Effect Of Electrical Double Layer Research Articles

Analytical treatment of electrokinetic microfluidics in hydrophobic microchannels

Microfluidics in microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) devices is complex due to the large surface area to volume ratio. Thus, surface properties play an important role in flow behavior. In this paper, we summarize the effects of electric double layer and surface hydrophobicity of rectangular microchannels on time-dependent electrokinetic flow. Theoretically, we have shown that flow resistance can, in principal, be significantly reduced so that a larger flow rate can be obtained for pressure-driven flow or electric-field-driven flow. This relies on the ability to change surface charges and surface hydrophobicity independently. Our theoretical results provide guidelines for the design and operation of microfluidic flow in rectangular microchannels. Because of liquid slippage, zeta potential determination by traditional method could be overestimated. Taking into account the effect of hydrophobicity, a modified method is proposed to determine the zeta potential and slip coefficient for parallel-plate microchannels with hydrophobic surfaces.

An Integrated Study of Small-Angle X-ray Scattering and Dynamic Light Scattering on Cylindrical Micelles of Sodium Glycodeoxycholate

Small-angle X-ray scattering (SAXS) and dynamic light scattering (DLS) measurements were carried out on aqueous micellar solutions of the ionic biological detergent sodium glycodeoxycholate (NaGDC). Apparent diffusion coefficients (Dapp) and SAXS spectra of NaGDC 0.1 M solutions at different ionic strengths (0−0.4 M NaCl added) were reported. Moreover, a Dapp study as a function of NaGDC concentration c (20−60 mM) in the range 0−0.3 M NaCl was performed. A drastic change of the Dapp versus c slope indicates that as the electrolyte concentration is increased, the effect of the repulsive electric double layer is lowered, until a dominance of the van der Waals attraction effect is evidenced at the highest ionic strengths. A comparative analysis of SAXS spectra and Dapp data confirms this result. A uniform cylinder was used to model the micelle in the data interpretation. The effect of interactions on SAXS spectra was explored in terms of the decoupling approximation. Restricted to the NaCl concentrations where the Coulombic repulsions predominate, the method of Hayter and Penfold for a charged hard sphere system was used to compute the interparticle structure factor S(q). To compare SAXS and DLS data in the same range, a solution of hard cylinders with larger effective dimensions was also used to represent the micelle samples, thus allowing the determination of the hydrodynamic radii. By increasing the NaCl concentration from 0 to 0.2 M, an almost constant micellar diameter of 32−34 Å and a growing micellar length from 38 to 64 Å were obtained. At the same time, increasing hydrodynamic radii from 16 to 26 Å were estimated.

ANALYSIS OF THE ELECTRIC DOUBLE LAYER EFFECT ON MICROCHANNEL FLOW STABILITY

It is shown that the microchannel flow under the electric double layer (EDL) effect is inviscidly unstable. A classical Orr–Sommerfeld analysis revealed that the critical Reynolds number of the primary (linear) instability may decrease by a decade, provided that the liquid contains a very small amount of ions and is associated with large enough zeta potential and low conductivity/viscosity. When the EDL layer is thick, the inflexion point moves away from the viscous near wall region, and the inviscid instability mechanism becomes more dominant. The EDL modes are slower than the Poiseuille ones and the spectrum of the eigenvalues shows its strong destabilizing effect. There are some strong arguments suggesting that the nonlinear stability mechanism under the EDL effect is also more severe compared with the macroscale flow. The present investigation suggests that early transition in microchannel flows is plausible and can be checked through well-controlled experiments.

Effects of Pore Size and Conductivity of Electrolyte Solution on the Measurement of Streaming Potential and Zeta Potential of Microporous Membrane

In order to clarify the effect of electric double layer overlapping in the pore of microporous membrane on the measurements of streaming potential (SP) and the apparent zeta potential, ζobs, of the pore surface, the mixed cellulose ester microporous membranes having different pore sizes ranging from 0.025 to 0.8 μ m were used. The dependence of SP on KCl concentration was measured by the continuous measuring method of SP over the wide range of KCl concentration. Both the SP and the ζ obs estimated from the measured SP had the maximum negative value at a certain value of KCl concentration, which depended on the pore size. The ζ obs obtained from the different pore sizes did not coincide with each other even at the higher κγ, which is the ratio of pore radius, γ, to Debye length, κ-1, where the electric double layer overlapping was assumed to be negligible. However, it was demonstrated that the relationship between SP and KCl concentration could be evaluated from the theoretical calculation by using the fitting parameters of surface charge density and pore size. The calculated pore size of membrane tested was the same order of nominal one.

Thermodynamic modeling and sensitivity analysis of porewater chemistry in compacted bentonite

Compacted bentonite is typically foreseen as the main component of the engineered barrier system of high-level radioactive waste repositories. To derive K d values and diffusion coefficients of radionuclides for performance assessment, it is critical to be able to describe the chemistry of the pore solution and to understand how it is influenced by different factors. The present paper presents a sensitivity analysis on the influence of important parameters on porewater chemistry in compacted bentonite. The principal parameters varied were the fractions of calcite, gypsum, and NaCl dissolving from bentonite, and pCO 2: Model calculations were done with the help of a surface chemical thermodynamic model that simultaneously treats solution/mineral equilibria as well as surface complexation and ion exchange reactions at the edge and siloxane surfaces of clay minerals. Some calculations were extended to take into account electric double layer effects in the porespace. The model results show that two powerful pH buffer systems are operative in compacted bentonite: Amphoteric edge SOH sites and the carbonate buffer system. If pCO 2 is imposed externally, the resulting porewater pH is mainly controlled by the carbonate buffer. If bentonite is treated as a closed system, the buffering action of the SOH sites becomes more important. In both cases, the dissolution of calcite and gypsum from the bentonite is important. The dissolution of impurities and the ion exchange reactions have an important influence in compacted bentonite, and porewater composition is relatively independent of groundwater composition. If the development of an electric double layer in the bentonite pores is considered, our results indicate that at higher dry densities (⩾1200 kg/m 3) the entire porespace may be occupied with (truncated) diffuse layers, leaving no space for free porewater.

NUMERICAL STUDIES OF DEVELOPING FLOW IN MICROCHANNEL

International Journal of Computational Engineering ScienceVol. 04, No. 02, pp. 389-392 (2003) Design, Modelling and SimulationNo AccessNUMERICAL STUDIES OF DEVELOPING FLOW IN MICROCHANNELS. T. TAN and E. Y. K. NGS. T. TANFerrotec Corporation, Kallang Basin Industrial estate, Singapore 339412, SingaporeSchool of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue Singapore 639798, Singapore Search for more papers by this author and E. Y. K. NGSchool of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue Singapore 639798, Singapore Search for more papers by this author https://doi.org/10.1142/S1465876303001344Cited by:6 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractMicrochannels have the potential to be ultra compact, very efficient heat exchangers, which capitalize on the large surface area to volume ratio of the channels, to transport high heat fluxes with small thermal resistance. This paper describes a 3-D developing flow model by using Navier stoke equations with electric double layer (EDL) effect to model the flow field in microchannel. The electric potential distribution is simulated using a Poisson-Boltzmann equation. Results comparing the performances of the microchannel under different nondimensionalized electric potential are shown and discussed. Nusselt numbers for each case such as with or without EDL effect is also calculated; so that the actual effectiveness of the micro-channel can be understand.Keywords:numericaldeveloping flowmicrochannelEDLNavier-Stoke References G. M. Mala, D. Li and J. D. Dale, Int. J. Heat Mass Transfer 40(13), 3079 (1997). Crossref, Google ScholarE. Y. K. Ng and S. T. Poh, Journal of Computer Modeling in Engineering & Sciences 3(3), 351 (2002). Google ScholarC. Yang, D. Li and J. H. Masliyah, International Journal of Heat and Mass Transfer 41, 4229 (1998). Crossref, Google Scholar S. V. Patankar , Numerical heat transfer and fluid flow ( McGraw-Hill , New York , 1980 ) . Crossref, Google Scholar FiguresReferencesRelatedDetailsCited By 6A NOVEL INVESTIGATION OF HEAT TRANSFER CHARACTERISTICS IN HYBRID MICRO-CHANNEL HEAT SINK STRUCTURE: OPPOSITION-BASED ANTLION OPTIMIZATIONR. DEENA and G. SAI SUNDARA KRISHNAN22 August 2019 | Surface Review and Letters, Vol. 27, No. 05Study of EDL effect on 3-D developing flow in microchannel with Poisson–Boltzmann and Nernst–Planck modelsE. Y. K. Ng and S. T. Tan1 January 2007 | International Journal for Numerical Methods in Engineering, Vol. 71, No. 7LATTICE BOLTZMANN SIMULATION OF VISCOUS DISSIPATION IN ELECTRO-OSMOTIC FLOW IN MICROCHANNELSZHEN-HUA CHAI, BAO-CHANG SHI, and LIN ZHENG21 November 2011 | International Journal of Modern Physics C, Vol. 18, No. 07Simulation of electro-osmotic flow in microchannel with lattice Boltzmann methodZhenhua Chai and Baochang Shi1 Apr 2007 | Physics Letters A, Vol. 364, No. 3-4Numerical Analysis of EDL Effect on Heat Transfer Characteristic of 3-D Developing Flow in a MicrochannelS. T. Tan and E. Y. K. Ng22 September 2006 | Numerical Heat Transfer, Part A: Applications, Vol. 49, No. 10Computational studies of the EDL effect in 3-D developing flow in microchannelS T Tan and E Y K Ng25 April 2006 | Journal of Physics: Conference Series, Vol. 34 Recommended Vol. 04, No. 02 Metrics History Keywordsnumericaldeveloping flowmicrochannelEDLNavier-StokePDF download

EFFECTS OF ELECTRIC DOUBLE LAYER AND VISCOUS DISSIPATION IN MICROCAPILLARY

International Journal of Computational Engineering ScienceVol. 04, No. 02, pp. 243-248 (2003) BioMEMS and MicrofluidsNo AccessEFFECTS OF ELECTRIC DOUBLE LAYER AND VISCOUS DISSIPATION IN MICROCAPILLARYK. T. OOI, C. YANG, C. K. CHAI, T. N. WONG and P. H. ANGK. T. OOISchool of Mechanical and Production Engineering, Nanyang Technological University, Republic of Singapore 639798, Singapore Search for more papers by this author , C. YANGSchool of Mechanical and Production Engineering, Nanyang Technological University, Republic of Singapore 639798, Singapore Search for more papers by this author , C. K. CHAISchool of Mechanical and Production Engineering, Nanyang Technological University, Republic of Singapore 639798, Singapore Search for more papers by this author , T. N. WONGSchool of Mechanical and Production Engineering, Nanyang Technological University, Republic of Singapore 639798, Singapore Search for more papers by this author and P. H. ANGSchool of Mechanical and Production Engineering, Nanyang Technological University, Republic of Singapore 639798, Singapore Search for more papers by this author https://doi.org/10.1142/S1465876303000995Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractIn this study, effects of electric double layer (EDL) near the solid-liquid interface and viscous dissipation on pressure-driven liquid flow characteristics and heat transfer through a microcapillary are analyzed. As both effects were previously postulated to have certain contrary influences on flow characteristics, this analysis aims to study the interaction between the two effects via a control volume method based CFD technique. The Poisson-Boltzmann equation is used to describe EDL field near the channel wall. An additional body force due to the presence of EDL is considered in the Navier-Stokes equation. Temperature fields are explored via the energy equation with consideration of the viscous dissipation term. Variations of thermophysical properties are readily incorporated to induce a thorough observation of any coupling or adjoined effects from the two phenomena. Overall results demonstrate that in a short microchannel, when diameter decreases, EDL effects are significant, resulting in higher fluid temperature and friction, as well as reduced flow rate. Also, the effect increases with decreasing solution concentration. However, when channel length is long and flow rate is high, viscous dissipation effect dominates. It is concluded that in microchannel studies, the two effects are always present and contributing to the flow characteristics. References C. L. Rice and R. Whitehead, Journal of Physical Chemistry 69, 4017 (1965). Crossref, Google ScholarG. M. Mala, D. Li and J. D. Dale, International Journal of Heat and Mass Transfer 40, 3079 (1997). Crossref, Google ScholarG. M. Mala and D. Li, International Journal of Heat and Fluid Flow 20, 142 (1999). Crossref, Google ScholarC. Yang, D. Li and J. H. Masliyah, International Journal of Heat and Mass Transfer 41, 4229 (1998). Crossref, Google ScholarL. Ren, D. Li and W. Qu, Journal of Colloid and Interface Science 23, 12 (2001). Google ScholarH. C. Brinkman, Applied Scientific Research A2, 120 (1951). Google Scholar J.-W. Ou and K. C. Cheng, Viscous dissipation effects on thermal entrance heat transfer in laminar and turbulent pipe flows with uniform wall temperature, ASME Paper No. 74 (1974) HT-50 . Google Scholar S. K. Lim, Microtube flow characteristics, MEng thesis, Nanyang Technological University (2002) . Google Scholar G. M. Mala, Heat transfer and fluid flow in microchannels, Ph. D. Thesis, University of Alberta (1999) . Google Scholar R. B. Bird , W. E. Stewart and E. N. Lightfoot , Transport phenomena ( John Wiley & Sons , New York , 1960 ) . Google ScholarR. C. Weast, CRC handbook of chemistry and physics, 67th edn. (CRC Press, Inc, Boca Raton, Florida, 1986). Google Scholar R. J. Hunter , Principles and Applications ( Academic Press , New York , 1981 ) . Google Scholar S. V. Patankar , Computation of conduction and duct flow heat transfer ( Innovative Research, Inc , USA , 1991 ) . Google Scholar FiguresReferencesRelatedDetails Recommended Vol. 04, No. 02 Metrics History PDF download

Oscillating laminar electrokinetic flow in infinitely extended circular microchannels

This article addresses the problem of oscillating laminar electrokinetic liquid flow in an infinitely extended circular microchannel. Based on the Debye–Huckel approximation for low surface potential at the channel wall, a complex variable approach is used to obtain an analytical solution for the flow. The complex counterparts of the flow rate and the current are linearly dependent on the pressure gradient and the external electric field. This property is used to show that Onsager's principle of reciprocity continues to be valid (involving the complex quantities) for the stated problem. During oscillating pressure-driven flow, the electroviscous effect for a given value of the normalized reciprocal electrical double-layer (EDL) thickness is observed to attain a maximum at a certain normalized frequency. In general, an increasing normalized frequency results in a reduction of EDL effects, leading to (i) a volumetric flow rate in the case of streaming potential approaching that predicted by the theory without EDL effects, and (ii) a reduction in the volumetric flow rate in the case of electroosmosis.

Electrokinetic flow velocity in charged slit-like microfluidic channels with linearized Poisson-Boltzmann field

In cases of the microfluidic channel, where the thickness of electric double layer is often comparable with the characteristic size of flow channels, the electrokinetic influence on the flow behavior can be found. The externally applied body force originating from the electrostatic interaction between the linearized Poisson-Boltzmann field and the flow-induced electrical field is applied in the equation of motion. An analytical solution to this Navier-Stokes equation of motion for well-defined geometry of slit-like microchannel is obtained by employing Green’s function. Also, an explicit analytical expression for the induced electrokinetic potential is successfully derived as functions of relevant physicochemical parameters. The effects of the ionic concentration of the fluid, the zeta potential of the solid surface, and the width of microchannels on the velocity profile as well as the streaming potential are examined. The electric double layer effect on the velocity profile becomes stronger as the channel width decreases, where the average fluid velocity is entirely reduced with the decrease in ionic concentration. The induced electrokinetic potential increases with an increase in pressure gradient, while it decreases as the ionic concentration increases.

Modeling of Electric Double Layer Effects through Pressure-driven Microchannel Flows

Modeling of Electric Double Layer Effects through Pressure-driven Microchannel Flows

Electrosorption of Ions from Aqueous Solutions by Nanostructured Carbon Aerogel

Electrosorption is generally defined as potential-induced adsorption on the surface of charged electrodes. After polarization of the electrodes, ions are removed from the electrolyte solution by the imposed electric field and adsorbed onto the surface of the electrodes. Experimental and modeling studies were conducted using two types of carbon aerogel composites of different surface areas to provide a better understanding on the mechanisms of electrosorption. The experimental results revealed that no significant specific adsorption of F− ions occurred, while strong specific adsorption was observed for NO3− and Cu2+ ions. In addition, although the two types of carbon aerogel electrodes had different surface areas, their capacities were found to be very similar because of the electrical double-layer overlapping effect in micropores. An electrical double-layer model developed in our previous work (16), in which the electrical double-layer overlapping correction is included, is expanded in the present work by considering the effect of the specific adsorption on the electrosorption process. Modeling results were compared with experimental data obtained under various conditions. When the overlapping effect and specific adsorption were considered, the model provided results that were in good agreement with experimental data.

On electroviscous effects in microchannels

This paper contains results of a theoretical investigation on the effect of the diffusive electric double layer (EDL) at the solid–liquid interface on liquid flow through a microchannel between two parallel plates. Unlike previous works, the electrical charge connected with the EDL at the inlet of a channel is accounted for. The Debye–Huckel linear approximation of the surface potential distribution is used to describe the EDL field near the solid–liquid interface. The electrokinetic distance is assumed to be arbitrary. The electrical body force resulting from the double layer field is considered in the equation of motion. This equation is solved for steady-state flow. Effects of the EDL field on the apparent viscosity are discussed.

Oil/Water‐Partitioning and Interfacial Behavior of Naphthenic Acids

Partitioning and dissociation constants for naphthenic acids from crude oils and several naphthenic acid model compounds are reported. The pK a for naphthenic acids from crude oil was found to be 4.9. The logarithm of the partition coefficients varies linearly vs. the number of carbons in the naphthenic acid molecules. The naphthenic acids with three rings were found to be more hydrophilic than acids with one or two rings. The data can be used to predict the content of different naphthenic acids in produced water at a given pH, given the acid content and mole weight distribution in the crude oil. By accounting for the dissociation in water and partitioning of undissociated acid a model for the total acid concentration in water was derived. Experiments with synthetic naphthenic acids were performed and the model proved to describe the experimental points at pH < 8. At higher pH there was a deviation between the model and the experimentally determined concentrations. This was suggested to be due to formation of ordinary and reversed micelles. The correlation between interfacial tension and pH was studied for several naphthenic acid systems. A decrease in interfacial tension was seen at high pH; this was explained by an increase in the total concentration of ionized naphthenic acids at the interface. The fraction of ionized naphthenic acids at the interface was lower than the fraction in the bulk phases. This effect is explained by the fact that interfacial pH is lower than the bulk pH due to electrical double layer effects.

The Zeolite ZSM-5 membrane study; synthesis, permeation and modeling.

ABSTRACTZeolite particles formed in the synthesis solution assume a negative charge due to electrical double layer effects. The membranes synthesized via electrophoretic deposition produce a thin continuous zeolite ZSM-5 layer on the porous alumina substrates. The thickness of membranes can be controlled by varying the precursor concentration, applied potential, and synthesis time. The permeation for a variety of gases through the membranes is examined. The diffusion properties are measured at near ambient temperature and pressure. Selectivity of n-butane over iso-butane is observed on every membrane. The diffusion coefficient of gases on ZSM-5 is also evaluated by gas adsorption on zeolite powders. The results of these studies show an ability to predict the effective diffusion coefficients. The estimation of molar fluxes across the membranes using the Maxwell-Stefan approach predicts a higher flux for thinner membranes. However, the calculations also show that even minor defects in the membrane have a great effect on the permeation rates.

CFD ANALYSIS OF DOUBLE-LAYER MICROCHANNEL CONJUGATE PARALLEL LIQUID FLOWS WITH ELECTRIC DOUBLE-LAYER EFFECTS

This work deals with a code development using a finite-volume scheme on a double-layer microchannel conjugate heat transfer problem consisting of the simultaneous determination of the temperature field in both the solid substrate and the fluid, with streaming potential as the driving force. The concept of electric double layer (EDL) was introduced to explain the microscale deviation. Governing equations were derived for fully developed rectangular microchannels' pressure-driven flows. Toward a realistic modeling of the problems, we conducted a conjugate analysis that solves both the solid and liquid regions. An additional source term resulting from the EDL effects was introduced in the conventional momentum equation, thereby modifying the flow and heat transfer characteristics. Analysis concerning the comparison of the double-layer configuration versus the conventional single-layer microchannel heat sink were included. The computed results reveal significant deviations in the velocity and temperature profiles under EDL effects, in particular, when the hydraulic diameter of the channel is less than 40 u m.

Electro-viscous effects on pressure-driven liquid flow in microchannels

The EDL and the flow-induced electrokinetic field have significant effects on the flow characteristics of dilute aqueous solutions in small microchannels. Although the electro-viscous effect is well-known, there is not many experimental evidence in the literature. This paper reviewed theoretical models of the electrokinetic effects on pressure-driven flow in microchannels, and reported a series of recent experimental studies on the electrokinetic or electro-viscous effects. The liquids used in these studies are DIUF water, 10 −4 and 10 −2 M aqueous KCl solutions, 10 −4 M AlCl 3 aqueous solutions and 10 −4 M LiCl aqueous solutions. Three slit silicon microchannels tested have a height ranging from 14 to 40 μm. Significantly higher flow resistance (i.e. d P/d x) was found for dilute electrolyte solutions in comparison with the prediction of the Poiseuille laminar flow equation. These results show a strong dependence of d P/d x ∼ Re relationship on the channel size, the ionic concentration, the ionic valence and the bulk conductivity of the liquids. The apparent viscosity corresponding to these measured d P/d x ∼ Re relationships was found to be up to 18% higher than the true viscosity depending on the liquids and the ratio of the channel height to the EDL thickness. The experimental data were compared with an electrokinetic flow model presented in this paper. It was found that without considering the surface conductance, the model's predictions agree well with the experimental data. The comparison confirms that the electrical double layer effect or the electro-viscous effect is the major cause of the significantly higher-pressure drop for pure water and dilute aqueous ionic solutions flowing through small microchannels.

The preparation and analysis of zeolite ZSM-5 membranes on porous alumina supports

Zeolite ZSM-5 particles formed in the synthesis solution assume a negative charge due to electrical double layer effects. Therefore, we investigated the use of electrophoretic techniques in addition to the hydrothermal synthesis method to attract the zeolite particles to the substrate surface before they precipitate out of the solution. This electrophoretic driving force produces a thin, continuous zeolite ZSM-5 membrane on the porous substrate. This research was conducted in order to produce zeolite membranes on a tubular support that could effect continuous gas phase separations. The thickness of membranes can be controlled by varying the precursor concentration, applied potential, and synthesis time. The selectivity of n-butane over iso-butane is observed on every membrane. The membranes were characterized by using scanning electron microscopy (SEM), X-ray diffractometry (XRD), and energy dispersive X-ray spectrometry (EDX).

Electrosorption of Ions from Aqueous Solutions by Carbon Aerogel: An Electrical Double-Layer Model

An electrical double-layer model is developed to predict electrosorption of ions from aqueous solutions by carbon aerogel electrodes. The carbon aerogel electrodes are treated as electrical double-layer capacitors, and electrosorption is modeled using classical electrical double-layer theory. Because of the porous characteristics of the electrodes, the total capacity of the system is obtained by summing the contributions of the individual pores. The pore size distribution of the carbon aerogel is measured by the physical adsorption of N2 and CO2 as well as by mercury intrusion porosimetry. When a pore has a width smaller than a specific value (cutoff pore width), it does not contribute to the total capacity because of the electrical double-layer overlapping effect. This effect greatly reduces the electrosorption capacity for electrodes with significant numbers of micropores, such as carbon aerogel; thus, it is considered in the electrical double-layer model. The model in this study focuses on the electros...

Effect of adsorbed anions on the outer-sphere electron-transfer reactions of cobalt complexes at platinum single-crystal electrodes

The redox-electrode reaction of [Co(phen)3]2+/3+ (phen=1,10-phenanthroline) in 0.1 M potassium halide solutions was studied kinetically at a platinum (111) single-crystal electrode (M=mol dm−3). The formal rate constants were found to be dependent on the electrolyte anions and to decrease in the order F−>Cl−>Br−. Furthermore, formal rate constants for this reaction in 0.1 M KF solution were obtained at platinum (111), (100), and (110) single-crystal electrodes and those modified with I−, SCN−, and CN− adlayers. It was found that Miller indices had little effect on the heterogeneous electron-transfer rate. The iodide monolayer retarded the electron-transfer reaction, whereas the reaction was accelerated by the modification with cyanide and thiocyanate. Similar results were obtained for the redox-electrode reaction of [Co(bpy)3]2+/3+ (bpy=2,2′-bipyridine) at the Pt(111) electrode and that modified with iodide and thiocyanate. These findings are discussed based on the electrical double layer effect and the theory of heterogeneous outer-sphere electron-transfer reactions reviewed by Weaver [M.J. Weaver, in: R.G. Compton, Comprehensive Chemical Kinetics, vol. 27, Elsevier, Amsterdam, 1987, Ch. 1].

An Improved Method of Determining the ζ-Potential and Surface Conductance

In the classical “slope–intercept” method of determining the zeta potential and the surface conductance, the relationship between ΔP and Es is measured experimentally at a number of different channel sizes (e.g., the height of a slit channel, h). The parameter (ϵrϵ0ΔP/μEsλb) is then plotted as a function of 1/h and linear regression is performed. The y-intercept of the regressed line is then related to the ζ-potential and its slope to the surface conductance. However, in this classical method, the electrical double layer effect or the electrokinetic effects on the liquid flow are not considered. Consequently, this technique is valid or accurate only when the following conditions are met: (1) relatively large channels are used; (2) the electrical double layer is sufficiently thin; and (3) the streaming potential is sufficiently small that the electroosmotic body force on the mobile ions in the double layer region can be ignored. In this paper a more general or improved slope–intercept method is developed to account for cases where the above three conditions are not met. Additionally a general least-squares analysis is described which accounts for uncertainty in the measured channel height as well as unequal variance in the streaming potential measurements. In this paper, both the classical and the improved slope–intercept techniques have been applied to streaming potential data measured with slit glass channels, ranging in height from 3 μm to 66 μm, for several aqueous electrolyte solutions. The comparison shows that the classical method will always overestimate both the ζ-potential and the surface conductance. Significant errors will occur when the classical method is applied to systems with small channel heights and low ionic concentrations. Furthermore, it is demonstrated that traditional regression techniques where the uncertainty is confined only to the dependent variable and each measurement is given equal weight may produce physically inconsistent results.