Electrokinetic transport and separations in fluidic nanochannels

This article presents a summary of theory, experimental studies, and results for the electrokinetic transport in small fluidic nanochannels. The main focus is on the effect of the electric double layer on the EOF, electric current, and electrophoresis of charged analytes. The double layer thickness can be of the same order as the width of the nanochannels, which has an impact on the transport by shaping the fluid velocity profile, local distributions of the electrolytes, and charged analytes. Our theoretical consideration is limited to continuum analysis where the equations of classical hydrodynamics and electrodynamics still apply. We show that small channels may lead to qualitatively new effects like selective ionic transport based on charge number as well as different modes for molecular separation. These new possibilities together with the rapid development of nanofabrication capabilities lead to an extensive experimental effort to utilize nanochannels for a variety of applications, which are also discussed and analyzed in this review.     

Transport and separation of charged macromolecules under nonlinear electromigration in nanochannels

In this work, we theoretically investigate the implications of nonlinear electrophoretic effects on the transport and size-based separation of charged macromolecules in nanoscale confinements. By employing a regular perturbation analysis, we address certain nontrivial features of interconnection among wall-induced transverse migrative fluxes, electrophoretic and electroosmotic transport, confinement-induced hindered diffusive effects, and hydrodynamic interactions in detail. We demonstrate that there occurs an optimal regime of influence of the nonlinear electrophoretic effects, within which high values of separation resolution may be achieved. This size-based optimal regime, however, can be effectively exploited only for nanochannel flows, as attributed to the strong electric double layer interactions prevalent within the same.     

Electrophoretic motion of a charged porous sphere within micro- and nanochannels

Electrophoretic motion of a charged porous sphere within micro- and nanochannels is investigated theoretically. The Brinkman model and the full non-linear Poisson-Boltzmann equation are adopted to model the system, with the charged porous sphere resembling polyelectrolytes like proteins and DNA. General electrokinetic equations are employed and solved with a pseudo-spectral method. Key parameters of electrokinetic interest are examined for their respective effect as well as overall impact on the particle motion. We found, among other things, that the confinement effect of the channel can be so drastic that 75% reduction of particle mobility is observed in some situations for a poorly permeable particle. However, only 15% for the corresponding highly permeable particle due to the allowance of fluid penetration which alleviates the retarding shear stress significantly. In particular, an intriguing phenomenon is observed for the highly permeable particle: the narrower the channel is, the faster the particle moves! This was experimentally observed as well in the literature on DNA electrophoresis within nanostructures. The reason behind it is thoroughly explained here. Moreover, charged channels can exert electroosmosis flow so dominant that sometimes it may even reverse the direction of the particle motion. Comparison with experimental data available in the literature for some polyelectrolytes is excellent, indicating the reliability of this analysis. The results of this study provide fundamental knowledge necessary to interpret experimental data correctly in various microfluidic and nanofluidic operations involving bio-macromolecules, such as in biosensors and Lab-on-a-chip devices.     

Electrokinetic separation of charged macromolecules in nanochannels within the continuum regime: effects of wall interactions and hydrodynamic confinements

In this paper, a detailed continuum-based theoretical model is proposed to investigate the effects of near-wall potentials and hydrodynamic confinement on separation of charged macromolecules in channels of nanoscale dimensions. These wall effects are primarily confined within a few nanometers from the channel wall, and hence have negligible influences in the conventional electrokinetic separation methods that are routinely performed in microchannels. However, in nanochannels, their zone of influence becomes significant in comparison to the channel height, thereby inducing certain nontrivial effects on the resultant separation characteristics. By executing a regular perturbation analysis, it is established that depending on the macromolecular size relative to the channel height and the extent of electrical double layer (EDL) interactions, the wall forces decide the speed of traverse and the extent of spreading (dispersion) of the macromolecular bands. These factors combine together to finally decide the separation characteristics (quantified by the resolution of separation) of the charged macromolecules in nanochannels. It is demonstrated that because of the near-wall effects, macromolecular pairs with less disparities in sizes give rise to higher values of resolution. Moreover, the wall-induced influences are shown to magnify the resolution for any given pair of macromolecules in the nanofluidic systems, thereby signifying greater separation efficiency.     

Electrokinetic pumping and detection of low-volume flows in nanochannels

Electrokinetic pumping of low-volume rates was performed on-chip in channels of small cross sectional area and height in the sub-microm range. The flow was detected with the current monitoring technique by monitoring the change in resistance of the fluid in the channel upon the electroosmosis-driven displacement of an electrolyte solution by a second electrolyte solution. Flow rates in the order of 0.1 pL/s were successfully generated and detected. The channels were fabricated with the sacrificial layer technology.     

The electrostatic and steric-hindrance model for the transport of charged solutes through nanofiltration membranes

Nanofiltration (NF) membranes possess the intermediate molecular weight cut-off between reverse osmosis membranes and ultrafiltration membranes, and also have rejection to inorganic salts. So one can assume that NF membranes have charged pore structure. We have developed the electrostatic and steric-hindrance (ES) model from the steric-hindrance pore (SHP) model and the Teorell-Meyer-Sievers (TMS) model (Wang et al., J. Chem. Eng. Japan, 28 (1995) 372) to predict the transport performance of charged solutes through NF membranes based on their charged pore structure. In this article, by doing the permeation experiments of aqueous solutions of neutral solutes and sodium chloride, the structural parameters (the pore radius and the ratio of membrane porosity to membrane thickness) and the charge density of NF membranes (Desal-S, NF-40, NTR7450 and G-20) were estimated on the basis of SHP model and the TMS model, respectively. Then, we selected an aqueous solution of different tracer charged solutes (sodium benzenesulfonate, sodium naphthalenesulfonate and sodium tetraphenyl-borate) and a supporting salt (sodium chloride) to verify the ES model. The prediction based on the ES model was in good agreement with the experimental results.     

Effect of multivalent ions on electroosmotic flow in micro- and nanochannels

In this work, the effect of multivalent ions on electroosmotic flow is investigated for multiple electrolyte components. The cases studied include incorporating Ca2+ and HPO4(2-) and other monovalent ions, such as K+ and H2PO4-, into an aqueous NaCl solution. The governing equations are derived and solved numerically. The boundary conditions for the governing equations are obtained from the electrochemical equilibrium requirements. In comparison with monovalent ions, the results show that in micro- and nanochannels having fixed surface charges, multivalent counterions, even in very small amounts, reduce electroosmotic flow significantly, while the multivalent co-ions have little effect on the electroosmotic flow. Due to the enhanced ion-wall interactions multivalent counterions compose the majority of ions in the electric double layer (EDL), causing a decrease of net charge at the surface.     

On the Knudsen transport of gases in nanochannels

We investigate the diffusion of gas molecules in nanochannels under the combinational effect of the vibration of the channel, gas-wall binding energy, and channel size through molecular dynamics simulations. It is found that the molecular vibration of the channel plays a critical role in gas transport process when the gas-wall binding energy is strong. For small binding energies, the influence of the flexibility of the wall can be neglected. In rigid channels, the gas self-diffusion coefficient increases with increasing gas-wall binding energy, while it decreases in nonrigid channels. The effect of the channel size on the self-diffusion coefficient is not significant except that a local maximum in the gas self-diffusion coefficient is found in 2 nm channels due to the strong repulsive force caused by the surface curvature of the channels.     

Measurements of diffusion coefficients in 1-D micro- and nanochannels using shear-driven flows

The present paper describes a method for measuring the molecular diffusion coefficient of fluorescent molecules in microfluidic systems. The proposed static shear-driven flow method allows one to perform diffusion measurements in a fast and accurate manner. The method also allows one to work in very thin (i.e. submicron) channels, hence allowing the investigation of diffusion in highly confined spaces. In the deepest investigated channels, the obtained results were comparable to the existing literature values, but when the channel size dropped below the micrometer range, a significant decrease (more than 30%) in molecular diffusivity was observed. The reduction of the diffusivity was most significant for the largest considered molecules (ssDNA oligomers with a size ranging between 25 to 100 bases), but the decrease was also observed for smaller tracer molecules (FITC). This decrease can be attributed to the interactions of the analyte molecules with the channel walls, which can no longer be neglected when the depth of the channel reaches a critical value. The change in diffusivity seems to become more explicit as the molecular weight of the analytes increases.     

Fabrication of non-biofouling polyethylene glycol micro- and nanochannels by ultraviolet-assisted irreversible sealing

We present a simple and widely applicable method to fabricate micro- and nanochannels comprised entirely of crosslinked polyethylene glycol (PEG) by using UV-assisted irreversible sealing to bond partially crosslinked PEG surfaces. The method developed here can be used to form channels as small as approximately 50 nm in diameter without using a sophisticated experimental setup. The manufactured channel is a homogeneous conduit made completely from non-biofouling PEG, exhibits robust sealing with minimal swelling and can be used without additional surface modification chemistries, thus significantly enhancing reliability and durability of microfluidic devices. Furthermore, we demonstrate simple analytical assays using PEG microchannels combined with patterned arrays of supported lipid bilayers (SLBs) to detect ligand (biotin)-receptor (streptavidin) interactions.     

The interplay of diffusional and electrophoretic transport mechanisms of charged solutes in the liquid film surrounding charged nonporous adsorbent particles employed in finite bath adsorption systems

A model that describes the diffusive and electrophoretic mass transport of the cation and anion species of a buffer electrolyte and of a charged adsorbate in the liquid film surrounding nonporous adsorbent particles in a finite bath adsorption system, in which adsorption of the charged adsorbate onto the charged surface of the nonporous particles occurs, is constructed and solved. The dynamic behavior of the mechanisms of this model explicitly demonstrates (a) the interplay between the diffusive and electrophoretic molar fluxes of the charged adsorbate and of the species of the buffer electrolyte in the liquid film surrounding the nonporous adsorbent particles, (b) the significant effect that the functioning of the electrical double layer has on the transport of the charged species and on the adsorption of the charged adsorbate, and (c) the substantial effect that the dynamic behavior of the surface charge density has on the functioning of the electrical double layer. It is found that at equilibrium, the value of the concentration of the charged adsorbate in the fluid layer adjacent to the surface of the adsorbent particles is significantly greater than the value of the concentration of the adsorbate in the finite bath, while, of course, the net molar flux of the charged adsorbate in the liquid film is equal to zero at equilibrium. This result is very different than that obtained from the conventional model that is currently used to describe the transport of a charged adsorbate in the liquid film for systems involving the adsorption of a charged adsorbate onto the charged surface of nonporous adsorbent particles; the conventional model (i) does not consider the existence of an electrical double layer, (ii) assumes that the transport of the charged adsorbate occurs only by diffusion in the liquid film, and (iii) causes at equilibrium the value of the charged adsorbate in the liquid layer adjacent to the surface of the particles to become equal to the value of the concentration of the charged adsorbate in the liquid of the finite bath. Furthermore, it was found that a maximum can occur in the dynamic behavior of the concentration of the adsorbate in the adsorbed phase when the value of the free molecular diffusion coefficient of the adsorbate is relatively large, because the increased magnitude of the synergistic interplay between the diffusive and electrophoretic molar fluxes of the adsorbate in the liquid film allows the adsorbate to accumulate (to be entrapped) in the liquid layer adjacent to the surface of the adsorbent particles faster than the concentrations of the electrolyte species, whose net molar fluxes are significantly hindered due to their opposing diffusive and electrophoretic molar fluxes, can adjust to account for the change in the surface charge density of the particles that arises from the adsorption of the charged adsorbate. The results presented in this work also have significant implications in finite bath adsorption systems involving the adsorption of a charged adsorbate onto the surface of the pores of charged porous adsorbent particles, because the diffusion and the electrophoretic migration of the charged solutes (cations, anions, and charged adsorbate) in the pores of the adsorbent particles will depend on the dynamic concentration profiles of the charged solutes in the liquid film surrounding the charged porous adsorbent particles. The results of the present work are also used to illustrate how the functioning of the electrical double layer could contribute to the development of inner radial humps (concentration rings) in the concentration of the adsorbate in the adsorbed phase of charged porous adsorbent particles.     

纳通道的物质传输特性及应用

近年来,随着材料科学、微纳加工技术和微纳尺度物质传输理论的发展,纳通道技术得到了越来越多的研究和关注。纳通道包括生物纳通道和人工纳通道,其孔径通常为1～100 nm。在这一尺度下,通道表面与通道内物质之间的作用概率大大增强,使得纳通道表现出许多与宏观体系不同的物质传输特性,例如通道表面电荷与通道内离子之间的静电作用产生了离子选择性,通道内电化学势的不对称分布产生了离子整流特性,物质传输过程中占据通道产生了阻塞脉冲特性等。纳通道中的这些物质传输特性在传感、分离、能源等领域具有广泛应用,例如通过对纳通道进行功能化修饰可以实现门控离子传输;利用亚纳米尺度的通道可以实现单分子传感;利用通道与传输物质之间的相互作用可以实现离子、分子、纳米粒子的分离;利用纳通道的离子选择性可以在通道内实现电荷分离,将不同形式的能量(如光、热、压力、盐差等)高效转化为电能。纳通道技术是化学、材料科学、纳米技术等多学科的交叉集合,在解决生物、环境、能源等基本问题方面具有良好的前景。该文综述了近10年来与纳通道物质传输理论以及纳通道技术应用相关的前沿研究,梳理了纳通道技术的发展过程,并对其在各个领域的应用进行了总结与展...     

Treatment of charged solutes in three-dimensional integral equation theory

Periodicity artifacts, which occur within three-dimensional reference interaction site model integral equation theory for net-charged solute systems, are analyzed and corrected by means of a renormalization procedure for long range interactions. The method is formulated for solute-solvent and solute-solute variants of the theory. Both dielectric and electrolyte solvents are considered. Comparison of the results for atomic ions with one-dimensional reference computations shows that structural and thermodynamic artifacts are efficiently removed.     

Electroosmosis in homogeneously charged micro- and nanoscale random porous media

Electroosmosis in homogeneously charged micro- and nanoscale random porous media has been numerically investigated using mesoscopic simulation methods which involve a random generation-growth method for reproducing three-dimensional random microstructures of porous media and a high-efficiency lattice Poisson-Boltzmann algorithm for solving the strongly nonlinear governing equations of electroosmosis in three-dimensional porous media. The numerical modeling and predictions of EOF in micro- and nanoscale random porous media indicate that the electroosmotic permeability increases monotonically with the porosity of porous media and the increasing rate rises with the porosity as well; the electroosmotic permeability increases with the average solid particle size for a given porosity and with the bulk ionic concentration also; the proportionally linear relationship between the electroosmotic permeability and the zeta potential on solid surfaces breaks down for high zeta potentials. The present predictions agree well with the available experimental data while some results deviate from the predictions based on the macroscopic theories.     

Fractional separation of polymers in nanochannels: Combined influence of wettability and structure

Trapping macromolecules in nanopits finds diverse applications in polymer separation, filtering biomolecules etc. However, tuning the locomotion of polymers in channels of nanoscopic dimensions is greatly restricted by the comparative advective and diffusive components of velocities. Using the polymer affinity toward the solvent and the wall, and the polymer structure, a mechanism is proposed to induce selective trapping of polymers. Similar to fractional distillation of hydrocarbons based on molecular weight, a technique of fractional segregation, depending on the channel wettability of polymeric chains at different depths in a pit that is located perpendicular to the flow is suggested. Depending on the properties of the polymeric chains and the surface chemistry, the segregation of the polymer at a particular level in the pit can be predicted. This behavior stems from the difference in polymer structure leading to a competition between wettability based enthalpic trapping and structure based entropic trapping. The results of this study suggest a novel way of separating biopolymers based on their structure without relying on the channel geometry. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2118–2125     

Fractal nanochannels as the basis of the ionic transport in AgI-based glasses

We propose a new model to explain the transport properties of AgI-based fast ion conducting glasses. The main factor affecting the ionic conductivity is the mobility of the Ag+ carriers, that is controlled by the Ag local environment. We model the ionic conductivity in terms of a percolation between a low-conducting phase (purely oxygen-coordinated sites), and a high-conducting one (iodine/oxygen, I/O, coordinated sites). The percolation takes place along pathways with fractal structure. The nature of the glass network, and namely its connectivity and dimensionality, plays a significant role only for low I/O values, originating the transport and thermal anomalies observed in borate and phosphate glasses.     

Dissipative particle dynamics simulation of depletion layer and polymer migration in micro- and nanochannels for dilute polymer solutions

The flows of dilute polymer solutions in micro- and nanoscale channels are of both fundamental and practical importance in variety of applications in which the channel gap is of the same order as the size of the suspended particles or macromolecules. In such systems depletion layers are observed near solid-fluid interfaces, even in equilibrium, and the imposition of flow results in further cross-stream migration of the particles. In this work we employ dissipative particle dynamics to study depletion and migration in dilute polymer solutions in channels several times larger than the radius of gyration (Rg) of bead-spring chains. We compare depletion layers for different chain models and levels of chain representation, solvent quality, and relative wall-solvent-polymer interactions. By suitable scaling the simulated depletion layers compare well with the asymptotic lattice theory solution of depletion near a repulsive wall. In Poiseuille flow, polymer migration across the streamlines increases with the Peclet and the Reynolds number until the center-of-mass distribution develops two symmetric off-center peaks which identify the preferred chain positions across the channel. These appear to be governed by the balance of wall-chain repulsive interactions and an off-center driving force of the type known as the Segre-Silberberg effect.     

Analysis and parametric sensitivity of the behavior of overshoots in the concentration of a charged adsorbate in the adsorbed phase of charged adsorbent particles: practical implications for separations of charged solutes

In this work, an analysis of the parametric sensitivity of the overshoot in the concentration of the adsorbate in the adsorbed phase, which occurs under certain conditions during an ion-exchange adsorption process, is presented and used to suggest practical implications of the concentration overshoot phenomenon on operational policies and configurations of chromatographic columns and finite bath adsorption systems. The results presented in this work demonstrate and explain how the development of an overshoot in the concentration of the adsorbate in the adsorbed phase could be enhanced or suppressed by (i) varying the diffusion coefficient, D3, of the adsorbate relative to the diffusion coefficients, D1 and D2, of the cations and anions, respectively, of the background/buffer electrolyte, (ii) altering the initial surface charge density, delta0, of the charged adsorbent particles, (iii) varying the Debye length, lambda, and (iv) changing the initial concentration, Cd3(0), of the adsorbate in the bulk liquid of the finite bath. The influence of the pH and ionic strength, Iinfinity, of the liquid solution on the development of an overshoot in the concentration of the adsorbate in the adsorbed phase is also presented and discussed through the relationships of these parameters to delta0 and lambda, respectively. Furthermore, a detailed explanation of the effects of each parameter on the interplay between the diffusive and electrophoretic molar fluxes, as well as on the structure and functioning of the electrical double layer, which are responsible for the concentration overshoot phenomenon, is presented.     

Transport of organic and inorganic solutes through charged mosaic composite membranes

A template pattern with alternating poly(4-vinylpyridine) (P4VP)/poly(vinyl alcohol) (PVA) lamellae was fabricated upon a microporous poly(vinyl chloride) (PVC) membrane by casting of poly[4-vinylpyridine(4VP)-g-vinyl alcohol (VA)] graft copolymer. After a treatment of both binding of microporous membrane with graft copolymer and domain fixing of the PVA matrix, a dilute solution of poly[acrylic acid (AA)-benzyl N,N-dimethyldithiocarbamate (DMTC)]/P4VP or poly[sodium p-styrenesulfonate (SSS)-DMTC]/P4VP binary blend was cast on this template surface. Two types of weak acid/strong base or strong acid/strong base microdomains formed by phase growth were oriented perpendicularly to the membrane surface. After the chemical treatments: introduction of the charge and domain fixing of ion exchange regions, two types of such mosaic microdomains could be constructed on a microporous membrane. We studied the transport behaviors of organic and inorganic solutes through charged mosaic composite membranes. The permeability of inorganic electrolyte, such as KCl was about 20-fold compared to those of organic nonelectrolytes, such as glucose and sucrose. l-Phenylalanine exhibits a low value of permeability at the pH of its isoelectric point.     

Electrokinetic transport of red blood cells in microcapillaries

Electrokinetic flow of a suspension of erythrocytes (red blood cells, RBCs) in 20 num cylindrical fused-silica capillaries is examined in the present work. Flow direction anomalies are observed experimentally and tentatively explained by the development of a pH gradient between the cathode well and the anode well due to electrolysis reactions at the electrodes. This pH gradient alters the local zeta potentials of both the capillary and the RBC and thus the local electroendosmotic liquid flow (EOF) velocities and RBC electrophoretic (EP) velocities. The two velocities are opposite in direction but with EOF dominating such that the RBC moves toward the cathode, opposite to the anode migration observed in bulk conditions. The opposing zeta potentials also lead to RBC aggregation at the anode end for low fields less than 25 V/cm. As the electroendosmotic velocity decreases at the anode end due to decreasing pH, pressure-driven back flow develops to oppose the original EOF at the remaining portions of the capillary ensuring constant fluid flux. When the anode EOF velocity is smaller in magnitude than the EP velocity, reversal of blood cell transport is observed after a short transient time in which a pH gradient forms. RBC velocities and pH dependencies on electric field and MgCl(2) concentration are presented along with data showing the accumulation of charge separation across the capillary. Also, a short-term solution to the pH gradient formation is presented that could help thwart development of pH gradients in micro-devices at lower voltages.