Exploring new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with overlapping Electric Double Layers

In this paper, we unravel new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with thick overlapping Electric Double Layers (EDLs). We observe that the streaming potential, for a given value of the capillary zeta (ζ) potential, varies with the EDL thickness and a dimensionless parameter R, quantifying the conduction current. Depending on the value of R, variation of the streaming potential with the EDL thickness demonstrates distinct scaling regimes: one can witness a Quadratic Regime where the streaming potential varies as the square of the EDL thickness, a Weak Regime where the streaming potential shows a weaker variation with the EDL thickness, and a Saturation Regime where the streaming potential ceases to vary with the EDL thickness. Effective viscosity, characterizing the electroviscous effect, obeys the variation of the streaming potential for smaller EDL thickness values; however, for larger EDL thickness the electroosmotic flow profile dictates the electroviscous effect, with insignificant contribution of the streaming potential.     

Electrokinetic flow in an elliptic microchannel covered by ion-penetrable membrane

The electrokinetic flow of an electrolyte solution in an elliptical microchannel covered by an ion-penetrable, charged membrane layer is examined theoretically. The present analysis extends previous results in that a two-dimensional problem is considered, and the system under consideration simulates the flow of a fluid, for example, in a microchannel of biological nature such as vein. The electroosmostic volumetric flow rate, the total electric current, the streaming potential, and the electroviscous effect of the system under consideration are evaluated. We show that, for a constant hydraulic diameter, the variations of these quantities as a function of the aspect ratio of a microchannel may have a local minimum or a local maximum at a medium level of ionic strength, which depends on the thickness of the membrane layer. For a constant cross-sectional area, the electroosmostic volumetric flow rate, the total electric current, and the streaming potential increase monotonically with the increase in the aspect ratio, but the reverse is true for the electroviscous effect.     

Electrokinetic flow in an elliptic microchannel covered by ion-penetrable membrane

The electrokinetic flow of an electrolyte solution in an elliptical microchannel covered by an ion-penetrable, charged membrane layer is examined theoretically. The present analysis extends previous results in that a two-dimensional problem is considered, and the system under consideration simulates the flow of a fluid, for example, in a microchannel of biological nature such as vein. The electroosmostic volumetric flow rate, the total electric current, the streaming potential, and the electroviscous effect of the system under consideration are evaluated. We show that, for a constant hydraulic diameter, the variations of these quantities as a function of the aspect ratio of a microchannel may have a local minimum or a local maximum at a medium level of ionic strength, which depends on the thickness of the membrane layer. For a constant cross-sectional area, the electroosmostic volumetric flow rate, the total electric current, and the streaming potential increase monotonically with the increase in the aspect ratio, but the reverse is true for the electroviscous effect.     

Effects of fluid slippage on pressure-driven electrokinetic energy conversion in conical nanochannels

The effects of fluid slippage on the pressure-driven electrokinetic energy conversion in conical nanochannels are systematically investigated in this paper. We present a multiphysical model that couples the Planck–Nernst–Poisson equations and the Navier–Stokes equation with a Navier slip condition to fulfill this purpose. We systematically look into the variation of various performance indicators of electrokinetic energy conversion, for example, streaming current, streaming potential, generation power, energy conversion efficiency, regulation parameter, and enchantment ratio, with the conicity of nanochannels and the slip length for two pressure differences of the same magnitude but opposite directions. Particularly, enhancement ratios related to streaming current, streaming potential, generation power, and energy conversion efficiency are defined to comprehensively measure the enhancement of the performance of electrokinetic energy conversion due to the slip length. The results demonstrate that a combination of large slip length and small conicity enhances the electrokinetic energy conversion performance significantly. Furthermore, the fluid slippage-induced enhancement of the electrokinetic energy conversion in the backward pressure difference mode is stronger than that in the forward pressure difference mode. Our results provide design and operation guidelines for pressure-driven electrokinetic energy conversion devices.     

Modeling of electrokinetic transport in silica nanofluidic channels

We present a theoretical and numerical modeling study of the multiphysicochemical process in electrokinetic transport in silica nanochannels. The electrochemical boundary condition is solved by considering both the chemical equilibrium on solid-liquid interfaces and the salt concentration enrichment caused by the double layer interaction. The transport behavior is modeled numerically by solving the governing equations using the lattice Poisson-Boltzmann method. The framework is validated by good agreements with the experimental data for all range of ionic concentrations. The modeling results suggest that when the double layers interact, the bulk salt concentration enrichment results in the saturation of conductances for low ionic concentrations. Both the streaming conductance and the electrical conductance are enhanced by the double layer interaction, and such enhancements diminish when the channel size is larger than 10 times of the Debye length. The streaming conductance increases with pH almost linearly when pH < 8, while the electrical conductance increases with pH exponentially.     

Determining the zeta-potential of ceramic microfiltration membranes using the electroviscous effect

The possibility of measuring the zeta-potentials of porous membranes using the electroviscous effect was investigated. The zeta-potential of Membralox^® ceramic microfiltration membranes was determined both with the newly developed electroviscous technique and by streaming potential measurements. It was found that the electroviscous technique provided a simple means of obtaining accurate values of zeta-potential, especially for higher zeta-potentials. The streaming potential measurements were found to be more suitable for the determination of the iso-electric point, i.e. the pH at which the zeta-potential is zero.The iso-electric points of new α-alumina, zirconia, and titania membranes were found to be 8.5, 8.0, and 6.3, respectively. Upon using the membranes and cleaning them with a detergent, the iso-electric point of the α-alumina membrane decreased to 6.5, and that of the zirconia membrane decreased to 5.2, while the iso-electric point of the titania membrane stayed virtually constant. Cleaning these membranes with a strong acid or base could not reverse the observed decreases in iso-electric point.     

Streaming current and wall dissolution over 48 h in silica nanochannels

We present theoretical and experimental studies of the streaming current induced by a pressure-driven flow in long, straight, electrolyte-filled nanochannels. The theoretical work builds on our recent one-dimensional model of electro-osmotic and capillary flow, which self-consistently treats both the ion concentration profiles, via the nonlinear Poisson-Boltzmann equation, and the chemical reactions in the bulk electrolyte and at the solid-liquid interface. We extend this model to two dimensions and validate it against experimental data for electro-osmosis and pressure-driven flows, using eight 1-μm-wide nanochannels of heights varying from 40 nm to 2000 nm. We furthermore vary the electrolyte composition using KCl and borate salts, and the wall coating using 3-cyanopropyldimethylchlorosilane. We find good agreement between prediction and experiment using literature values for all parameters of the model, i.e., chemical reaction constants and Stern-layer capacitances. Finally, by combining model predictions with measurements over 48 h of the streaming currents, we develop a method to estimate the dissolution rate of the silica walls, typically around 0.01 mg/m(2)/h, equal to 45 pm/h or 40 nm/yr, under controlled experimental conditions.     

Electrokinetic flow through an elliptical microchannel: effects of aspect ratio and electrical boundary conditions

The electrokinetic flow of an electrolyte solution through an elliptical microchannel is studied theoretically. The system under consideration simulates the flow of a fluid, for example, in vein. We show that, for a constant cross-sectional area, both the electroosmotic volumetric flow rate and the streaming potential increase monotonically with an increase in the aspect ratio, and both the total electric current and the electroviscous effect may exhibit a local minimum as the aspect ratio varies. Also, for a constant average potential on the channel wall, the difference between the results based on three kinds of boundary conditions, which include constant surface charge, constant surface potential, and charge-regulated surface, is inappreciable if the hydraulic diameter is larger than 1 mum.     

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.     

Oscillating laminar electrokinetic flow in infinitely extended rectangular microchannels

This paper has addressed analytically the problem of laminar flow in microchannels with rectangular cross-section subjected to a time-dependent sinusoidal pressure gradient and a sinusoidal electric field. The analytical solution has been determined based on the Debye-Hückel approximation of a low surface potential at the channel wall. We have demonstrated that Onsager's principle of reciprocity is valid for this problem. Parametric studies of streaming potential have shown the dependence of the electroviscous effect not only on the Debye length, but also on the oscillation frequency and the microchannel width. Parametric studies of electroosmosis demonstrate that the flow rate decreases due to an increase in frequency. The obtained solutions for both the streaming potential and electroosmotic flows become those for flow between two parallel plates in the limit of a large aspect ratio.     

The primary electroviscous effect of polystyrene latexes

An investigation on the primary electroviscous effect of polystyrene latexes has been made. Capillary viscometers of Ubbelohde type have been used. The comparison of the results obtained with the theories allow us to conclude that the effect is underestimated for low electrolyte concentrations. We suggest that this underestimation is due to an additional surface conductance into the electric double layer. This interpretation is consistent with previous studies on electrophoretic mobility of the same system.     

The primary electroviscous effect,free solution electrophoretic mobility,and diffusion of dilute prolate ellipsoid particles (minor axis = 3 nm) in monovalent salt solution

The principal objective of the present work is the modeling of the primary electroviscous effect of charged prolate ellipsoid models of low axial ratio. Other transport properties examined include (free solution) electrophoretic mobilities and translational diffusion constants. A numerical boundary element method is employed to solve the coupled Poisson, low Reynolds number Navier-Stokes, and ion transport equations. The methodology is first applied to the primary electroviscous effect of spheres with a centrosymmetric charge distribution and excellent agreement with independent theory is obtained. Specific model studies are also carried out for prolate ellipsoid models with axial ratios less than 4 and a minor axis equal to 3 nm. Most studies are carried out in aqueous NaCl solution (2 to 50 mM) at 20 degrees C for a range of different particle charges, although limited results are also presented in LiCl and KCl solution. The primary electroviscous effect for weakly charged prolate ellipsoids is smaller than that of a sphere under similar conditions. These studies are also carried out at high absolute particle charge. A comparison is made between the primary electroviscous effect and electrophoretic mobilities of prolate ellipsoids and corresponding spherical models.     

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.     

Solute transport and separation in nanochannel chromatography

An analytical model is developed to study the solute transport and separation in pressure-driven liquid flow through cylindrical nanochannels. The flow-induced streaming potential is found to significantly affect the solute speed, retention and dispersion in nanochannel chromatography. These effects are sensitive to the solute charge, and found to be mainly dependent on an electrokinetic "figure of merit".     

平流式流动电位测试系统的研制

分离膜表面的荷电化显著地影响着膜的分离性能和耐污染能力。因此,定量化表征膜表面电性能具有重要的理论价值和实际意义。作者在前期透过式膜流动电位测试系统研发工作的基础上成功地研制了平流式流动电位测试系统,并且首次将恒电流法测膜体电导引入膜表面ζ(Zeta)电位的确定过程中。以自制不同共混比的合金荷电膜为测试对象,利用该测试系统和经典的Helmholtz-Smoluchowski(H-S)方程及其变体得到了不同pH下的膜表面Zeta电位,从而揭示了膜表面电导、膜体电导对膜表面Zeta电位的贡献,并展示了该流动电位测试系统的有效性。     

The electroviscous effect in ethylcellulose latex suspensions. Effect of ionic strength and correlation between theory and experiments

 This article describes an experimental and theoretical investigation of the so-called primary electroviscous effect, i.e., the increase in suspension viscosity due to the existence of an electrical double layer around the particles. By measuring the viscosity of ethylcellulose latex suspensions, the electroviscous coefficient, the quantity measuring the effect, was estimated for different concentrations of 1-1 electrolyte in the dispersion medium. These data were compared with the predictions of Watterson and White's model, using the zeta potential of the particles deduced from electrophoretic mobility measurements. It was found that the theory considerably underestimates the effect. In an attempt to improve the agreement between data and predictions, the model was generalized to include the possibility (dynamic Stern layer) that ions in the inner part of the double layer have nonzero mobility. The general theory, however, predicts even lower values of the electroviscous coefficients, thus increasing the separation between calculated and measured electroviscous coefficients. A careful analysis of the ionic concentrations and velocity profiles with and without dynamic Stern layer corrections can account for this fact, but leaves unsolved the problem of the large discrepancies found in the theoretical explanation of the strength of the electroviscous effect. Received: 19 October 1999/Accepted: 17 December 1999     

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.     

The electrokinetic properties of colloidal magnetic iron oxides

A novel electrokinetic streaming potential technique has been used to determine the ζ potential behavior of three magnetic iron oxides, (Fe(3)O(4), γ-Fe(2)O(3), and CoFe(2)O(4)) as a function of pH and salt concentration. These colloidal materials, (nanosize in one dimension), are held in the form of a plug by means of external magnets. The streaming potential (E) is measured as a function of fluid flow induced by a pressure drop (ΔP) across the plug. The magnetically held plug is found to obey the requirements of the streaming potential technique; in each case an iso-electric point, (iep) independent of salt concentration is observed. However, if one uses the appropriate quantities in the standard formula, the calculated ζ potentials are very much lower than for oxides such as silica, alumina or goethite and other colloidal oxide, latex, etc. particulates in aqueous salt solutions. Furthermore, at a given pH, the measured ζ potentials anomalously increase in magnitude rather than decrease as observed conventionally as the salt concentration is increased. This apparent anomalous behavior could not be eliminated by incorporating surface conductance effects. However by including a conductance pathway, independent of pH or salt concentration, through the magnetic particle network itself, the anomaly was removed. Confirmation of the role of a conductance pathway through the magnetic particle network was obtained by using silica coated magnetic particles which displayed normal electrokinetic behavior. Finally, we have redesigned the plug-electrode assembly to allow measurement of streaming current, a technique know to eliminate contributions from plug network conductances of any kind. The resulting ζ potentials, derived from this streaming current technique are normal.     

Streaming Potential and Streaming Current Methods for Characterizing Heterogeneous Solid Surfaces

By monitoring changes in electrokinetic parameters, the streaming potential technique has been used as a method of characterizing heterogeneous surfaces, for example, due to protein adsorption. In general it is assumed that the change in the streaming potential is proportional to the degree of heterogeneity. In this study a simple model of the electrokinetic flow through heterogeneous slit channels has been developed with the goal of comparing the streaming potential and streaming current techniques and determining under what conditions the aforementioned proportionality assumption will produce erroneous results. The flow simulations have shown that, when the streaming potential induces significant flow impedance, a severe deviation from the linear assumption is observed. Since streaming current measurements are unaffected by electrokinetic flow effects, more consistent results are predicted and they are preferred for measurements made in small channels. Additionally it has been shown that the distribution of the heterogeneous coverage has a negligible effect on both the streaming potential and the streaming current in cases where the double-layer overlap is not significant. Copyright 2001 Academic Press.