Transient electrokinetic transport in a finite length microchannel: currents, capacitance, and an electrical analogy

Numerical simulations with the fluid mechanics based on the unsteady Navier-Stokes equations and the Poisson-Nernst-Planck formulation of electrostatics and ion transport were used to explore the transient transport of charge through a finite length cylindrical microchannel that is driven by a pressure difference. The evolution of the transcapillary potential from a no-flow equilibrium to the steady-state-steady-flow streaming potential was analyzed by following the convection, migration, and net currents. Observations of the unsteady characteristics of the streaming current, electrical resistance, and capacitance led to an electrical analogy. This electrical analogy was made from a current source (to represent convection current), which was placed in parallel with a capacitor (to allow the accumulation of charge) and a resistor (to permit a migration current). A parametric study involving a range of geometries, fluid mechanics, electrostatics, and mass transfer states allowed predictive submodels for the current source, capacitor, and resistor to be developed based on a dimensional analysis.     

Fluid rheological effects on streaming dielectrophoresis in a post-array microchannel

Recent studies have demonstrated the strong influences of fluid rheological properties on insulator-based dielectrophoresis (iDEP) in single-constriction microchannels. However, it is yet to be understood how iDEP in non-Newtonian fluids depends on the geometry of insulating structures. We report in this work an experimental study of fluid rheological effects on streaming DEP in a post-array microchannel that presents multiple contractions and expansions. The iDEP focusing and trapping of particles in a viscoelastic polyethylene oxide solution are comparable to those in a Newtonian buffer, which is consistent with the observations in a single-constriction microchannel. Similarly, the insignificant iDEP effects in a shear-thinning xanthan gum solution also agree with those in the single-constriction channel except that gel-like structures are observed to only form in the post-array microchannel under large DC electric fields. In contrast, the iDEP effects in both viscoelastic and shear-thinning polyacrylamide solution are significantly weaker than in the single-constriction channel. Moreover, instabilities occur in the electroosmotic flow and appear to be only dependent on the DC electric field. These phenomena may be associated with the dynamics of polymers as they are electrokinetically advected around and through the posts.     

Transient analysis of electroosmotic flow in a slit microchannel

The transient aspects of electroosmotic flow in a slit microchannel are studied. Exact solutions for the electrical potential profile and the transient electroosmotic flow field are obtained by solving the complete Poisson-Boltzmann equation and the Navier-Stokes equation under an analytical approximation for the hyperbolic sine function. The characteristics of the transient electroosmotic flow are discussed under influences of the electric double layer and the geometric size of the microchannel.     

Measurement of the streaming potential and streaming current near a rotating disk to determine its zeta potential

Methodology for determining the zeta potential of a disk-shaped sample by both streaming potential and streaming current measurements is presented. Integration of Laplace's equation within one radius of the disk surface revealed that the streaming potential decreased strongly in the surface normal direction. With this solution, the zeta potential can be calculated from measurements of the streaming potential near the surface of the disk provided the position of the working electrode near the disk surface is known. Determining the zeta potential of a disk-shaped sample by means of streaming current measurements required determination of a current collection efficiency because not all the streaming current from a disk flows through the auxiliary electronic current path. While the working electrode near the disk should be pointlike, several possible variants on counter electrode shape and size were explored. Although the current collection efficiency was only a few percent in each case, the measured current was of 10 nA order. The current collection efficiency depended only on system geometry and was independent of a disk's zeta potential and solution concentration. Streaming current measurements of zeta potential on silicon wafers in potassium chloride solutions up to 10 mM agreed well with published values.     

On the streaming potential across a cation-exchange membrane

Electrical potentials developed during streaming of methanol, water and their mixtures through a Zeokarb 225 (Al⁺⁺⁺ form) membrane have been investigated. Build-up of streaming potential with time has been examined and discussed. Results indicate that dependence of streaming potential on applied pressure difference is non-linear and shows sign reversals. An attempt has been made to explain the results in terms of changes in the structure of electrical double layer at the membrane-permeant interface under the action of streaming pressure.With 4 figures     

Zeta potential of particle bilayers on mica: a streaming potential study

The streaming potential of mica covered by bilayers of latex particles was measured using the parallel-plate channel cell. The size of the first latex (A500) bearing amidine charged groups was 503 nm and the second latex (L800) bearing sulfonate groups was 810 nm (at pH 5.5 and an ionic strength of 10(-2)M). The A500 latex exhibited an isoelectric point at pH 10.5, whereas the L800 latex was strongly negative at all pH. Mica sheets were precovered first by the A500 latex particles under diffusion transport conditions. The coverage of this supporting layer was regulated between 0.02 and 0.5 by changing the bulk concentration of latex and the deposition time. Then, the second layer of the L800 latex of regulated coverage up to 0.55 was deposited under the diffusion transport. The coverage of particles and their distributions in both layers were determined by a direct enumeration of particles by optical microscopy under wet conditions and by AFM. It was shown that the structure of the L800 particle layers and the maximum coverage were in accordance with theoretical simulations performed according to the random sequential adsorption (RSA) model. After forming bilayers of desired composition and structure, streaming potential measurements were carried out. The influence of the mica substrate, the supporting layer coverage, and its zeta potential on the apparent zeta potential of bilayers was systematically studied. It was established that for a bilayer coverage exceeding 0.20, the net zeta potential became independent of the substrate and the supporting layer zeta potentials. Then, the asymptotic values of the zeta potential of the bilayer approach 1/√2=0.71 of the bulk zeta potential of the particles forming the external (second) layer. This behavior was interpreted theoretically in terms of the electrokinetic model derived previously for monolayers. It was also concluded that results obtained in this work can be exploited for interpretation of polyelectrolyte film formation in the layer by layer (LbL) processes and protein adsorption pertinent to the antigen/antibody interactions.     

Calculation of the streaming potential near a rotating disk

A corrected theory of the streaming potential in the vicinity of a disk-shaped sample rotating in an electrolytic solution is presented. When streaming-potential measurements on a variety of materials were reduced to a zeta potential according to a prior theory, the results exceeded expected values by a factor of approximately 2, even though other aspects of the same experiments seemed to confirm the theory. Investigation of the source of the discrepancy revealed a flaw in the prior theory. The crucial understanding is that the surface current produced by the rotation of the disk emerges from the diffuse layer and enters the bulk solution at the periphery of the disk. The new treatment accounts entirely for the discrepancy between literature data and results based on the prior theory.     

Controlling the photochemical reactions of alkenes by light-path length effects of a microchannel reactor

Photoirradiation of Me₂CO–H₂O solution of pent-4-en-1-ol (1a) with a high-pressure mercury lamp in a test tube gave 8-hydroxyoctan-2-one (3a) in 66 % yield along with oxetane (4a) and the isomer (4a′) in 10 % yield. Irradiation of the running Me₂CO–H₂O solution of 1a in the flow system of a microchannel reactor (MCR) gave mainly 4a. The photoreaction of 1,1-diphenylethene (2a) with triethylamine gave a Markovnikov-type adduct (5a) and an anti-Markovnikov-type adduct (6a). The use of the MCR enhanced the production of 5a. These phenomena were explained by the light-path length effects of the MCR.     

Investigation of dynamic streaming potential by dimensional analysis

The theory of streaming potential at sinusoidal flow of liquid in a porous medium is a convenient and fruitful tool for determination of the interface properties of materials and also for construction of apparatus for zeta potential measurements and electrokinetic transducers. An investigation of the dynamic streaming potential by the method of dimensional analysis is presented. This method provides a wider approach to the problem under consideration. As a result, relationships between streaming potential in a porous medium and mechanical quantities are established. These quantities include pressure gradient in a liquid inside pores and capillaries, acceleration of capillaries, and the solid part of a porous medium, and the viscous friction force the liquid exerts on the solid part. The corresponding formulas for streaming potential are presented. The relationship between the streaming potential and viscous friction force does not depend on the frequency of oscillation and pore size. All these formulas in particular cases are transformed to known formulas for the streaming potential.     

A quantum particle in a moving finite harmonic potential

In this paper a quantum particle trapped in a finite harmonic oscillator confined in the moving interval is investigated. With a help of a suitable unitary transform, the wave functions and time-dependent energy levels are obtained.     

Computational electrochemistry: finite element simulation of a disk electrode with ultrasonic acoustic streaming

Computer simulations using the finite element method (FEM) are used to predict the correlation between the transport limiting current (I(lim)) and parameters such as diffusion coefficient, source to electrode separation, source power, and medium viscosity for a sonicated disk electrode in "face on" mode. The fluid dynamics and diffusion layer are modeled directly using FEM and predict that the electrode is uniformly accessible, I(lim) is proportional to the diffusion coefficient to the 2/3 power and I(lim) is proportional to the square root of the source power. Curves are also calculated relating I(lim) to the source to electrode separation and liquid viscosity.     

Tangential streaming potential as a tool in modeling of ion transport through nanoporous membranes

Tangential streaming potential (TSP) measurements have been carried out so as to assess the electrokinetic properties of the active layer of organic nanofiltration (NF) membranes. Due to the porous structure of NF membranes, cares must be taken to convert the experimental data into zeta potential. Indeed, an assumption that is implicitly made in Smoluchowski's theory (or in related approaches accounting for the surface conduction phenomenon) is that both streaming and conduction currents involved in the streaming potential process flow through an identical path. Such an assumption does not hold with porous membranes since the conduction current is expected to flow wherever the electric conductivity differs from zero. Consequently, a non-negligible share of the conduction current is likely to flow through the membrane body filled with the electrolyte solution. This phenomenon has been taken into account by carrying out a series of TSP measurements at various channel heights. Experiments have been conducted with various electrolyte solutions. The inferred zeta potentials have been further converted into membrane volume charge densities which have been used to predict the membrane performances in terms of rejection rates. The conventional NF theory, i.e. based on a steric/Donnan exclusion mechanism, has been found to be unable to describe the experimental rejection rates. Using the volume charge density of the membrane as an adjustable parameter, it has been shown that the conventional theory even predicts the opposite sign for the membrane charge. On the other hand, the experimental rejection rates have been well described by including dielectric effects in the exclusion mechanism. In this case, a noticeable lowering of the effective dielectric constant of the electrolyte solution inside pores has been predicted (with respect to the bulk value).     

Inorganic membrane selectivity to ions in relation with streaming potential

The streaming potential, permeate flux and ion transmission are measured on an inorganic ultra filtration membrane (ZrO₂). The streaming potential depends on charge distribution, which is modified by changing the pH, the ionic strength, and the nature of ions. This study points out the effect of membrane net charge on ion transmission for monovalent and divalent salt filtration (NaCl and CaCl₂), even in the case of large pore radius (2 nm, MWCO=10 000 g/mol) compared to the ionic radius in the case of the tangential filtration. The filtration of a mixture of both the salts put into the fore that sodium ion transmission is slowed down when calcium is present in solution because of the relative ion mobility.     

Zeta potential of ion-conductive membranes by streaming current measurements

Surface charge properties have a significant influence on membrane retention and fouling performance. As a key parameter describing the surface charge of membranes used in aqueous applications, zeta potential measurements on membranes of various types have attracted great attention. During the zeta potential characterization of a series of ion-conductive sulfonated poly(sulfone) membranes, it was found that the measured streaming current varied with the thickness of the sample, which is not predicted by the classical Smoluchowski equation. Moreover, for higher conductivity membranes with an increased concentration of sulfonate groups, the zeta potential tended toward zero. It was determined that the influence of membrane bulk conductance on the measured streaming current must be taken into account in order to correctly interpret the streaming current data for ion-conductive polymers and understand the relationship between membrane chemical composition and zeta potential. Extrapolating the measured streaming current to a membrane thickness of zero has proven to be a feasible method of eliminating the error associated with measuring the zeta potential on ion conductive polymer membranes. A linear resistance model is proposed to account for the observed streaming currents where the electrolyte channel is in parallel with the ion-conductive membranes.     

Characterization of polyelectrolyte multilayers by the streaming potential method

Polyelectrolyte multilayer adsorption on mica was studied by the streaming potential method in the parallel-plate channel setup. The technique was calibrated by performing model measurements of streaming potential by using monodisperse latex particles. Two types of polyelectrolytes were used in our studies: poly(allylamine) hydrochloride (PAH), of a cationic type, and poly(sodium 4-styrenesulfonate) (PSS) of an anionic type, both having molecular weight of 70,000. The bulk characteristics of polymers were determined by measuring the specific density, diffusion coefficient for various ionic strengths, and zeta potential. These measurements as well as molecular dynamic simulations of chain shape and configurations suggested that the molecules assume an extended, wormlike shape in the bulk. Accordingly, the diffusion coefficient was interpreted in terms of a simple hydrodynamic model pertinent to flexible rods. These data allowed a proper interpretation of polyelectrolyte multilayer adsorption from NaCl solutions of various concentrations or from 10(-3) M Tris buffer. After completing a bilayer, periodic variations in the apparent zeta potential between positive and negative values were observed for multilayers terminated by PAH and PSS, respectively. These limiting zeta potential values correlated quite well with the zeta potential of the polymers in the bulk. The stability of polyelectrolyte films against prolonged washing (reaching 26 h) also was determined using the streaming potential method. It was demonstrated that the PSS layer was considerably more resistant to washing, compared to the PAH layer. It was concluded that the experimental data were consistent with the model postulating particle-like adsorption of polyelectrolytes with little chain interpenetration. It also was concluded that due to high sensitivity, the electrokinetic method applied can be effectively used for quantitative studies of polyelectrolyte adsorption, desorption, and reconformation.     

Characterization of capillary inner surface conditions with streaming potential

Streaming potential is created when an electrolyte solution is forced to flow pass a charged surface. For an uncoated fused silica capillary, the streaming potential is measured between the inlet and outlet vials while applying a pressure across the capillary. The changes in streaming potential can be used to characterize the properties of the capillary inner surface. In this work, HCl, NaCl, and NaOH solutions ranging from 0.4 to 6 mM were used as the background electrolyte (BGE) at temperatures of 15 to 35 °C for the mesurements. The streaming potential decreases with the increase in BGE concentration, and the trend is amplified at higher temperatures. When buffer solutions in the pH range of 1.5 to 12.7 were used as the BGE, streaming potential was shown to be sensitive to changes in pH but reaches a maximum at around 9.5. At pH < 3.3, no streaming potentials were observed. The pH of zero surface charge (streaming potential equals 0) changes with temperature, and is measured to be 3.3 to 3.1 when the temperature is changed from 15 to 35°C. Zeta potentials can be calculated from the measured streaming potential, conductivity, and the solution viscosity. Surface charge densities were calculated in this work using the zeta potentials obtained. We demonstrated that capillary surface conditions can significantly change the streaming potential, and with three different solutions, we showed that analyte-dependent adsorption can be monitored and mitigated to improve the peak symmetry and migration times reproducibility.     

Droplet formation in a microchannel network

A method is given for generating droplets in a microchannel network. With oil as the continuous phase and water as the dispersed phase, pico/nanoliter-sized water droplets can be generated in a continuous phase flow at a -junction. The channel for the dispersed phase is 100 microm wide and 100 microm deep, whereas the channel for the continuous phase is 500 microm wide and 100 microm deep. For given experimental parameters, regular-sized droplets are reproducibly formed at a uniform speed. The diameter of these droplets is controllable in the range from 100-380 microm as the flow velocity of the continuous phase is varied from 0.01 m s(-1) to 0.15 m s(-1).