Theory of transport in nanofluidic channels with moderately thin electrical double layers: effect of the wall potential modulation on solutions of symmetric and asymmetric electrolytes

Electrokinetic phenomena play an important role for the transport in submicrometer-size channels since the electric double layers formed at the walls can occupy a substantial part of the channel volume. This presents a theoretical difficulty and specific problems are usually treated numerically or not comprehensively. In our work we present a theoretical model that allows one to obtain analytical expressions for the transport of fluid (electro-osmotic flow), ions (electric current), and dissolved charged molecules (analytes). The model is based on the weak double layer approximation and has a wide range of validity. An important feature of this theoretical approach is that it is applicable not only to symmetric but also to asymmetric 2:1 and 1:2 electrolytes which exhibit very interesting properties in nanoscale channels. The possibility of affecting the wall electrokinetic zeta potential by applying a transverse voltage bias is analyzed. This transverse bias is used in an attempt to control the transport in the channel and such devices are often called "fluidic field-effect transistors." Our model quantifies the effect of the voltage bias on the zeta potential of the channel wall and therefore can be used for prediction of transport and optimization of separations in such fluidic devices.     

微通道中高分子运动的耗散粒子动力学模拟

对不同长度及不同数量的高分子链在微直通道及微缩通道中的流动进行了模拟与分析.研究表明,高分子链的伸展状态与微通道的形状密切相关,微直通道中高分子链能较充分地伸展,方形微缩通道中高分子链未能充分伸展,而斜坡微缩通道中高分子链的伸展状态介于微直通道与方形微缩通道之间.高分子的存在对微通道系统的温度没有明显影响,对密度与水平流动速度有较明显的影响.高分子链的运动直接影响到周围的简单流体粒子,降低其周围流体粒子的流动速度,对密度与速度产生局部扰动,形成"拖曳"现象.高分子链分布越密集,长度越长,高分子链的拖曳现象越明显.     

粘度法研究壳聚糖与两性聚氨酯胶束间的相互作用

通过粘度法考察了壳聚糖(CS)在盐酸水溶液中与表面带有正电荷的两性聚氨酯(APU)胶束的相互作用，并研究了小分子盐浓度、pH及不同混合方式对复合体系粘度的影响．结果表明：在壳聚糖／APU盐酸混合体系中，较高浓度下APU胶束与壳聚糖分子间的静电斥力作用导致壳聚糖大分子链的伸展，使体系粘度提高，同时降低了壳聚糖溶液对电解质、pH的敏感性；不同混合过程导致壳聚糖大分子构像及其与APU组装、复合形态有很大差别，使混合体系流变性表现出明显的不同．     

Nonlinear electrophoresis of dielectric particles in Newtonian fluids

In classical electrokinetics, the electrophoretic velocity of a dielectric particle is a linear function of the applied electric field. Theoretical studies have predicted the onset of nonlinear electrophoresis at high electric fields because of the nonuniform surface conduction over the curved particle. However, experimental studies have been left behind and are insufficient for a fundamental understanding of the parametric effects on nonlinear electrophoresis. We present in this work a systematic experimental study of the effects of buffer concentration, particle size, and particle zeta potential on the electrophoretic velocity of polystyrene particles in a straight rectangular microchannel for electric fields of up to 3 kV/cm. The measured nonlinear electrophoretic particle velocity is found to exhibit a 2(±0.5)-order dependence on the applied electric field, which appears to be within the theoretically predicted 3- and 3/2-order dependences for low and high electric fields, respectively. Moreover, the obtained nonlinear electrophoretic particle mobility increases with decreasing buffer concentration (for the same particle) and particle size (for particles with similar zeta potentials) or increasing particle zeta potential (for particles with similar sizes). These observations are all consistent with the theoretical predictions for high electric fields.     

The efficiency of electrokinetic pumping at a condition of maximum work

Numerical methods are employed to examine the work, electric power input, and efficiency of electrokinetic pumps at a condition corresponding to maximum pump work. These analyses employ the full Poisson-Boltzmann equations and account for both convective and conductive electric currents, including surface conductance. We find that efficiencies at this condition of maximum work depend on three dimensionless parameters, the normalized zeta potential, normalized Debye layer thickness, and a fluid property termed the Levine number indicating the nominal ratio of convective to conductive electric currents. Efficiencies at maximum work exhibit a maximum for an optimum Debye layer thickness when the zeta potential and Levine number are fixed. This maximum efficiency increases with the square of the zeta potential when the zeta potential is small, but reaches a plateau as the zeta potential becomes large. The maximum efficiency in this latter regime is thus independent of the zeta potential and depends only on the Levine number. Simple analytical expressions describing this maximum efficiency in terms of the Levine number are provided. Geometries of a circular tube and planar channel are examined.     

Analytical study of Joule heating effects on electrokinetic transportation in capillary electrophoresis

Electric fields are often used to transport fluids (by electroosmosis) and separate charged samples (by electrophoresis) in microfluidic devices. However, there exists inevitable Joule heating when electric currents are passing through electrolyte solutions. Joule heating not only increases the fluid temperature, but also produces temperature gradients in cross-stream and axial directions. These temperature effects make fluid properties non-uniform, and hence alter the applied electric potential field and the flow field. The mass species transport is also influenced. In this paper we develop an analytical model to study Joule heating effects on the transport of heat, electricity, momentum and mass species in capillary-based electrophoresis. Close-form formulae are derived for the temperature, applied electrical potential, velocity, and pressure fields at steady state, and the transient concentration field as well. Also available are the compact formulae for the electric current and the volume flow rate through the capillary. It is shown that, due to the thermal end effect, sharp temperature drops appear close to capillary ends, where sharp rises of electric field are required to meet the current continuity. In order to satisfy the mass continuity, pressure gradients have to be induced along the capillary. The resultant curved fluid velocity profile and the increase of molecular diffusion both contribute to the dispersion of samples. However, Joule heating effects enhance the sample transport velocity, reducing the analysis time in capillary electrophoretic separations.     

Electroosmotic flow in a capillary annulus with high zeta potentials

The electroosmotic flow through an annulus is analyzed under the situation when the two cylindrical walls carry high zeta potentials. The analytical solutions for the electric potential profile and the electroosmotic flow field in the annulus are obtained by solving the Poisson-Boltzmann equation and the Stokes equation under an analytical scheme for the hyperbolic sine function. A mathematical expression for the average electroosmotic velocity is derived in a fashion similar to the Smoluchowski equation. Hence, a correction formula is introduced to modify the Smoluchowski equation, taking into account contributions due to the finite thickness of the electric double layer (EDL) and the geometry ratio-dependent correction. Specifically, under a circumstance when the two annular walls are oppositely charged, the flow direction can be determined from the sign of such correction formula, and there exists a zero-velocity plane inside the annulus. With the assumption of large electrokinetic diameters, the location of the zero-velocity plane can be estimated from the analytical expression for the velocity distribution. In addition, the characteristics of the electroosmotic flow through the annulus are discussed under the influences of the EDL parameters and geometric ratio of the inner radius to the outer radius of the annulus.     

Strong effect of hydrodynamic coupling on the electric dichroism of bent rods

The effect of hydrodynamic coupling on the spatial orientation of rigid bent rods in electric fields has been analyzed by Brownian dynamics simulations. Bead models for smoothly bent rods were constructed with dimensions of DNA double helices, and established simulation procedures were used to calculate their diffusion tensor, including the translational-rotational coupling tensor. The electric and optical parameters were assigned on the basis of known properties of double helices. Brownian dynamics simulations of the orientation of these models in electric fields showed that both transients and amplitudes of the calculated dichroism are very strongly dependent on translational-rotational coupling over a wide range of electric field strengths. For example, the stationary dichroism of a smoothly bent 179 bp DNA fragment calculated at low field strengths is positive in the presence and negative in the absence of hydrodynamic coupling. The transients are converted from a biphasic to a monophasic shape, when hydrodynamic coupling is turned off. The large changes resulting from hydrodynamic coupling were controlled by calculations based on analytical expressions derived for electrooptical response curves in the limit of low electric field strengths; the results obtained by this independent approach are in very satisfactory agreement with our Brownian dynamics simulations. The effect is strongly dependent on the electric dipole and on its direction. In the absence of any dipole the coupling effect was not observed. The coupling effect increases with the size of the bent rods. Because most macromolecular structures are known to have induced and/or permanent dipole moments, large effects of hydrodynamic coupling on both the amplitudes and the transients of the electric dichroism/birefringence must be expected in general for structures with nonsymmetric shape.     

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.     

Profiling pH gradients across nanocapillary array membranes connecting microfluidic channels

Nanocapillary array membranes (NCAMs), comprised of thin (d approximately 5-10 microm) nuclear track-etched polycarbonate sheets containing approximately 10(8) cm(-2) nearly parallel nanometer-diameter capillaries, may act to gate fluid transport between microfluidic channels to effect, for example, sample collection. There is interest in H+-transport across these NCAMs because there is significant practical interest in being able to process analyte-containing samples under different pH conditions in adjacent layers of an integrated microfluidic circuit and because protons, with their inherently high mobility, present a challenge in separating microfluidic environments with different properties. To evaluate the capability of NCAMs to support pH gradients, the proton transport properties of NCAMs were studied using laser scanning confocal fluorescence microscopy (LSCFM). Spatiotemporal maps of [H+] in microfluidic channels adjacent to the NCAMs yield information regarding diffusive and electrokinetic transport of protons. The NCAMs studied here are characterized by a positive zeta potential, zeta > 0, so at small nanocapillary diameters, the overlap of electrical double layers associated with opposite walls of the nanocapillary establish an energy barrier for either diffusion or electrokinetic transport of cations through the nanometer-diameter capillaries due to the positive charge on the nanocapillary surface. Proton transfer through an NCAM into microchannels is reduced for pore diameters, d < or = 50 nm and ionic strengths I < or = 50 mM, while for large pore diameters or solution ionic strengths, the incomplete overlap of electric double layer allows more facile ionic transfer across the membranes. These results establish the operating conditions for the development of multilevel integrated nanofluidic/microfluidic architectures which can support multidimensional chemical analysis of mass-limited samples requiring sequential operations to be implemented at different pH values.     

Near-surface ion distribution and buffer effects during electrochemical reactions

The near-surface ion distribution at the solid-liquid interface during the Hydrogen Oxidation Reaction (HOR)/Hydrogen Evolution Reaction (HER) on a rotating platinum disc electrode is demonstrated in this work. The relation between reaction rate, mass transport and the resulting surface pH-value is used to theoretically predict cyclic voltammetry behaviour using only thermodynamic and diffusion data obtained from the literature, which were confirmed by experimental measurements. The effect of buffer addition on the current signal, the surface pH and the ion distribution is quantitatively described by analytical solutions and the fragility of the surface pH during reactions that form or consume H(+) in near-neutral unbuffered solutions or poorly buffered media is highlighted. While the ideal conditions utilized in this fundamental study cannot be directly applied to real scenarios, they do provide a basic understanding of the surface pH concept for more complex heterogeneous reactions.     

Immunoelectrophoresis of red blood cells performed on microcapillary chips

Immunoanalysis of blood cells on a microcapillary electrophoresis (nuCE) chip has been studied using sheep erythrocytes (ShE) as an example. Two different buffer solutions, the phosphate-buffered saline (PBS) and the gelatin veronal buffer (GVB) were examined in regard to the electrokinetic transport behavior of ShE suspended in these solutions inside the rectangular channel engraved on a quartz chip. This clarified two advantages of the use of GVB for on-chip cell electrophoresis: gelatin coatings prevent (i) nonspecific sticking of ShE on the channel wall, and cause (ii) an appreciable reduction in the zeta potential of the wall suppressing the electroosmotic flow of the buffer solution. As a result ShE suspended in the GVB can smoothly migrate from the cathode to the anode, which is the opposite flow direction of immunoglobulin G (IgG) antibodies under the physiological pH condition of 7.4. Based on these results, on-chip capillary cell immunoelectrophoresis of ShE and rabbit anti ShE antibodies (IgG) have been proposed and successfully accomplished using the GVB. It is demonstrated that the variation of the cell migration velocity originating from the change in the surface charge after binding antibodies is applicable to the fast detection of immune reactions and also to single-cell typing.     

Approximate analytic expressions for the electrophoretic mobility of spheroidal particles

Approximate analytic expressions are derived for the electrophoretic mobility of spheroidal particles (prolate and oblate) carrying low zeta potential in an electrolyte solution under an applied tangential or transverse electric field. The present approximation method, which is based on the observation that the electrophoretic mobility of a particle is determined mainly by the distortion of the applied electric field by the presence of the particle. The exact expression for the equilibrium electric potential distribution around the particle, which can be expressed as an infinite sum of spheroidal wave functions, is not needed in the present approximation. The electrophoretic mobility values calculated with these approximate expressions for spheroidal particles with constant surface potential or constant surface charge density are in excellent agreement with the exact numerical results of previous reports with the relative errors less than about 4%.     

Influence of electrolytes on the dynamic surface tension of ionic surfactant solutions: expanding and immobile interfaces

Here, we derive analytical asymptotic expressions for the dynamic surface tension of ionic surfactant solutions in the general case of nonstationary interfacial expansion. Because the diffusion layer is much wider than the electric double layer, the equations contain a small parameter. The resulting perturbation problem is singular and it is solved by means of the method of matched asymptotic expansions. The derived general expression for the dynamic surface tension is simplified for the special case of immobile interface and for the maximum bubble pressure method (MBPM). The case of stationary interfacial expansion is also considered. The effective diffusivity of the ionic surfactant essentially depends on the concentrations of surfactant and nonamphiphilic salt. To test the theory, the derived equations are applied to calculate the surfactant adsorption from MBPM experimental data. The results excellently agree with the adsorption determined independently from equilibrium surface-tension isotherms. The derived theoretical expressions could find application for interpreting data obtained by MBPM and other experimental methods for investigating interfacial dynamics.     

The zeta potential of cyclo-olefin polymer microchannels and its effects on insulative (electrodeless) dielectrophoresis particle trapping devices

While cyclo-olefin polymer microchannels have the potential to improve both the optical detection sensitivity and the chemical resistance of polymer microanalytical systems, their surface properties are to date not thoroughly characterized. These surface properties dictate, among other things, electrokinetic effects when electric fields are present. Here, we report the measurement of the zeta potential of cyclo-olefin polymers (injection-molded and hot-embossed Zeonor 1060R and 1020R) microchannels as a function of pH, counter-ion concentration, storage conditions, and chemical treatment in aqueous solutions both with and without EOF-suppressing additives. In contrast with previous reports, significant surface charge is measured, consistent with titration of charged sites with pK(a) = 4.8. Storage in air, acetonitrile, or aqueous solutions has relatively minor effects. While the source of the surface charge is unclear, chemical functionalization has shown that carboxylic acid groups are not present at the surface, consistent with the chemical structure of Zeonor. EOF-suppressing additives (hydroxypropylmethylcellulose) and conditioning in perchloric acid allow the surface charge to be suppressed. We demonstrate dielectrophoretic particle trapping devices in Zeonor 1060R substrates that show reduced trapping voltage thresholds as compared to previous implementations in glass.     

Diffusiophoresis of charged particles and diffusioosmosis of electrolyte solutions

A review is presented on the theoretical basics and recent developments about the diffusiophoresis of charged particles and diffusioosmosis of electrolyte solutions driven by imposed electrolyte concentration gradients with particular emphasis on the principal analytical formulas and their physical interpretations. For diffusiophoresis, migrations of particles with thin polarized electric double layers but arbitrary zeta potentials and with arbitrary double layers but relatively low surface potentials are both discussed in detail, covering not only diffusiophoresis of single particles but also their motions near solid boundaries or other particles. For diffusioosmosis, fluid flows along single plane walls, in micro/nano-channels, and in porous media are considered, in which the solid walls may have arbitrary zeta potentials or surface charge densities, and both the effect of the lateral distribution of the diffuse ions and the relaxation effect in the double layers on the tangential electric field induced by the prescribed electrolyte concentration gradient are included.     

The Electrophoretic Mobility and Electric Conductivity of a Concentrated Suspension of Colloidal Spheres with Arbitrary Double-Layer Thickness

The electrophoresis in a monodisperse suspension of dielectric spheres with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations, which govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution surrounding the charged sphere in a unit cell, are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. Analytical expressions for the electrophoretic mobility of the colloidal sphere in closed form correct to O(zeta) are obtained. Based on the solution of the electrokinetic equations in a cell, a closed-form formula for the electric conductivity of the suspension up to O(zeta(2)) is derived from the average electric current density. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made for both the electrophoretic mobility and the electric conductivity. Copyright 2001 Academic Press.     

Electrophoresis and electric conduction in a salt-free suspension of charged particles

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.     

Zeta potentials of PDMS surfaces modified with poly(ethylene glycol) by physisorption

Controlling zeta potential of PDMS surface coated with a layer of PEG is important for electroosmosis and electrophoresis in PDMS made microfluidic chips. Here, zeta potentials of PDMS surfaces modified by simple physisorption of PEG of different concentrations in phosphate buffer solutions, pure water, and PEG solution were reported. Coating PEG on PDMS surfaces was achieved by immersing a PDMS layer into the PEG solution for 10 min and then taking it out and placing it in an oven at 80℃ for 10 h. To avoid damaging the PEG layer on the PDMS surface, an induction current method was employed for zeta potential measurement. Zeta potentials of PEG modified PDMS in electrolyte solutions were measured. The results show that 2.5% PEG can effectively modify PDMS surface with positive zeta potential value in phosphate buffer solutions, pure water and 10% PEG solution. Further increase in PEG solution beyond 5% for surface modification has no obvious effect on zeta potential change.     

Colloidal deposition on remotely controlled charged micropatterned surfaces in a parallel-plate flow chamber

This article describes a method to influence colloid deposition by varying the zeta potential at microelectrodes with remotely applied electric potentials. Deposition experiments were conducted in a parallel-plate flow chamber for bulk substrates of glass, indium tin oxide (ITO), and ITO-coated glass microelectrodes in 10 and 60 mM potassium chloride solutions. Colloid deposition was found to be a function of solution chemistry and the small locally delivered electric surface potentials. Electric fields and physical surface heterogeneity can be ruled out as cause of the observed deposition. Results are reported using experimentally determined Sherwood numbers and compared to the predictions of a previously developed patch model. Minor deviations between predicted and experimental Sherwood numbers imply that physical and chemical interactions occur. Specifically, we propose that colloidal particles respond to local variations in surface potential through electrostatic interactions, altering particle streamlines flowing along the surface and ultimately the extent of deposition.