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.     

A pressure driven injection system for an ultra-flat chromatographic microchannel

A pressure-actuated on-chip injection system has been developed that is compatible with shallow microchannels with a very large aspect ratio, i.e. 1 microm deep and up to 1000 microm wide. Such channels offer potential advantages in the miniaturisation of liquid chromatography and other separation methods as they allow high loadability and low sample dispersion at the same time. Computational fluid dynamics simulations were performed to predict the flow profiles and the transport of a sample in the system and to justify the injection principle. Based on these simulations, a prototype integrated into a chip for hydrodynamic chromatography has been realised and tested experimentally. The performance of the device is satisfactory and the results are in qualitative agreement with the numerical models.     

Optimization of parameters for gas-diffusion flow-injection systems

The effects of flow rate, flow direction, flow ratio, pressure, membrane area, channel depth and channel shape on the optimization of gas-diffusion flow-injection systems are described in detail. A nonreacting chemical system, chlorine dioxide, was used to study the physical dispersion of the gas-diffusion systems. It was found that slow flow rates and shallow channels are optimal. Stopped-flow conditions in a nonreacting chemical system may not be worth the cost in time. For chemical systems in which the analyte is consumed, the optimized parameters included stopped flow.     

Ionic dispersion in nanofluidics

An analytical solution for dispersion of ionic and neutral solutes in nanoscale channels is presented. Results suggest that in the presence of relatively thick electrical double layers (EDLs) characteristic of nanofluidics, the dispersion of ionic solutes differs from that of neutral solutes on which previous theory is based. Ionic dispersion for circular cross-section channels is quantified as a function of a valance parameter, the relative EDL thickness, and the form of the velocity profile. Two unique mechanisms governing ionic dispersion in both pressure- and electrokinetically driven flows are identified. The results of the analytical solution, employing the linearized form of the Poisson-Boltzmann equation, are supported and extended by the results of an independent computational model employing the nonlinear Poisson-Boltzmann equation. Applicability of the computational results is not limited by the Debye-Hückel approximation. Collectively, these results indicate that dispersion of ionic species in nanoscale channels is markedly charge dependent, and substantially deviates from that of neutral solutes in the same flow.     

System-oriented dispersion models of general-shaped electrophoresis microchannels

This paper presents a system-oriented model for analyzing the dispersion of electrophoretic transport of charged analyte molecules in a general-shaped microchannel, which is represented as a system of serially connected elemental channels of simple geometry. Parameterized analytical models that hold for analyte bands of virtually arbitrary initial shape are derived to describe analyte dispersion, including both the skew and broadening of the band, in elemental channels. These models are then integrated to describe dispersion in the general-shaped channel using appropriate parameters to represent interfaces of adjacent elements. This lumped-parameter system model offers orders-of-magnitude improvement in computational efficiency over full numerical simulations, and is verified by results from experiments and numerical simulations. The model is used to perform a systematic parametric study of serpentine channels consisting of a pair of complementary turn microchannels, and the results indicate that dispersion in a particular turn can contribute to either an increase or decrease of the overall band broadening. The efficiency and accuracy of the system model is further demonstrated by its application to general-shaped channels that occur in practice, including a serpentine channel with multiple complementary turns and a multi-turn spiral-shaped channel. The results indicate that our model is an accurate and efficient simulation tool useful for designing optimal electrophoretic separation microchips.     

Flow-induced deformation of shallow microfluidic channels

We study the elastic deformation of poly(dimethylsiloxane) (PDMS) microchannels under imposed flow rates and the effect of this deformation on the laminar flow profile and pressure distribution within the channels. Deformation is demonstrated to be an important consideration in low aspect ratio (height to width) channels and the effect becomes increasingly pronounced for very shallow channels. Bulging channels are imaged under varying flow conditions by confocal microscopy. The deformation is related to the pressure and is thus non-uniform throughout the channel, with tapering occurring along the stream-wise axis. The measured pressure drop is monitored as a function of the imposed flow rate. For a given pressure drop, the corresponding flow rate in a deforming channel is found to be several times higher than expected in a non-deforming channel. The experimental results are supported by scaling analysis and computational fluid dynamics simulations coupled to materials deformation models.     

Fabrication and characterization of 20 nm planar nanofluidic channels by glass-glass and glass-silicon bonding

We have characterized glass-glass and glass-Si bonding processes for the fabrication of wide, shallow nanofluidic channels with depths down to the nanometer scale. Nanochannels on glass or Si substrate are formed by reactive ion etching or a wet etching process, and are sealed with another flat substrate either by glass-glass fusion bonding (550 degrees C) or an anodic bonding process. We demonstrate that glass-glass nanofluidic channels as shallow as 25 nm with low aspect ratio of 0.0005 (depth to width) can be achieved with the developed glass-glass bonding technique. We also find that silicon-glass nanofluidic channels, as shallow as 20 nm with aspect ratio of 0.004, can be reliably obtained with the anodic bonding technique. The thickness uniformity of sealed nanofluidic channels is confirmed by cross-sectional SEM analysis after bonding. It is shown that there is no significant change in the depth of the nanofluidic channels due to anodic bonding and glass-glass fusion bonding processes.     

A nonlinear RDF model for waves propagating in shallow water

In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs's relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refracti     

A nonlinear RDF model for waves propagating in shallow water

In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs’s relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refraction and diffraction of shallow-water waves.     

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.     

Continuum transport model of Ogston sieving in patterned nanofilter arrays for separation of rod-like biomolecules

This article proposes a simple computational transport model of rod-like short dsDNA molecules through a microfabricated nanofilter array. Using a nanochannel consisting of alternate deep wells and shallow slits, it is demonstrated that the complex partitioning of rod-like DNA molecules of different sizes over the nanofilter array can be well described by continuum transport theory with the orientational entropy and anisotropic transport parameters properly quantified. In this model, orientational entropy of the rod-like DNA is calculated from the equilibrium distribution of rigid cylindrical rod near the solid wall. The flux caused by entropic differences is derived from the interaction between the DNA rods and the solid channel wall during rotational diffusion. In addition to its role as an entropic barrier, the confinement of the DNA in the shallow channels also induces large changes in the effective electrophoretic mobility for longer molecules in the presence of EOF. In addition to the partitioning/selectivity of DNA molecules by the nanofilter, this model can also be used to estimate the dispersion of separated peaks. It allows for fast optimization of nanofilter separation devices, without the need of stochastic modeling techniques that are usually required.     

Optimization of flow-through cells for dialysis and other membrane separations in flow-injection analysis using a laminar flow model

The mass transfer in the liquid channels of flow-through dialysers can be described fairly accurately by a laminar flow model. The mass transfer resistance in the liquid channels was of the same magnitude as that of a cellulose acetate membrane for the most effective dialysis cell. Thin channels are therefore of importance both for efficiency and for low dispersion in flow injection. A cell with a pressed membrane support provided the lowest dispersion and pressure dependence. A computer-based model provides a means for the determination of membrane permeabilities.     

Flow injection analysis simulations and diffusion coefficient determination by stochastic and deterministic optimization methods

Stochastic and deterministic simulations of dispersion in cylindrical channels on the Poiseuille flow have been presented. The random walk (stochastic) and the uniform dispersion (deterministic) models have been used for computations of flow injection analysis responses. These methods coupled with the genetic algorithm and the Levenberg–Marquardt optimization methods, respectively, have been applied for determination of diffusion coefficients. The diffusion coefficients of fluorescein sodium, potassium hexacyanoferrate and potassium dichromate have been determined by means of the presented methods and FIA responses that are available in literature. The best-fit results agree with each other and with experimental data thus validating both presented approaches.     

Pillar-structured microchannels for on-chip liquid chromatography: evaluation of the permeability and separation performance

The chromatographic characteristics were determined for a set of microfabricated separation channels structured with cylindrical and diamond-shaped pillars with a characteristic size of 5 microm. Channels with different structures and porosities were etched in a silicon wafer using lithographic techniques. The permeability for flow of the channels was shown to increase strongly with the overall porosity. Diamond-shaped pillars appeared to yield a slightly higher permeability than cylindrical pillars at the same channel porosity. Compared to packed columns, permeabilities were higher by a factor of up to 5. Band dispersion in the channels was measured with an unretained fluorescent probe compound using a fluorescence microscope. A relatively large variation in the observed plate heights between channels was found, which was mainly attributed to the inaccurate geometry of the structure close to the side walls. Reduced plate heights between 0.2 and 1.0 were obtained. The lowest plate heights were found for channels with low porosity. The chromatographic impedances were calculated and compared to the values for the traditional chromatographic systems. For one of the structured microchannels the impedance was found to be more than ten times lower than for a column packed with nonporous spherical particles. With the data collected, predictions are given on the possibilities in terms of efficiency and speed offered by structured microchannels for pressure-driven separations, taking practical constraints into account.     

Computer simulation and theory of the diffusion- and flow-induced concentration dispersion in microfluidic devices and HPLC systems based on rectangular microchannels

The dynamics of formation of solute peaks in microfluidic systems are investigated by computer simulation. A finite-element numerical procedure is applied to analyze the diffusion- and flow-controlled concentration dispersion in a 40 microm-high rectangular flow-through channel. Two-dimensional concentration profiles are shown for channels with cross sections of large aspect ratio. The final shapes of the peaks are formed during a very short time period, ranging from a few milliseconds to about 1s for low and high flow velocities, respectively. The observed standard half-width sigma of the peaks is found to strictly follow a linear function of t(1/2) over the whole time range. The extrapolated long-term peak characteristics are in perfect agreement with theoretical predictions. For comparison, theoretical results on the concentration dispersion for solute peaks in open-channel liquid-chromatography (HPLC) are re-examined and applied.     

Synchronized cyclic capillary electrophoresis using channels arranged in a triangle and low voltages

Synchronized cyclic capillary electrophoresis (SCCE) makes use of a closed loop separation channel by which the same sample can be separated during many cycles. This enables the repeated use of the same voltage for separations such that a high total voltage, and thus high efficiency, is obtained for the synchronized components. This can be accomplished by using any type of polygon geometry for the separation channel; and calculations of the available field and number of connections needed for polygons from 3 to 5 sides are presented. Triangular designs have the advantage of using the lowest number of wells. Such designs are described, with two additional features compared to that of earlier work: 1. voltage connections that are much shallower than the separation channel, to reduce losses and dispersion at the intersections; and 2. corners that are narrower than the separation channels to reduce dispersion in the turns. Experimental data is presented for the separation of a mixture of amino acids, and for a DNA separation in a polymeric sieving matrix. The DNA separation is most sensitive to the corner dispersion problem, which reduces the observed efficiency for that separation.     

Microfluidic waves

The propagation of pressure waves in fluidic channels with elastic covers is discussed in view of applications to flow control in microfluidic devices. A theory is presented which describes pressure waves in the fluid that are coupled to bending waves in the elastic cover. At low frequencies, the lateral bending of the cover dominates over longitudinal bending, leading to propagating, non-dispersive longitudinal pressure waves in the channel. The theory addresses effects due to both the finite viscosity and compressibility of the fluid. The coupled waves propagate without dispersion, as long as the wave length is larger than the channel width. It is shown that in channels of typical microfluidic dimensions, wave velocities in the range of a few 10 m s(-1) result if the channels are covered by films of a compliant material such as PDMS. The application of this principle to design microfluidic band pass filters based on standing waves is discussed. Characteristic frequencies in the range of a few kHz are readily achieved with quality factors above 30.     

Band spreading control in electrophoresis microchips by localized zeta-potential variation using field-effect

The paper proposes a new technique, which varies the zeta potential along the channel walls in the vicinity of the microchannel corners in such as a way as to minimize the effects of turn-induced dispersion within U-shaped separation channels. The effects of the separation channel geometry, the fluid velocity profile, and boundary control of the zeta potential on the band distribution in the detection area are all discussed within this paper. The results for the folded square U-shaped separation channel indicate that boundary control of the zeta potential by field-effect significantly reduces the band dispersion induced by the 90[degree] turns. Finally, the results confirm that application of the proposed localized zeta potential variation method results in a correction of the band tilting phenomenon and a reduction in the racetrack effect.     

Biomimetic membranes with aqueous nano channels but without proteins: impedance of impregnated cellulose ester filters

Earlier we have shown that many important properties of ionic aqueous channels in biological membranes can be imitated using simple biomimetic membranes. These membranes are composed of mixed cellulose ester-based filters, impregnated with isopropyl myristate or other esters of fatty acids, and can be used for high-throughput drug screening. If the membrane separates two aqueous solutions, combination of relatively hydrophilic polymer support with immobilized carboxylic groups results in the formation of thin aqueous layers covering inner surface of the pores, while the pore volume is filled by lipid-like substances. Because of these aqueous layers biomimetic membranes even without proteins have a cation/anion ion selectivity and specific (per unit of thickness) electrical properties, which are similar to typical properties of biological membranes. Here we describe frequency-dependent impedance of the isopropyl myristate-impregnated biomimetic membranes in the 4-electrode arrangement and present the results as Bode and Nyquist diagrams. When the membranes are placed in deionized water, it is possible to observe three different dispersion processes in the frequency range 0.1 Hz to 30 kHz. Only one dispersion is observed in 5 mM KH(2)PO(4) solution. It is suggested that these three dispersion features are determined by (a) conductivity in aqueous structures/channels, formed near the internal walls of the filter pores at high frequencies, (b) dielectric properties of the whole membrane at medium frequencies, determined by polymer support, aqueous layers and impregnating oil, and, finally, (c) by the processes in hydrated liquid crystal structures formed in pores by impregnating oil in contact with water at low frequencies.     

Dispersion control in microfluidic chips by localized zeta potential variation using the field effect

A new technique to minimize the effects of turn-induced dispersion within U-shaped separation channels by using the field effect within a capacitor to vary the zeta potential along the channel walls in the vicinity of the microchannel is described. The effects of the separation channel geometry, the fluid velocity profile, and the use of the field effect to control the zeta potential on the band distribution in the detection area are extensively discussed. The results for a U-shaped separation channel indicate that varying the zeta potential by controlling the field effect significantly reduces the band dispersion induced by the 90 degrees turns within the channel. Finally, it is shown that the application of the proposed localized zeta potential variation method also results in a correction of the band tilting phenomenon and a reduction in the racetrack effect.