Electrical potential in a cylindrical double layer: a functional theory approach

Employing an iterative method in functional theory, the electrical potential distribution for the case of a cylindrical surface is solved. Although the analytical result derived is of an iterative nature, the second-order solution is found to be sufficiently accurate under conditions of practical significance. For the case of constant surface potential, the radius and the surface potential of a cylindrical surface can be estimated based on the extreme of the electrical potential distribution. The effects of the key parameters, including the number and the valence of the ions on a surface, the length of a particle, the relative permittivity of the liquid phase, the temperature, and the concentration of electrolyte on the surface potential, are examined. The general behavior of these effects is similar to that for a spherical surface, except that the surface potential of a cylindrical surface is independent of the electrolyte concentration. The present approach is also applicable to the case where a cylindrical surface remains at a constant charge density.     

Liquid flow inside a cylindrical capillary with walls covered with a porous layer (Gel)

Viscous incompressible liquid flow in a long cylindrical capillary, the internal surface of which is covered with a permeable porous layer, is studied within the frameworks of three mathematical models. In the first model, the liquid flow in the porous layer is described by the Brinkman equation; according to the second one, the presence of the porous layer is taken into account using the Navier slip boundary conditions; and, in the third model, the Navier condition is imposed on the porous layer-liquid interface, with the flow inside the porous layer being excluded. The theoretical predictions are compared with the experimental data that one of us has obtained for liquid flow rates in porous capillaries. The validity and appropriateness of the application of the proposed models are discussed.     

The electric double layer capacitance for a hard sphere ion-dipole electrolyte in the mean field approximation

The electric double layer capacitance for a hard sphere ion-dipole system in the neighbourhood of a plane charged wall is calculated in the mean field approximation. To order ka the capacitance predicts the same structural features as the MSA capacitance.     

Electrokinetic boundary condition compatible with the Onsager reciprocal relation in the thin double layer approximation

The boundary condition, which has been used in the conventional electrokinetic calculation in the thin double layer approximation, has a flaw that it does not give the Onsager reciprocal relation for the sedimentation of charged particle. We propose a new boundary condition, which satisfies the reciprocal relation, and derive a general form for the mobility matrix for the motion of a charged particle under the action of external force, torque, and electric field. We then calculate the mobility matrix explicitly for homogeneously charged spherical particle and discuss the effect of the surface slippage and the surface conductivity on the particle mobility and electric conductivity.     

Diffusioosmosis of electrolyte solutions in a capillary slit with adsorbed polyelectrolyte layers

A theoretical study is presented for the steady diffusioosmotic flow of an electrolyte solution in a fine capillary slit with each of its inside walls coated with a layer of polyelectrolytes generated by an imposed tangential concentration gradient. In this solvent-permeable and ion-penetrable surface charge layer, idealized polyelectrolyte segments are assumed to be distributed at a uniform density. The electric double layer and the surface charge layer may have arbitrary thicknesses relative to the gap width between the slit walls. The Poisson-Boltzmann equation and a modified Navier-Stokes/Brinkman equation are solved numerically to obtain the electrostatic potential, dynamic pressure, tangentially induced electric field, and fluid velocity as functions of the lateral position in the slit in a self-consistent way, with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions. The existence of the surface charge layers can lead to a diffusioosmotic flow quite different from that in a capillary with bare walls. The effect of the lateral distribution of the induced tangential electric field and the relaxation effect due to ionic convection in the slit on the diffusioosmotic flow are found to be very significant in practical situations.     

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.     

Electrokinetic flow in a capillary with a charge-regulating surface polymer layer

An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson-Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.     

Surface instability of a thin electrolyte film undergoing coupled electroosmotic and electrophoretic flows in a microfluidic channel

We consider the stability of a thin liquid film with a free charged surface resting on a solid charged substrate by performing a general Orr-Sommerfeld (O-S) analysis complemented by a long-wave (LW) analysis. An externally applied field generates an electroosmotic flow (EOF) near the solid substrate and an electrophoretic flow (EPF) at the free surface. The EPF retards the EOF when both the surfaces have the same sign of the potential and can even lead to the flow reversal in a part of the film. In conjunction with the hydrodynamic stress, the Maxwell stress is also considered in the problem formulation. The electrokinetic potential at the liquid-air and solid-liquid interfaces is modelled by the Poisson-Boltzmann equation with the Debye-Hückel approximation. The O-S analysis shows a finite-wavenumber shear mode of instability when the inertial forces are strong and an LW interfacial mode of instability in the regime where the viscous force dominates. Interestingly, both the modes are found to form beyond a critical flow rate. The shear (interfacial) mode is found to be dominant when the film is thick (thin), the electric field applied is strong (weak), and the zeta-potentials on the liquid-air and solid-liquid interfaces are high (small). The LW analysis predicts the presence of the interfacial mode, but fails to capture the shear mode. The change in the propagation direction of the interfacial mode with the zeta-potential is predicted by both O-S and LW analyses. The parametric range in which the LW analysis is valid is thus demonstrated.     

System peaks and optimization of anion separation in capillary electrophoresis with non-reversed electroosmotic flow

We studied system peaks present in the electropherograms obtained in the separation of anions by capillary electrophoresis with indirect spectrophotometric detection and cathode electroosmotic flow (EOF) with a chromate background electrolyte. The system peaks correspond to the zones with changed concentration of the background electrolyte; they formed when the zones of each analyte passed through the outlet of the capillary and then moved towards the EOF detector. It has been revealed that the height and area of the system peaks linearly depends on the concentration of the corresponding anion and the areas of the system peaks can achieve 10% of the anion peak area. An algorithm has been proposed for the determination of the optimal conditions for anion separation using hydrodynamic pressure for the regulation of the EOF flow rate. This algorithm prevents the overlapping of the anion and system peaks.     

Dynamic interfacial effect of electroosmotic slip flow with a moving capillary front in hydrophobic circular microchannels

Miniaturization of chemical analysis using microfabrication is an emerging technology. The use of polymeric materials as opposed to conventional glass substrate is also a promising alternative. As most polymeric materials are hydrophobic relative to glass, we describe here the implication for the loading process of electroosmotic flow (EOF) when a three-phase (solid-liquid-vapor) contact line exists. The presence of these interfaces can result in a large Laplace pressure that resists EOF and hence hinders its flow performance. This effect depends on the phenomenological contact angle at the solid-liquid interface. In our model for EOF, we considered simultaneously the presence of an electric double layer, liquid slips via a weaker solid-liquid interaction and Laplace pressure across a liquid-vapor interface.     

Electrophoresis of a sphere along the axis of a cylindrical pore: effects of double-layer polarization and electroosmotic flow

The electrophoresis of a rigid sphere along the axis of a cylindrical pore is investigated theoretically. Previous analysis is extended to the case where the effects of double-layer polarization and electroosmotic flow can be significant. The influences of the surface potential, the thickness of the double layer, and the relative size of a pore on the electrophoretic behavior of a sphere are discussed. Some interesting results are observed. For example, if both a sphere and a pore are positively charged, then the mobility of the sphere has a local minimum as the thickness of its double layer varies. Depending upon the level of the surface potential of a sphere and the degree of significance of the boundary effect, the mobility of the sphere may change its sign twice as the thickness of its double layer varies. This result can play a significant role in electrophoresis measurements.     

Multi-gradient hydrogels produced layer by layer with capillary flow and crosslinking in open microchannels

This technical note describes a new bench-top method for producing anisotropic hydrogels composed of gradient layers of soluble factors, particles, polymer concentrations or material properties. Each gradient layer was produced by a previous gradient method in which a droplet of one precursor solution was added to a thin layer of a second solution. The ensuing rapid capillary flow along the open channel generated a gradient precursor solution, which was then crosslinked to form a gradient gel. Repeating these steps allowed a layered gel to be iteratively constructed with as many gradient layers as desired. This technique renders the synthesis of multi-layered gradient gels accessible to virtually any researcher and should help simplify the production of more biologically relevant cellular microenvironments.     

The electrical double layer of micelles in ionic surfactant solutions in the presence of a background electrolyte: 1. Diluted micellar solutions of sodium dodecyl sulfate

The structure of the electrical double layer (EDL) of micelles in dilute micellar solutions in the presence of a background electrolyte is studied within the framework of the Gouy-Chapman-Stern theory. On the basis of the Stern isotherm for counterion adsorption, conditions of electroneutrality, and the Gauss condition at the interface between the diffuse and dense parts of EDL, three equations are derived for the electrostatic potentials of the surface of micelle cores and the diffuse part of EDL as well as for the potential of the specific adsorption of counterions. Model parameters are verified by the example of sodium dodecyl sulfate (SDS). Potentials of the diffuse part of EDL, the degree of binding of counterions with micelles, and the specific adsorption potential are calculated from the experimental data on the potential of the surface of SDS micelle cores and their sizes, critical micellization concentration, aggregation numbers, and the constants of premicellar association. The specific adsorption potential of SDS is found to be ?(4.6 ± 0.1)?, where ? is the product of Boltzmann’s constant and absolute temperature. The specific adsorption potential is independent of the background electrolyte concentration, remains constant within the determination error of the parameters, and substantially contributes to the formation of EDL of micelles.     

Visualizing the transient electroosmotic flow and measuring the zeta potential of microchannels with a micro-PIV technique

We have demonstrated a transient micro particle image velocimetry (micro-PIV) technique to measure the temporal development of electroosmotic flow in microchannels. Synchronization of different trigger signals for the laser, the CCD camera, and the high-voltage switch makes this measurement possible with a conventional micro-PIV setup. Using the transient micro-PIV technique, we have further proposed a method on the basis of inertial decoupling between the particle electrophoretic motion and the fluid electroosmotic flow to determine the electrophoretic component in the particle velocity and the zeta potential of the channel wall. It is shown that using the measured zeta potentials, the theoretical predictions agree well with the transient response of the electroosmotic velocities measured in this work.     

Salient features of the electrical double layer structure on mechanically renewed gold-silver electrodes in aqueous solutions of a surface-inactive electrolyte

The behavior of electrodes, which are made of binary Au-Ag alloys (Ag content 1–15 at %) and renewed by mechanical cutting in aqueous solutions of sodium fluoride, is studied with the aid of cyclic voltammetry and impedance methods. It is established that, in the region of potentials corresponding to ideal polarizability, the differential capacitance of the electrical double layer rapidly changes with time elapsed after the renewal of the surface of the electrodes. The change in the capacitance is brought about by the exit of silver atoms into a surface layer. The implication is that silver is the surface-active component in these alloys. The rate of the surface segregation of silver atoms depends on the electrode potential. The segregation rate substantially increases upon going into the region that corresponds to positive charges of the silver electrode surface and to the beginning of adsorption of atomic oxygen on the electrode. Based on phenomenological models, a method for processing capacitance curves is realized, which links experimentally observed time effects to variations that occur in the surface composition, and assumptions concerning the mechanism of relaxation processes that are responsible for the observed time effects are put forth. Explicit data on the effect, which is exerted by mechanical renewal on the composition of the surface layer of Au-Ag alloys at different distances from the interface with a vacuum, are obtained with the aid of an x-ray photoelectron spectroscopy method. It is established that the surface layer (～0.5 nm) is enriched by silver atoms as compared with the alloy’s bulk.     

Peak broadening in capillary zone electrophoresis with electroosmotic flow: Dependence of plate number and resolution on charge number

Summary Based on the Einstein-Nernst equation, describing the relation between diffusion coefficient and ionic mobility, and expression for the plate height and plate number can be obtained which is independent of the diffusion coefficient. This approach was supported by experimental data, obtained from anionic and cationic solutes. An expression for the electrophoretic resolution is introduced that is also independent on diffusion coefficients. The effect of electro-osmotic flow on the separation of anions and cations based on the expressions derived for the plate number and the resolution is discussed.     

Streaming potential and electroosmotic flow in heterogeneous circular microchannels with nonuniform zeta potentials: requirements of flow rate and current continuities

Real surfaces are typically heterogeneous, and microchannels with heterogeneous surfaces are commonly found due to fabrication defects, material impurities, and chemical adsorption from solution. Such surface heterogeneity causes a nonuniform surface potential along the microchannel. Other than surface heterogeneity, one could also pattern the various surface potentials along the microchannels. To understand how such variations affect electrokinetic flow, we proposed a model to describe its behavior in circular microchannels with nonuniform surface potentials. Unlike other models, we considered the continuities of flow rate and electric current simultaneously. These requirements cause a nonuniform electric field distribution and pressure gradient along the channel for both pressure-driven flow (streaming potential) and electric-field-driven flow (electroosmosis). The induced nonuniform pressure and electric field influence the electrokinetic flow in terms of the velocity profile, the flow rate, and the streaming potential.