmotic velocity was observed when the hydrodynamic flow and EOF were opposed in Zirchrom-PBD columns. This behaviour has been observed at high or low pH on several columns. Separations of neutral and charged compounds have been performed with these columns in PEC mode.     

Characterizing electroosmotic flow in microfluidic devices

The current-monitoring method was used to measure the electroosmotic flow (EOF) in borosilicate glass capillaries and zeonor plastic microfluidic devices. The surface of the zeonor devices must be oxidized to support EOF and this treatment shows signs of aging within 6 days. Oxidized zeonor devices showed the same response to changes in applied field, pH, and ionic concentration as the capillaries. The effects of several common dynamic surfactant coatings on the walls were also studied (0.1%, v/v solutions of POP-6, POP4, Pluronics L81, and NP-40). These generally significantly suppressed the EOF but required several days to stabilize.     

Diffusioosmotic flow in rectangular microchannels

The diffusioosmosis of an electrolyte solution inside a uniformly charged rectangular channel at steady locally developed conditions is the subject of this study. Utilizing a finite element based numerical procedure, we try to estimate the errors incurred by modeling the actual rectangular geometry of typical microchannels as a slit. We demonstrate that the flow pattern and direction are generally dependent upon the width‐to‐height ratio of the channel. Such a finding, besides showing the ineffectiveness of the slit geometry in representing a rectangular channel of small aspect ratio, informs us of another mechanism of controlling the diffusioosmotic flow. Inspections of the mean velocity reveal that, although it drastically grows by increasing the aspect ratio at smaller values of this parameter, no significant change is observed when the aspect ratio is 5 or higher. The same trend is observed when EDL is shrunk and is considered as a basis for the introduction of a slip‐like velocity, similar to the concept of the Helmholtz–Smoluchowski electroosmotic velocity, which will be of high practical importance when dealing with a micronsized channel. Because of its significance, an expression is presented for this slip velocity utilizing the curve fitting of the results, assuming a typical Peclet number.     

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.     

Nonstationary electroosmotic flow in closed cylindrical capillaries

A theoretical model of the EOF and hydrodynamic flow in wide closed cylindrical capillaries, after the application of a stepwise voltage, is developed. Analytical expressions have been obtained as a sum of the solutions for the direct flow and backflow in both periodical and aperiodical regimes with arbitrary pulse/pulse or pulse/pause durations and amplitudes. The numerical analysis, performed for a few types of periodical and aperiodical regimes, shows the qualitative peculiarities of the liquid velocity profiles and its displacement for different numbers of pulses. The obtained results are compared with those obtained in the case of open capillaries. The possibility of the application of aperiodical stepwise regime for the investigation of electrophoresis is discussed.     

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.     

Nonstationary electroosmotic flow in open cylindrical capillaries

A theoretical model of the EOF established in a wide capillary after the application of a stepwise voltage has been developed. Both periodical and aperiodical flow regimes were studied with arbitrary pulse/pulse or pulse/pause durations and amplitudes. The numerical analysis performed for a few types of periodical regimes showed the peculiarities of the profiles of liquid velocity and its displacement both for the transition to the stationary regime and for the quasi-stationary periodical and aperiodical regimes.     

Control of electroosmotic flow in zirconia-coated capillaries

Investigations concerning the qualitative and quantitative determination of the organic wood preservative component N-cyclohexyl-diazeniumdioxide (HDO) in treated timber were carried out by means of direct thermal desorption-gas chromatography-mass spectrometry (DTD-GC-MS). It could be shown that the identification of HDO in treated pine sapwood (Pinus sylyestris L.) is relatively simple using this analytical technique. Quantification of this active ingredient can be carried out using the peak area of the specific mass fragment m/z 114. A calibration curve with a high correlation coefficient was obtained in the range from 40 to 550 mg HDO per kg timber. Furthermore it can be deduced that the results obtained are characterised by an excellent reproducibility with standard deviations ranging from 5 to 10% in general. For the chosen experimental set up a detection limit of 4 mg HDO per kg treated pine sapwood was calculated, although merely 20% of the active ingredient was desorbed.