A model for Joule heating-induced dispersion in microchip electrophoresis

This paper presents an analytical and parameterized model for analyzing the effects of Joule heating on analyte dispersion in electrophoretic separation microchannels. We first obtain non-uniform temperature distributions in the channel resulting from Joule heating, and then determine variations in electrophoretic velocity, based on the fact that the analyte's electrophoretic mobility depends on the buffer viscosity and hence temperature. The convection-diffusion equation is then formulated and solved in terms of spatial moments of the analyte concentration. The resulting model is validated by both numerical simulations and experimental data, and holds for all mass transfer regimes, including unsteady dispersion processes that commonly occur in microchip electrophoresis. This model, which is given in terms of analytical expressions and fully parameterized with channel dimensions and material properties, applies to dispersion of analyte bands of general initial shape in straight and constant-radius-turn channels. As such, the model can be used to represent analyte dispersion in microchannels of more general shape, such as serpentine- or spiral-shaped channels.     

Turn-induced isotachophoretic focusing in microfluidic channels

Multifunctional microfluidic platforms that use ITP for sample stacking require the use of serpentine channels. When ITP is carried out in serpentine passages, the sample band shows dramatically different behavior than that observed in conventional on-chip CE. The band skew, defined as the distance between the leading and trailing edge of the band, is reduced and the sample is focused on the outside wall of the turn. This effect is explained using a simplified analytical model for the infinite Peclet number limit and the predicted trends are compared to full numerical simulations and experimental measurements. The outward focusing is driven by a wall-normal electric field that results from the skewed leading buffer-trailing buffer (LB-TB) interface. The results indicate that the degree of outward focusing is controlled by the ratio of the LB and TB conductivities, the ratio of the channel width to turn radius, and the Peclet number. Increasing the band skew, which shows a complex dependence on the nondimensional parameters, maximizes the outward focusing effect.     

Peak compression and resolution for electrophoretic separations in diverging microchannels

We report the results of experiments and simulations on electrokinetic flow in diverging microchannels (with cross-sectional area that increases with distance along the channel). Because of conservation of mass and charge, the velocity of an analyte in the channel decreases as the channel cross-section increases. Consequently, the leading edge of a band of sample moves more slowly than the trailing edge and the sample band is compressed. Sample peak widths, rather than increasing diffusively with time, can then be controlled by the geometry of the channel and can even be made to decrease with time. We consider the possibility of using this peak compression effect to improve the resolution of electrophoretic separations. Our results indicate that for typical separations that are dispersion limited, this peak compression effect is more than offset by the decreased distance between peaks, and the separation resolution in diverging channels is worse than that found for straight channels at the same applied voltage. For separations in very short channels or at very high field strengths, however, when the separation efficiency is injection limited, the peak compression effect is dominant and diverging channels can then be used to achieve improved separation resolution.     

Density gradients in packed columns: II. Effects of density gradients on efficiency in supercritical fluid separations

To investigate how fluid compressibility affects efficiency in supercritical fluid separations, band dispersion along a packed capillary column was measured from on-column elution rate profiles obtained under solvating gas chromatography (SGC) conditions; this allowed efficiency to be determined with respect to position along the column. Theoretical efficiency was also modeled. The model indicates that the primary cause of band broadening in SGC is high mobile phase velocity near the column outlet. However, the experimental results show that significant band broadening also occurs near the column inlet in a region that corresponds to high elution rates of the analyte. On-column detection also revealed spatial focusing of the analyte as it moves down the column density gradient.     

Peak dispersion and contributions to plate height in nonaqueous capillary electrophoresis at high electric field strengths: ethanol as background electrolyte solvent

Nonaqueous capillary electrophoretic separations were performed under high electric field strengths (up to 2000 Vcm(-1)) in ethanolic background electrolyte solution and the contributions of different band broadening effects to plate height were evaluated. Under optimum conditions, increasing the field strength will provide faster separations and increased separation efficiency. Decrease in the separation efficiency at high field strengths was, however, observed in a previous study and now in the present paper an attempt is made to quantify various band broadening effects by applying a plate height model, which included the contributions of the injection plug length, diffusion, electromigration dispersion, Joule heating, analyte adsorption to the capillary wall, and detector slit aperture length. Of special interest were the contributions of Joule heating and analyte adsorption to the capillary wall. Poly(glycidylmethacrylate-co-N-vinylpyrrolidone)-coated fused-silica capillaries were used with internal diameters (ID) ranging from 30 to 75 microm. The separation efficiencies obtained experimentally were compared with the theoretically calculated efficiencies and fairly good agreement was observed for the 30 microm ID capillary. Relatively large deviation from the predictions of the model was found for the other capillary diameters especially at higher field strengths. The possible reasons for the deviation were discussed.     

Microchip electrophoresis of N-glycans on serpentine separation channels with asymmetrically tapered turns

We designed and fabricated microfluidic devices with serpentine separation channels and asymmetrically tapered turns, thus allowing high efficiency separations and minimizing band broadening associated with the “racetrack” effect. We evaluated the performance of these devices by measuring the variation in separation efficiency with separation length, electric field strength, taper ratio of the turns, and number of turns. N‐Glycans derived from ribonuclease B and labeled with 8‐aminopyrene‐1,3,6‐trisulfonic acid were electrophoretically separated on serpentine channels with separation lengths of 11, 18, 22, and 36 cm at electric field strengths from 750 to 1750 V/cm. Separations on the 36‐cm channel produced plate numbers up to 940 000 with an analysis time under 3.1 min, whereas separations on the 22‐cm channel had a shorter analysis time (less than 1.25 min), still with respectable efficiencies (up to 600 000 plates). Turn‐induced dispersion was minimized with taper ratios 2 and 3, whereas having two or four 180° turns along with the separation length did not impact the overall efficiency. The developed device was used to analyze native and desialylated N‐glycans derived from the blood serum of an ovarian cancer patient and a disease‐free individual. Separation efficiencies similar to that achieved with the model glycans from ribonuclease B were attained for these biological samples.     

Characterization of voltage degradation in dynamic field gradient focusing

Dynamic field gradient focusing (DFGF) is an equilibrium gradient method that utilizes an electric field gradient to simultaneously separate and concentrate charged analytes based on their individual electrophoretic mobilities. This work describes the use of a 2-D nonlinear, numerical simulation to examine the impact of voltage loss from the electrodes to the separation channel, termed voltage degradation, and distortions in the electric field on the performance of DFGF. One of the design parameters that has a large impact on the degree of voltage degradation is the placement of the electrodes in relation to the separation channel. The simulation shows that a distance of about 3 mm from the electrodes to the separation channel gives the electric field profile with least amount of voltage degradation. The simulation was also used to describe the elution of focused protein peaks. The simulation shows that elution under constant electric field gradient gives better performance than elution through shallowing of the electric field. Qualitative agreement between the numerical simulation and experimental results is shown. The simulation also illustrates that the presence of a defocusing region at the cathodic end of the separation channel causes peak dispersion during elution. The numerical model is then used to design a system that does not suffer from a defocusing region. Peaks eluted under this design experienced no band broadening in our simulations. Preliminary experimental results using the redesigned chamber are shown.     

Scaling behavior in on‐chip field‐amplified sample stacking

Field amplified sample stacking (FASS) uses differential electrophoretic velocity of analyte ions in the high‐conductivity background electrolyte zone and low conductivity sample zone for increasing the analyte concentration. The stacking rate of analyte ions in FASS is limited by molecular diffusion and convective dispersion due to nonuniform electroosmotic flow (EOF). We present a theoretical scaling analysis of stacking dynamics in FASS and its validation with a large set of on‐chip sample stacking experiments and numerical simulations. Through scaling analysis, we have identified two stacking regimes that are relevant for on‐chip FASS, depending upon whether the broadening of the stacked peak is dominated by axial diffusion or convective dispersion. We show that these two regimes are characterized by distinct length and time scales, based on which we obtain simplified nondimensional relations for the temporal growth of peak concentration and width in FASS. We first verify the theoretical scaling behavior in diffusion‐ and convection‐dominated regimes using numerical simulations. Thereafter, we show that the experimental data of temporal growth of peak concentration and width at varying electric fields, conductivity gradients, and EOF exhibit the theoretically predicted scaling behavior. The scaling behavior described in this work provides insights into the effect of varying experimental parameters, such as electric field, conductivity gradient, electroosmotic mobility, and electrophoretic mobility of the analyte on the dynamics of on‐chip FASS.     

Development of a positive pressure driven micro-fabricated liquid chromatographic analyzer through rapid-prototyping with poly(dimethylsiloxane) Optimizing chromatographic efficiency with sub-nanoliter injections

A rapid and low-cost means of developing a working prototype for a positive-displacement driven open tubular liquid chromatography (OTLC) analyzer is demonstrated. A novel flow programming and injection strategy was developed and implemented using soft lithography, and evaluated in terms of chromatographic band broadening and efficiency. A separation of two food dyes served as the model sample system. Sample and mobile phase flowed continuously by positive displacement through the OTLC analyzer. Rectangular channels, of dimensions 10 μm deep by 100 μm wide, were micro-fabricated in poly-dimethylsiloxane (PDMS), with the separation portion 6.6 cm long. Using a novel flow programming method, in contrast to electroosmotic flow, sample injection volumes from 0.5 to 10 nl were made in real-time. Band broadening increased substantially for injection volumes over 1 nl. Although underivatized PDMS proved to be a sub-optimal stationary phase, plate heights, H, of 12 μm were experimentally achieved for an unretained analyte with the rectangular channel resulting in a reduced plate height, h, of 1.2. Chromatographic efficiency of the unretained analyte followed the model of an OTLC system limited by mass-transfer in the mobile phase. Flow rates from 6 nl min⁻¹ up to 200 nl min⁻¹ were tested, and van Deemter plots confirmed plate heights were optimum at 6 nl min⁻¹ over the tested flow rate range. Thus, the best separation efficiency, N of 5500 for the 6.6 cm length separation channel, was achieved at the minimum flow rate through the column of 6 nl min⁻¹, or 3 ml year⁻¹. This analyzer is a low-cost sampling and chemical analysis tool that is intended to complement micro-fabricated electrophoretic and related separation devices.     

Peak tailing in electrophoresis due to alteration of the wall charge by adsorbed analytes a: Numerical simulations and asymptotic theory

When analytes containing cationic components, such as proteins, are separated in fused silica capillaries or micro-chips, they adsorb strongly to the negatively charged channel walls. Broadened and highly asymmetric peaks in the detector signal is symptomatic of the presence of such wall interactions. Band broadening is caused by the introduction of shear into the electroosmotic flow which leads to Taylor dispersion. The shearing flow in turn is caused by axial variations in zeta-potential due to adsorbed analytes. In this paper, numerical solutions of the coupled electro-hydrodynamic equations for fluid flow and the advection-diffusion equation for analyte concentration are presented in the limit of thin Debye layers. The simulations reproduce many of the qualitative effects of wall adsorption familiar from observation. Further, the simulation results are compared, and found to agree very well (to within a percent for characteristic values of the parameters) with a recently developed asymptotic theory.     

Study on the influence of cross-sectional area and zeta potential on separation for hybrid-chip-based capillary electrophoresis using 3-D simulations

Hybrid chips combing microchips with capillaries have displayed particular advantages in achieving UV-vis and mass spectroscopic detection. In this work, systematic 3-D numerical simulations have been carried out to explore the influence of junction interface cross-sectional area and ζ-potential distribution on sample band broadening in hybrid-chip electrophoresis separation. In this case, the ratio of cross-sectional area of chip to capillary channel (S(ratio) ) is used as the parameter of the variation in junction interface cross-sectional area. Theoretical simulations demonstrated that the decrease of the S(ratio) would increase the separation efficiency in the hybrid-chip-based CE with uniform ζ-potential distribution. ζ-potential distribution along the axial direction of the channel also affects mass transport in hybrid-chip-based CE. Therefore, the effect of ζ-potential distribution has been considered in the 3-D simulation. Theoretical simulation results reveal that ζ-potential distribution rather than the interface cross-sectional area variation (S(ratio) ) controls the sample band broadening and manipulates sample separation efficiency in the hybrid-chip-based CE with non-uniform ζ-potential distribution. Both the theoretical simulations and experimental results show that optimal hybrid-chip CE separation efficiency can be achieved at S(ratio) =1.     

Analysis of geometry effects on band spreading of microchip electrophoresis

The geometry and the flow field conditions in the separation microchannel of an electrophoresis chip system may have important impact on the system's separation efficiency. Understanding the geometry effect on the flow field physics in the separation microchannel is beneficial to the design or operation of an electrophoresis system. The turns in a microfabricated separation microchannel generally results in degraded separation quality. To avoid this limitation, channels are constructed with different types of turns to determine the optimum design that minimizes turn-induced band broadening. We have designed and tested various geometric bend ratios to greatly reduce this so-called "racetrack" effect. The effects of the separation channel geometry, fluid velocity profile and bend ratio on the band distribution in the detection area are discussed. Results show that the folded square U-shaped channel is better for miniaturization and simplification. The band tilting was corrected and the racetrack effect reduced in the detection area when the bend ratio is 4:1. The detection time obtained from the present numerical solution matches very well with the experimental data.     

Denaturing gradient-based two-dimensional gene mutation scanning in a polymer microfluidic network

An integrated two-dimensional (2-D) DNA separation platform, combining standard gel electrophoresis with temperature gradient gel electrophoresis (TGGE) on a polymer microfluidic chip, is reported. Rather than sequentially sampling DNA fragments eluted from standard gel electrophoresis, size-resolved fragments are simultaneously electrokinetically transferred into an array of orthogonal microchannels and screened for the presence of sequence heterogeneity by TGGE in a parallel and high throughput format. A bulk heater assembly is designed and employed to externally generate a temporal temperature gradient along an array of TGGE channels. Extensive finite element modeling is performed to determine the optimal geometries of the microfluidic network for minimizing analyte band dispersion caused by interconnected channels in the network. A pH-mediated on-chip analyte stacking strategy is employed prior to the parallel TGGE separations to further reduce additional band broadening acquired during the electrokinetic transfer of DNA fragments between the first and second separation dimensions. A comprehensive 2-D DNA separation is completed in less than 5 min for positive detection of single-nucleotide polymorphisms in multiplex PCR products that vary in size and sequence.     

Dispersion effects of laminar flow and spray chamber volume in capillary electrophoresis-inductively coupled plasma-mass spectrometry: a numerical and experimental approach

Band broadening related to laminar flow and spray chamber dead volume is a potential problem in flow injection (FI)-inductively coupled plasma-mass spectrometry (ICP-MS). We studied these two dispersion effects with a sheath flow capillary electrophoresis (CE)-ICP-MS interface. A numerical model was used to simulate advection diffusion processes in the CE-capillary and dispersion in the spray chamber. Experimental results of FI with this CE-ICP-MS interface agree well with numerical modeling results. Dispersion due to laminar flow depends strongly on capillary diameter and analyte diffusion coefficient and to a lesser extent on laminar velocity and capillary length and typically amounts to one order of magnitude peak width increase. Three spray chambers of 5, 20 and 150 ml dead volume showed an increase in band broadening and peak tailing with increasing dead volume. The use of standard Scott-type spray chambers (>90 ml volume) increases peak widths by 5-10 s regardless of injection time. The use of a low dead volume spray chamber is recommended for experiments where resolution is critical. The modeling approach can be extended to the coupling of other flow injection techniques, like micro-LC and nano-LC with ICP-MS.     

Efficiency studies in nonaqueous capillary electrophoresis

Nonaqueous capillary electrophoresis (NACE) is a relatively new area with several advantages that include enhanced efficiency and improved detection sensitivity. The goal of this study was to investigate the influence of NACE compared to aqueous CE on the separation efficiency of oligosaccharides. The applied voltage and buffer concentration were optimized for the aqueous and nonaqueous buffer media to minimize the band broadening effects of Joule heating and electrophoretic dispersion. At the optimized conditions a 1.5-fold enhancement in efficiency was obtained with the nonaqueous buffer medium.     

Low-dispersion electrokinetic flows for expanded separation channels in microfluidic systems: multiple faceted interfaces

A novel methodology to design on-chip conduction channels is presented for expansion of low-dispersion separation channels. Designs are examined using two-dimensional numerical solutions of the Laplace equation with a Monte Carlo technique to model diffusion. The design technique relies on trigonometric relations that apply for ideal electrokinetic flows. Flows are rotated and stretched along the abrupt interface between adjacent regions having differing specific permeability. Multiple interfaces can be placed in series along a channel. The resulting channels can be expanded to extreme widths while minimizing dispersion of injected analyte bands. These channels can provide a long path length for line-of-sight optical absorption measurements. Expanded sections can be reduced to enable point detection at the exit section of the channel. Designed to be shallow, these channels have extreme aspect ratios in the wide section, greatly increasing the surface-to-volume ratio to increase heat removal and decrease unwanted pressure-driven flow. The use of multiple interfaces is demonstrated by considering several three-interface designs. Faceted flow splitters can be constructed to divide channels into any number of exit channels while minimizing dispersion. The resulting manifolds can be used to construct medians for structural support in wide, shallow channels.     

On-chip fraction collection for multiple selected ssDNA fragments using isolated extraction channels

High efficiency and high-purity fraction collection is highly sought in analysis of fragments-of-interest from selective polymerase chain reaction (PCR) products generated by High Coverage Gene Expression Profiling (HiCEP) methods. Here we demonstrate a new electrophoretic chip device enabling automatic high-efficient fractionation of multiple ssDNA target fragments during a run of separation. We used thoroughly isolated extraction channels for each selected target to reduce the risk of cross-contamination between targets due to cross-talk of extraction channels. Fragments of 35, 108 and 138 b, were successfully isolated, then the recovery was PCR-amplified and assessed by capillary electrophoresis (CE) analysis. Total impurity level of the targets due to unwanted fragments of 0.7%, 2% and 6% respectively, was estimated. Difficulties in collecting multiple target factions are due to band diffusion and DNA adsorption to the walls for the fragments in the separation channel, which is generated by transferring the DNA target fraction from the extraction section to the target reservoir. Therefore, we have carefully measured band broadening and analyzed its influence on the separation resolution due to the delay.     

Experimental characterization of hydrodynamic dispersion in shallow microchannels

Hydrodynamic dispersion in shallow microchannels with almost parabolic cross-sectional shapes and with heights much less than their widths is studied experimentally. Both long serpentine channels and rotary mixers are used. The experimental results demonstrate that the dispersion depends on the width rather than the height of the channel. The results are in quantitative agreement with a recently proposed theory of dispersion in shallow channels.     

平面二维毛细管电泳初探

在石英单晶表面制成短形截面的毛细管柱上进行了电泳实验。由于矩形柱比国形住有更大散热侧面积且石英单晶的导热性能远远优于熔融石英,所以可施加较高的场强,不仅提高了住效,而且缩短了分离时间。两个相交的通道之间形成自然连接,可实现二维分离,并消除了死体积。