毛细管电泳样品电堆积富集过程的数值研究

毛细管电泳样品电堆积富集过程可以浓缩样品组分,从而提高检测灵敏度,是一种有效的样品富集技术。本文通过合理的简化和假设,把毛细管中电堆积富集过程中所涉及的主要变量根据电势分布方程、缓冲溶液的浓度方程和样品粒子的质量传输方程进行耦合求解,建立了一个一维的数学模型,并应用有限元的方法对该模型进行了求解。计算结果给出了毛细管中缓冲溶液浓度及电场强度的分布随时间变化的过程,以及富集过程中毛细管中的电势分布曲线;得到了样品粒子浓度在电堆积富集过程和富集之后的再次扩散过程中的分布曲线以及正、负样品粒子的分离过程;最后分析了不同缓冲溶液浓度比对样品富集效果的影响。该研究为样品电堆积富集技术的进一步完善提供了一种简单可行的理论研究方法。     

Effects of liquid conductivity differences on multi-component sample injection, pumping and stacking in microfluidic chips

As an increasing number of processes are being integrated into Lab-on-a-chip devices, there is an increasing need for flexible and accurate sample manipulation techniques for effective transport and separation. Conductivity differences between running buffer and analyte samples can arise as a product of on-chip processing, or by design. The two situations studied here are sample pumping (where bulk transport is increased and separation of charged analytes is delayed using a relatively high conductivity sample), and sample stacking (where bulk transport is decreased and separation of charged analytes is expedited using a relatively low conductivity sample). A recently developed dynamic loading method for on-chip sample injection in a straight-cross channel configuration is applied here to both pumping and stacking cases. A key characteristic of the dynamic loading method is the ability to inject samples of high concentration density and uniformity of any length. By employing the conductivity differences alone, the effectiveness of either sample transport or sample separation are shown to improve over the uniform conductivity case. Then it is demonstrated that increasing the sample length, through dynamic loading, greatly increases the effectiveness of sample pumping, evidenced in an eight-fold increase in peak height as well as a decrease in total sample length at a downstream detector. Dynamic loading in the sample stacking case was shown to also increase peak intensity height (three-fold) in rapid separations. These results demonstrate that the dynamic loading technique, used in conjunction with strategic conductivity differences, significantly extends the capabilities of microfluidic chips.     

A microchip electrophoresis system with integrated in-plane electrodes for contactless conductivity detection

We present a new approach for contactless conductivity detection for microchip-based capillary electrophoresis (CE). The detector integrates easily with well-known microfabrication techniques for glass-based microfluidic devices. Platinum electrodes are structured in recesses in-plane with the microchannel network after glass etching, which allows precise positioning and batch fabrication of the electrodes. A thin glass wall of 10-15 microm separates the electrodes and the buffer electrolyte in the separation channel to achieve the electrical insulation necessary for contactless operation. The effective separation length is 34 mm, with a channel width of 50 microm and depth of 12 microm. Microchip CE devices with conductivity detection were characterized in terms of sensitivity and linearity of response, and were tested using samples containing up to three small cations. The limit of detection for K+ (18 microM) is good, though an order of magnitude higher than for comparable capillary-based systems and one recently reported example of contactless conductivity on chip. However, an integrated field-amplified stacking step could be employed prior to CE to preconcentrate the sample ions by a factor of four.     

Numerical modeling of Joule heating-induced temperature gradient focusing in microfluidic channels

Temperature gradient focusing (TGF) is a recently developed technique for spatially focusing and separating ionic analytes in microchannels. The temperature gradient required for TGF can be generated either by an imposed temperature gradient or by Joule heating resulting from an applied electric field that also drives the flow. In this study, a comprehensive numerical model describing the Joule heating induced temperature development and TGF is developed. The model consists of a set of governing equations including the Poisson-Boltzmann equation, the Laplace equation, the Navier-Stokes equations, the energy equations and the mass transport equation. As the thermophysical and electrical properties including the liquid dielectric constant, viscosity, and electric conductivity are temperature-dependent, these governing equations are coupled, and therefore the coupled governing equations are solved numerically by using a CFD-based numerical method. The numerical simulations agree well with the experimental results, suggesting the valid mathematical model presented in this study.     

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier-Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye-Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study.     

Study of Joule heating effects on temperature gradient in diverging microchannels for isoelectric focusing applications

IEF is a high-resolution separation method taking place in a medium with continuous pH gradients, which can be set up by applying electrical field to the liquid in a diverging microchannel. The axial variation of the channel cross-sectional area will induce nonuniform Joule heating and set up temperature gradient, which will generate pH gradient when proper medium is used. In order to operationally control the thermally generated pH gradients, fundamental understanding of heat transfer phenomena in microfluidic chips with diverging microchannels must be improved. In this paper, two 3-D numerical models are presented to study heat transfer in diverging microchannels, with static and moving liquid, respectively. Through simulation, the temperature distribution for the entire chip has been revealed, including both liquid and solid regions. The model for the static liquid scenario has been compared with published results for validation. Parametric studies have showed that the channel geometry has significant effects on the peak temperature location, and the electrical conductivity of the medium and the wall boundary convection have effects on the generated temperature gradients and thus the generated pH gradients. The solution to the continuous flow model, where the medium convection is considered, shows that liquid convection has significant effects on temperature distribution and the peak temperature location.     

Stacking due to ionic transport number mismatch during sample sweeping on microchips

Sample stacking can occur in isoconductive buffer systems as a result of ion transport mismatches that cause changes in buffer conductivity during electrophoresis. Fluorescence imaging was used to examine this effect in the sweeping of hydrophobic dyes with sodium dodecyl sulfate (SDS) on microchips. Imaging revealed the occurrence of a stacking effect in a sodium borate buffer system in which the sample buffer and SDS-containing run buffer had the same initial conductivity. Injected sample plugs were first swept by SDS micelles and the swept band was then stacked at the trailing end of the sample zone. This effect is due to changes in conductivity at both the front and back interfaces of the injected sample plug and can be modeled by moving boundary equations. Maximum signal enhancements of 86-, 160- and 560-fold were obtained for Rhodamine 560, Rhodamine B and Rhodamine 6G, respectively, by the combination of sweeping and stacking within a 1 cm section of microchannel. Based on sample sweeping/stacking and manipulation of the electric field polarity, a method of trapping and concentrating analyte from multiple injections was also demonstrated.     

Finite sample effect in temperature gradient focusing

Temperature gradient focusing (TGF) is a new and promising equilibrium gradient focusing method which can provide high concentration factors for improved detection limits in combination with high-resolution separation. In this technique, temperature-dependent buffer chemistry is employed to generate a gradient in the analyte electrophoretic velocity. By the application of a convective counter-flow, a zero-velocity point is created within a microchannel, at which location the ionic analytes accumulate or focus. In general, the analyte concentration is small when compared with buffer ion concentrations, such that the focusing mechanism works in the ideal, linearized regime. However, this presumption may at times be violated due to significant sample concentration growth or the use of a low-concentration buffer. Under these situations the sample concentration becomes non-negligible and can induce strong nonlinear interactions with buffer ions, which eventually lead to peak shifting and distortion, and the loss of detectability and resolution. In this work we combine theory, simulation, and experimental data to present a detailed study on nonlinear sample-buffer interactions in TGF. One of the key results is the derivation of a generalized Kohlrausch regulating function (KRF) that is valid for systems in which the electrophoretic mobilities are not constant but vary spatially. This generalized KRF greatly facilitates analysis, allowing reduction of the problem to a single equation describing sample concentration evolution, and is applicable to other problems with heterogeneous electrophoretic mobilities. Using this sample evolution equation we have derived an understanding of the nonlinear peak deformation phenomenon observed experimentally in TGF. We have used numerical simulations to validate our theory and to quantitatively predict TGF. Our simulation results demonstrate excellent agreement with experimental data, and also indicate that the proper inclusion of Taylor dispersion is important for the accurate modeling of TGF. This work is an important first step towards the understanding and prediction of the more complex, nonlinear, and multi-species interactions which often occur in on-chip electrophoretic assays such as TGF.     

Assessing the scalability of dynamic field gradient focusing by linear modeling

Dynamic field gradient focusing (DFGF) separates and concentrates proteins in native buffers, where proteins are most soluble, using a computer-controlled electric field gradient which lets the operator adjust the pace and resolution of the separation in real-time. The work in this paper assessed whether DFGF could be scaled up from microgram analytical-scale protein loads to milligram preparative-scale loads. Linear modeling of the electric potential, protein transport, and heat transfer simulated the performance of a preparative-scale DFGF instrument. The electric potential model showed where the electrodes should be placed to optimize the shape and strength of the electric field gradient. Results from the protein transport model suggested that in 10 min the device should separate 10 mg each of two proteins whose electrophoretic mobilities differ by 5 x. Proteins with electrophoretic mobilities differing by only 5% should separate in 3 h. The heat transfer model showed that the preparative DFGF design could dissipate 1 kW of Joule heat while keeping the separation chamber at 25 degrees C. Model results pointed to DFGF successfully scaling up by 1000 x using the proposed instrument design.     

Simultaneous concentration and separation of microorganisms: insulator-based dielectrophoretic approach

Microanalytical methods offer attractive characteristics for rapid microbial detection and concentration. There is a growing interest in the development of microscale separation techniques. Dielectrophoresis (DEP), a nondestructive electrokinetic transport mechanism, is a technique with great potential for microbe manipulation, since it can achieve concentration and separation in a single step. DEP is the movement of particles due to polarization effects in nonuniform electric fields. The majority of the work on dielectrophoretic manipulation of microbes has employed alternating current fields in arrays of microelectrodes, an approach with some disadvantages. An alternative is to employ insulator-based DEP (iDEP), a dielectrophoretic mode where nonuniform fields are produced by employing arrays of insulating structures. This study presents the concentration and fractionation of a mixture of bacteria and yeast cells employing direct current-iDEP in a microchannel containing an array of cylindrical insulating structures. Negative dielectrophoretic trapping of both types of microorganisms was demonstrated, where yeast cells exhibited a stronger response, opening the possibility for dielectrophoretic differentiation. Simultaneous concentration and fractionation of a mixture of both types of cells was carried out analogous to a chromatographic separation, where a dielectropherogram was obtained in less than 2 min by applying an electric field gradient and achieving concentration factors in the order of 50 and 37 times the inlet concentration for Escherichia coli and Saccharomyces cerevisiae cells, respectively. Encouraging results were also obtained employing a sample of water taken from a pond. The findings demonstrated the great potential of iDEP as a rapid and effective technique for intact microorganism concentration and separation.     

Influence of ionic constituents and electrical conductivity on the propagation of charged nanoscale objects in passivated gel electrophoresis

When determining the electric field E acting on charged objects in gel electrophoresis, the electrical conductivity of the buffer solution is often overlooked; E is typically calculated by dividing the applied voltage by a separation distance between electrodes. However, as a consequence of electrolytic reactions, which occur at the electrodes, gradients in the ionic content of the buffer solution and its conductivity can potentially develop over time, thereby impacting E and affecting propagation velocities of charged objects, v, directly. Here, we explore how the types and concentrations of ionic constituents of the buffer solution, which largely control its conductivity, when used in passivated gel electrophoresis (P‐gelEP), can influence E, thereby altering v of charged nanospheres propagating through large‐pore gels. We measure the conductivity of the buffer solution in the center of the gel region near propagating bands of nanospheres, and we show that predictions of E based on conductivity closely correlate with v. We also explore P‐gelEP involving two different types of passivation agents: nonionic polyethylene glycol (PEG) and anionic sodium dodecyl sulfate (SDS). Our observations indicate that using a conductivity model to determine E from the local current density and the conductivity where spheres are propagating can lead to a better estimate than the standard approach of a voltage divided by a separation. Moreover, this conductivity model also provides a starting point for interpreting the complex behavior created by amphiphilic ionic passivation agents, such as SDS, on propagating nanospheres used in some P‐gelEP experiments.     

Quantification of pH gradients and implications in insulator-based dielectrophoresis of biomolecules

Direct current (DC) insulator-based dielectrophoretic (iDEP) microdevices have the potential to replace traditional alternating current dielectrophoretic devices for many cellular and biomolecular separation applications. The use of large DC fields suggest that electrode reactions and ion transport mechanisms can become important and impact ion distributions in the nanoliters of fluid in iDEP microchannels. This work tracked natural pH gradient formation in a 100?μm wide, 1?cm-long microchannel under applicable iDEP protein manipulation conditions. Using fluorescence microscopy with the pH-sensitive dye FITC Isomer I and the pH-insensitive dye TRITC as a reference, pH was observed to drop drastically in the microchannels within 1?min in a 3000?V/cm electric field; pH drops were observed in the range of 6-10 min within a 100?V/cm electric field and varied based on the buffer conductivity. To address concerns of dye transport impacting intensity data, electrokinetic mobilities of FITC were carefully examined and found to be (i) toward the anode and (ii) 1 to 2 orders of magnitude smaller than H? transport which is responsible for pH drops from the anode toward the cathode. COMSOL simulations of ion transport showed qualitative agreement with experimental results. The results indicate that pH changes are severe enough and rapid enough to influence the net charge of a protein or cause aggregation during iDEP experiments. The results also elucidate reasonable time periods over which the phosphate buffering capacity can counter increases in H? and OH? for unperturbed iDEP manipulations.     

Capillary and microchip electrophoresis of basic drugs with contactless conductivity detection

The extension of contactless conductivity detection in electrophoresis to the determination of basic drugs is demonstrated using beta-adrenergic blocking agents (beta-blockers) and other physiologically active amines as examples. The high-voltage approach to conductivity detection was employed for conventional capillaries as well as microchip devices. Acidic buffers were used in all cases. A buffer consisting of 100 mM acetic acid and 1 mM histidine was deemed most optimal for the separation of six beta-blockers and best results for the analysis of the other amines were achieved with a 20 mM lactic acid buffer at low pH-value. The detection limits ranged from 0.06 to 5 microM. To demonstrate potential practical applications, a main component assay was conducted for three pharmaceutical formulations. On-chip, five pharmaceutical amines could be baseline-resolved in a 8 cm long microchannel in 90 s, albeit a reduced sensitivity and peak capacity compared to conventional capillary electrophoresis.     

毛细管电泳样品电堆积富集过程影响因素的数值分析

毛细管电泳样品电堆积富集是一种通过缓冲溶液浓度的差异在毛细管中形成电场强度梯度,从而对样品进行浓缩的富集技术。本文在已有数学模型的基础上,对影响毛细管电堆积富集过程的因素进行了分析。计算结果发现,样品粒子表面所带的电荷电性以及带电量会影响粒子的电泳速度,进而影响富集过程;外加电势的大小会影响样品粒子到达检测窗口的迁移时间;而样品塞的初始长度则会影响样品所能达到的最大富集浓度以及达到最佳的富集效果所需要的时间。所得到的结果对样品电堆积富集技术的进一步完善具有一定的理论指导意义。     

A chip-based capillary electrophoresis-contactless conductivity microsystem for fast measurements of low-explosive ionic components

A miniaturized analytical system for separating and detecting inorganic explosive residues, based on the coupling of a micromachined capillary electrophoresis (CE) chip with a contactless conductivity detector is described. The low electroosmotic flow (EOF) of the poly(methylmethacrylate) (PMMA) chip material facilitates the rapid switching between analyses of cations and anions using the same microchannel and run buffer (and without an EOF modifier), and hence offers rapid (< 1 min) measurement of seven explosive-related cations and anions. Experimental parameters relevant to the separation and detection processes have been optimized. Addition of a 18-crown-6 ether modifier has been used for separating the peaks of co-migrating potassium and ammonium ions. The ionic-explosive microchip system combines the distinct advantages of contactless conductivity detection with the attractive features of plastic CE microchips. The new microsystem offers great promise for monitoring explosive-related ions at the sample source, with significant advantages of speed/warning, efficiency, cost, or sample size.     

Electrokinetics in microfluidic channels containing a floating electrode

Electrokinetic transport within a buffer-filled microchannel incorporating a flat bipolar electrode is investigated. The key finding is that the presence of the electrode disrupts the passage of electrical current through the microchannel and thereby alters the uniformity of the local electric field. Electroosmotic flow further modulates the local field gradient. These dynamics are demonstrated experimentally by utilizing the field gradient for concentration enrichment of negatively charged tracer molecules, and a set of computer simulations is presented to interpret the underlying electrokinetics.     

On the surface conductance, flow rate, and current continuities of microfluidics with nonuniform surface potentials

The characteristics of electrokinetic flow in a microchannel depend on both the nature of surface potentials, that is, whether it is uniform or nonuniform, and the electrical potential distribution along the channel. In this paper, the nonlinear Poisson-Boltzmann equation is used to model the electrical double layer and the lattice Boltzmann model coupled with the constraint of current continuity is used to simulate the microfluidic flow field in a rectangular microchannel with a step variation of surface potentials. This current continuity, including surface conduction, convection, and bulk conduction currents, has often been neglected in the literature for electroosmotic flow with nonuniform (heterogeneous) microchannels. Results show that step variation of ion distribution caused by step variation surface potential will influence significantly the electrical potential distribution along the channel and volumetric flow rate. For the system considered, we showed that the volumetric flow rate could have been overestimated by as much as 70% without consideration of the current continuity constraint.     

Fabrication and performance of a microfluidic traveling-wave electrophoresis system

A microfluidic traveling-wave electrophoresis (TWE) system is reported that uses a locally defined traveling electric field wave within a microfluidic channel to achieve band transport and separation. Low voltages, over a range of -0.5 to +0.5 V, are used to avoid electrolysis and other detrimental redox reactions while the short distance between electrodes, ～25 μm, provides high electric fields of ～200 V cm(-1). It is expected that the low voltage requirements will simplify the future development of smaller portable devices. The TWE device uses four interdigitated electrode arrays: one interdigitated electrode array pair is on the top of the microchannel and the other interdigitated electrode array pair is on the microchannel bottom. The top and bottom substrates are joined by a PDMS spacer that has a nominal height of 15 μm. A pinched injection scheme is used to define a narrow sample band within an injection cross either electrokinetically or hydrodynamically. Separation of two dyes, fluorescein and FLCA, with baseline resolution is achieved in less than 3 min and separation of two proteins, insulin and casein is demonstrated. Investigation of band broadening with fluorescein reveals that sample band widths equivalent to the diffusion limit can be achieved within the microfluidic channel, yielding highly efficient separations. This low level of band broadening can be achieved with capillary electrophoresis, but is not routinely observed in microchannel electrophoresis. Sample enrichment can be achieved very easily with TWE using a device with converging electric field waves controlled by two sets of independently controlled interdigitated electrodes arrays positioned serially along the microchannel. Sample enrichment of 40-fold is achieved without heterogeneous buffer/solvent systems, sorptive, or permselective materials. While there is much room for improvement in device fabrication, and many capabilities are yet to be demonstrated, it is anticipated that the capabilities and performance demonstrated herein will enable new lab-on-a-chip processes and systems.     

Electroviscous effects on pressure-driven flow of dilute electrolyte solutions in small microchannels

A fundamental understanding of the flow characteristics of electrolyte solutions in microchannels is critical to the design and control of microfluidic devices. Experimental studies have shown that the electroviscous effect is appreciable for a dilute solution in a small microchannel. However, the experimentally observed electroviscous effects cannot be predicted by the traditional theoretical model, which involves the use of the Boltzmann distribution for the ionic concentration field. It has been found that the Boltzmann distribution is not applicable to systems with dilute electrolyte solutions in small microchannels because it violates the ion number conservation condition. A new theoretical model is developed in this paper using the Nernst equation and the ion number conservation, instead of the Boltzmann distribution, to obtain the ionic concentration field. The ionic concentration field, electrical potential field, and flow field in small microchannels are studied using the model developed here. In order to verify this model, the model-predicted dP/dx (applied pressure gradient) Re (Reynolds number) relationship is compared with the experimentally determined dP/dx approximately Re relationship. Strong agreement between the model predictions and the experimental results supports this model.     

Numerical simulation of DNA sample preconcentration in microdevice electrophoresis

A numerical model is presented for the accurate and efficient prediction of preconcentration and transport of DNA during sample introduction and injection in microcapillary electrophoresis. The model incorporates conservation laws for the different buffer ions, salt ions, and DNA sample, coupled through a Gaussian electric field to account for the field modifications that cause electromigration. The accuracy and efficiency required to capture the physics associated with such a complex transient problem are realized by the use of the finite element-flux corrected transport (FE-FCT) algorithm in two dimensions. The model has been employed for the prediction of DNA sample preconcentration and transport during electrophoresis in a double-T injector microdevice. To test its validity, the numerical results have been compared with the corresponding experimental data under similar conditions, and excellent agreement has been found. Finally, detailed results from a simulation of DNA sample preconcentration in electrophoretic microdevices are presented using as parameters the electric field strength and the other species concentrations. The effect of the Tris concentration on sample stacking is also investigated. These results demonstrate the great potential offered by the model for future optimization of such microchip devices with respect to significantly enhanced speed and resolution of sample separation.