Determination of the Navier slip coefficient of microchannels exploiting the streaming potential

For most microchannels made of hydrophobic materials such as polymers, velocity slip occurs at the wall, affecting volumetric flow rate of electroosmotic flow Q(eof) and streaming potential (??(str)/?z). Since most techniques exploit Q(eof) or (??(str)/?z) to determine the zeta potential, ζ, it is very difficult to measure ζ of hydrophobic walls, if the slip coefficient b is not found a priori. Until now, Q(eof) and (??(str)/?z) are known to depend on ζ and b in a same functional form, which makes it impossible to estimate ζ or b separately using measurements of Q(eof) and (??(str)/?z). However, exploiting the analytic formula for Q(eof) and (??(str)/?z) derived in the present work, it is found that the effect of ζ and that of b on Q(eof) and (??(str)/?z) can be separated from each other by varying the bulk ionic concentration. Thus, the slip coefficient as well as the zeta potential of hydrophobic microchannels can be found with reasonable accuracy by means of a nonlinear curve fitting method using measured data of Q(eof) and (??(str)/?z) at various bulk ionic concentrations. The present method allows an accurate estimation of slip coefficient of hydrophobic microchannels, which is quite simple and cheap compared with methods employing microparticle velocimetry.     

Electrokinetic characterization of porous plugs from streaming potential coupled with electrical resistance measurements

The zeta potential of mixed nickel-iron oxide particles is evaluated by a new laboratory instrument. This latter allows the measurement of streaming potential together with the electrical resistance of porous plugs. The conductivity of electrolyte inside plug (pore conductivity) is deduced from electrical resistance measurements and is used together with streaming potential to evaluate the zeta potential by accounting for the surface conduction phenomenon. It is shown that neglecting the surface conduction phenomenon leads to a substantial underestimation of the zeta potential. The coupled measurements of streaming potential and plug electrical resistance yield zeta potential values that are in very good agreement with those obtained by electrophoresis. The densification of the porous plug with increasing pressure increments is put in evidence by the decrease in measured streaming potentials. Electrical resistance measurements make it possible to account for the increase in surface conductivity resulting from the more compacted structure of the plug. By doing so, the calculated zeta potential is found to be virtually independent of the pressure difference involved in streaming potential experiments, whereas the negligence of surface conduction phenomenon leads to a decrease in the apparent zeta potential with increasing pressure level.     

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.     

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.     

Polyelectrolyte adsorption layers studied by streaming potential and particle deposition

Adsorption of a cationic polyelectrolyte, polyallylamine hydrochloride (PAH), having a molecular weight of 70,000 on mica was characterized by the streaming potential method and by deposition of negative polystyrene latex particles. Formation of PAH layers was followed by determining the apparent zeta potential of surface zeta as function of bulk PAH concentration. The zeta potential was calculated from the streaming potential measured in the parallel-plate channel formed by two mica plates precovered by the polyelectrolyte. The experimental data were expressed as the dependence of the reduced zeta potential zeta/zeta0 on the PAH coverage Theta(PAH), calculated using the convective diffusion theory. It was found that for the ionic strength of 10(-2) M, the dependence of zeta/zeta0 on Theta(PAH) can be reflected by the theoretical model formulated previously for surfaces covered by colloid particles. The electrokinetic measurements were complemented by particle deposition experiments on PAH-covered mica surfaces. A direct correlation between the polymer coverage and the initial deposition rate of particles, as well as the jamming coverage, was found. For ThetaPAH > 0.3 the initial deposition rate attained the value predicted from the convective diffusion theory for homogeneous surfaces. The initial deposition rates for surfaces modified by PAH were compared with previous experimental and theoretical results obtained for heterogeneous surfaces formed by preadsorption of colloid particles. It was revealed that negative latex deposition occurred at surfaces exhibiting negative apparent zeta potential, which explained the anomalous deposition of particles observed in previous works. It was suggested that the combined electrokinetic and particle deposition methods can be used for detecting adsorbed polyelectrolytes at surfaces for coverage range of a percent. This enables one to measure bulk polyelectrolyte concentrations at the level of 0.05 ppm.     

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.     

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.     

Fibrinogen adsorption on mica studied by AFM and in situ streaming potential measurements

Adsorption of fibrinogen from aqueous solutions on mica was studied using AFM and in situ streaming potential measurements. In the first stage, bulk physicochemical properties of fibrinogen and the mica substrate were characterized for various ionic strength and pH. The zeta potential and number of uncompensated (electrokinetic) charges on the protein surfaces were determined from microelectrophoretic measurements. Analogously, using streaming potential measurements, the electrokinetic charge density of mica was determined for pH range 3-10 and the NaCl background electrolyte concentration of 10(-3) and 10(-2) M. Next, the kinetics of fibrinogen adsorption at pH 3.5 and 7.4 in the diffusion cell was studied using a direct AFM determination of the number of molecules per unit area of the mica substrate. Then, streaming potential measurements were performed to determine the apparent zeta potential of fibrinogen-covered mica for different pH and ionic strength in terms of its surface concentration. A quantitative interpretation of these streaming potential measurements was achieved in terms of the theoretical model postulating a side-on adsorption of fibrinogen molecules as discrete particles. On the basis of these results, the maximum coverage of fibrinogen Θ close to 0.29 was predicted, in accordance with previous theoretical predictions. It was also suggested that anomalous adsorption for pH 7.4, where fibrinogen and the mica substrate were both negatively charged, can be explained in terms of a heterogeneous charge distribution on fibrinogen molecules. It was estimated that the positive charge was 12 e (for NaCl concentration of 10(-2) M and pH 7.4) compared with the net charge of fibrinogen at this pH, equal to -21 e. Results obtained in this work proved that the coverage of fibrinogen can be quantitatively determined using the streaming potential method, especially for Θ < 0.2, where other experimental methods become less accurate.     

An improved method for determining zeta potential and pore conductivity of porous materials

An improved method based on streaming potential and streaming current was proposed to determine zeta potential and surface conductance of porous material simultaneously. In the electrokinetic generation mode, a resistor is connected to the generator and by measuring the voltage drop across resistors with different resistance, a true streaming current can be determined. The zeta potential and surface conductivity can be obtained simultaneously from their relation to streaming potential and streaming current. The electrode and ion concentration polarization effects during the measurement were also discussed. The resistance from channel ends to electrodes, which has typically been ignored in the literature, was shown to have a significant influence on the calculated zeta potential and surface conductance. Ignorance of this resistance would lead to underestimation of both zeta potential and surface conductance values.     

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.     

Influence of roughness and capillary size on the zeta potential values obtained by streaming potential measurements

Streaming potential measurements are performed to determine the zeta potential of flat surfaces, particles, or fibers. Although the zeta potential is a well-defined property of solid surfaces in a liquid, there are indications that the absolute values of the zeta potential calculated using the Helmholtz-Smoluchowski equation are affected by surface roughness and—in case of particle or fiber assemblies—their packing density. The study at hand investigates these influences using flat polymer surfaces with different roughness and topography and assemblies of basalt spheres. It was found that increasing roughness of the flat surface and larger size or smaller number of particles in particle assemblies result in flatter slopes of the streaming potential versus pressure and thus lower apparent absolute values of the zeta potential. The interpretation of streaming potential measurements should therefore not focus on absolute zeta potential values but on trends in pH- and concentration-dependent measurements.     

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).     

Measurement of the zeta potential of planar solid surfaces by means of a rotating disk

A method for measuring the zeta potential of disks is described. Combining the hydrodynamic properties of a rotating disk, the solution of Laplace's equation for the potential, and the electrokinetic boundary condition, one obtains an equation that relates the zeta potential of the disk to the streaming potential in the disk's vicinity. Theory predicts a dependence of the streaming potential on the rotation rate raised to the 3/2 power. Theory also shows that placement of one reference electrode on the axis of rotation near the disk surface and the other far from the disk is favorable. Measurement of the streaming potential of silicon oxide and indium tin oxide in contact with a solution of potassium chloride demonstrated the expected 3/2 power dependence on rotation rate. The zeta potentials calculated from the combination of the theory and experimental data agreed with published values.     

Probing of polyelectrolyte monolayers by zeta potential and wettability measurements

Detection of the very first step of polyelectrolyte adsorption onto a solid support is of great importance for understanding mechanisms of solid surface modification. It was shown that streaming potential and contact angle measurements can be successfully used for polyelectrolyte (PE) adsorption characterization in a broad range of surface coverage. Cationic polyallylamine hydrochloride (PAH) was used for the formation of the layer. The electrokinetic characteristics of the substrate covered by the PAH layer were compared with contact angles measured under wet (captive air bubble/substrate in water) and dry (sessile water droplet/dried substrate) conditions. It has been demonstrated that contact angle values determined under both conditions are in good agreement. The observed rapid increase in the contact angle from zero for the bare mica surface to the value close to one characteristic of the PAH monolayer appears in the same PAH coverage range as zeta potential value changes due to adsorption. These results show that wettability can be as sensitive to the presence of small amounts of adsorbed species as electrokinetic measurements.     

Tangential flow streaming potential measurements: Hydrodynamic cell characterization and zeta potentials of carboxylated polysulfone membranes

Computational fluid dynamics calculations were carried out to ensure that a self-made tangential flow mode streaming potential measurement cell meets the hydrodynamic stipulations of laminar, steady and established electrolyte flow necessary for reproducible electrokinetic measurements. The calculations show that the cell design meets all of these conditions.Six carboxylated polysulfones with a range of different degrees of substitution (DS) from 0.26 to 1.74 carboxyl groups per polymer repeat unit were synthesized in a two-stage process of lithiation and carboxylation. Ultrafiltration membranes were made from both the unmodified polysulfone and these hydrophilic materials. The zeta potentials of these membrane surfaces were determined in 0.001 M KCl solution as a function of pH. The curves show the theoretically expected profiles for non-ionic and weakly acidic materials. The growing influence of the COOH dissociation on the surface charge formation is indicated by the flattening of the curves at low pH values. The magnitude of the negative zeta potentials plateau values ranged from −52 to −20 mV. While unmodified PSU has a plateau value of −52 mV this value decreases continuously with increasing DS to −20 mV for the PSU-COOH 1.74 material. It is suggested that this arises from a shift of the electrokinetic shear plane into the bulk electrolyte solution due to an extended swelling layer reflecting the enhanced hydrophilicity of these membrane surfaces.     

Characterization of chitosan nanofiber fabric by electrospray deposition: electrokinetic and adsorption behavior

Cationic biopolymer nanofiber fabrics were prepared from a chitosan/poly(ethylene oxide) blend solution by electrospray deposition. Their electrokinetic properties and DNA adsorption behavior were analyzed as a function of pH. The zeta potential was determined from streaming potential/streaming current measurements. The adsorption of DNA onto the fabrics was investigated by spectrophotoscopy. The adsorption behavior of DNA correlated well with the electrokinetic properties of the fabrics. This revealed that the electrokinetic approach was a useful option for characterization of novel nanofiber assemblies made by the electrostatic spray process. In addition, these results provided fundamental information about chitosan nanofiber fabrics for both biomedical and analytical applications.     

Fabrication and validation of a multi-channel type microfluidic chip for electrokinetic streaming potential devices

To elaborate on the applicability of the electrokinetic micro power generation, we designed and fabricated the silicon-glass as well as the PDMS-glass microfluidic chips with the unique features of a multi-channel. Besides miniaturizing the device, the key advantage of our microfluidic chip utilization lies in the reduction in water flow rate. Both a distributor and a collector taking the tapered duct geometry are positioned aiming the uniform distribution of water flow into all individual channels of the chip, in which several hundreds of single microchannels are assembled in parallel. A proper methodology is developed accompanying the deep reactive ion etching as well as the anodic bonding, and optimum process conditions necessary for hard and soft micromachining are presented. It has been shown experimentally and theoretically that the silicon-based microchannel leads to increasing streaming potential and higher external current compared to those of the PDMS-based one. A proper comparison between experimental results and theoretical computations allows justification of the validity of our novel devices. It is useful to recognize that a material inducing a higher magnitude of zeta potential has an advantage for obtaining higher power density under the same external resistance.     

Characterisation of the electrokinetic properties of plane inorganic membranes using streaming potential measurements

We present and test a device designed to measure the streaming potential of plane inorganic membrane during filtration.Two kinds of microporous membranes (a membrane made of a mixture of alumina-titania and this same type of membrane covered with an additional titania layer) are studied with different pH, ionic strength and electrolyte nature. The modification of the surface acid-basic equilibriums is analysed from the streaming potential measurements. The pores size of the studied membranes is large enough to avoid overlapping of the double layers. Streaming potential measurements are used to determine the zeta potential of the membranes from the Helmholtz-Smoluchowski relationship, corrected for the lowest ionic strengths studied. The shifting of the isoelectric point of the membranes studied with CaCl₂ and Na₂SO₄ solutions shows specific adsorption of calcium and sulfate ions onto the surface. The additional titania layer on the alumina-titania support does not seem to modify the electrokinetic properties of the membrane.The interactions of the alumina-titania membrane with the H⁺ and OH⁻ ions are analysed by studying the variations of pH between permeate and retentate compartments. These variations allow determining the isoelectric point of the membrane with a reasonable precision.     

Determination of the electrokinetic potential of dispersed and macromolecular colloids by means of streaming potential measurements. II.

A principle for determining the electrokinetic potential, based on the measurement of the streaming potential has been developed for the investigation of dispersions of low concentration (10–100 ppm) and ultrafiltrable macromolecular solutions. An ultrafiltration apparatus operating with a permanent pressure difference was constructed, in which the streaming potential E produced on the filter layer and the filtration rate W were measured simultaneously on an XY recorder. The so-called apparent electrokinetic potential was calculated from the axial intercept E_∞ obtained by the extrapolation of the E vs. W curves. It was pointed out that the filtration mechanism which depended on the relation between the pore size of the filter and the dispersity of the colloid played a basic role in the e.k.p. measurement mentioned above.Simultaneously with our method comparative measurements were carried out on Nabentonite by electrophoresis. The difference between the electrokinetic potential data obtained by the two different methods was considered to be a consequence of the surface conductivity of the particles. On the basis of our investigations performed on agar solutions it is expected that the electrokinetic potential measuring method based on ultrafiltration is suitable for the investigation of macromolecular colloid solutions.     

Streaming potential in open and packed fused-silica capillaries

The surface properties of novel stationary phases in packed and open tubular columns for capillary electrochromatography (CEC) were examined by measuring the streaming potential in a home made apparatus. The surfaces investigated include materials such as porous styrenic sorbents and octadecyl-silica as well as fused-silica tubing, in both raw and surface modified forms. Functionalization of the surface was carried out, for instance, by reductive amination or organosilane grafting on to capillary inner wall. The dependence of the streaming potential on pH was examined with aqueous solutions in the pH range from 2.5 to 9.0. Electrokinetic properties of 50 microm I.D. fused-silica capillaries have been determined by both streaming potential and electrosmotic flow measurements. Both methods gave similar pH profiles of the zeta-potential and the isoelectric points. This confirms the viability of our approach to evaluate the specific charged groups of the packing which is one of the important factors influencing electrosmotic flow (EOF) velocity and protein adsorption during a chromatographic run. In addition to bare silica capillaries, styrenic monolithic columns with different surface functionalities, which have been extensively used in our laboratory for CEC separation of peptides and proteins, were employed for comparison of two methods. Plots of zeta potential as a function of percent ACN show a complex behavior, indicating that zeta potential cannot be predicted simply from binary mixture solvent properties. It is demonstrated that the evaluation of the zeta potential by the streaming potential method is nondestructive, relatively fast, without untoward effects introduced by Joule heating and yet another means for the characterization of the surfaces under conditions employed in CEC.