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.     

Streaming Potential Collection and Data Processing Techniques

To date, no comprehensive comparison of streaming potential coupling coefficient collection or processing techniques has been made. Here, time-varying streaming potential and dc streaming potential data collection and processing techniques are presented and compared. The time-varying streaming potential data include sinusoidal and transient data. The collection techniques include acquiring dc streaming potentials at various pressures, acquiring time-varying streaming potentials at varying pressure, acquiring streaming potentials as a function of frequency, and collecting time-varying raw data. The processing techniques include dc filtering, rms processing, cross-correlation, spectral analysis, and plotting of raw time-varying streaming potential versus raw pressure data. The results show that all processing methods yield the same coupling coefficient within 3%. The analysis also shows that if there is a good signal-to-noise ratio, all processing methods perform satisfactorily. If the signal-to-noise ratio is poor, then the spectral analysis outperforms the other processing methods. The data collection methods are all adequate, but individual applications may make one method superior to another. Copyright 2001 Academic Press.     

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.     

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 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.     

Electrokinetic flow in a planar slit covered by an ion-penetrable charged membrane

The electrokinetic flow of an electrolyte solution in a planar slit covered by an ion-penetrable charged membrane layer is analyzed theoretically. An approximate analytical expression for the spatial variation in the electrical potential is derived, and the electroosmotic velocity, the total electric current, and the streaming potential of the system under consideration are evaluated. The effects of epsilon' (relative permittivity of liquid phase/relative permittivity of membrane layer), eta' (viscosity of liquid phase/viscosity of membrane layer) and the valence of anions (coions) on the volumetric flow rate and total current are examined. We show that the effect of the valence of cations (counterions) on the volumetric flow rate is less significant than that of epsilon' and that of eta'. However, the effect of epsilon' on the total current is less significant than that of the valence of cations and that of eta'. The variation of total current as a function of ionic strength is found to have a local minimum, regardless of whether a pressure gradient is applied or not. The absolute streaming potential has a local maximum as the concentration of fixed charge varies, which was not found in previous studies.     

Electrokinetic studies on a thorium oxide membrane : I. Electroosmosis and electrophoresis

Electroosmotic transport of dimethyl formamide through a thorium oxide plug membrahe has been studied and the data have been analysed from the standpoint of thermodynamics of irreversible processes. Electroosmotic flow and eleetroosmotic pressure have been found to be nonlinearly dependent on the applied potential difference. Various phenomenological coefficients have been evaluated from the nonlinear transport equation. Onsager's reciprocity relation has been verified by measurements of streaming potentials. The electrophoretic velocity of thorium oxide particles dispersed in dimethyl formamide has also been found to be nonlinear. Zeta potentials have been evaluated from electroosmotic and electrophoretic data. The results have been explained on the basis of the change in the structure of the electrical double layer. The degree of coupling and the efficiency of electrokinetic energy conversion have been calculated for both electroosmosis and streaming potential.     

Frequency-Dependent Streaming Potentials

An experimental apparatus and data acquisition system was constructed to measure the streaming potential coupling coefficients as a function of frequency. The purpose of the experiments was to measure, for the first time, the real and imaginary portion of streaming potentials. In addition, the measured frequency range was extended beyond any previous measurements. Frequency-dependent streaming potential experiments were conducted on one glass capillary and two porous glass filters. The sample pore diameters ranged from 1 mm to 34 μm. Two frequency-dependent models (Packard and Pride) were compared to the data. Both Pride's and Packard's models have a good fit to the experimental data in the low- and intermediate-frequency regime. In the high-frequency regime, the data fit the theory after being corrected for capacitance effects of the experimental setup. Pride's generalized model appears to have the ability to more accurately estimate pore sizes in the porous medium samples. Packard's model has one unknown model parameter while Pride's model has four unknown model parameters, two of which can be independently determined experimentally. Pride's additional parameters may allow for a determination of permeability. Copyright 2001 Academic Press.     

A note on the streaming potential method for measuring surface potentials

Due to the fact that the classical analysis of the streaming potential method for measuring surface potential is somewhat crude, the problem was analyzed by applying the fundamental principles of electrochemistry. It was found that the classical Helmholz-Smoluchowski equation is valid provided that the duct is long and narrow, in which case the potential in the bulk is uniform over the duct's cross-sectional area and varies linearly over its length.In order to follow how the surface potential of a filter varies with time, investigators have measured the streaming potential across the filter's length as well as across segments of the filter. The problem is what do such measurements mean and do the classical equations apply. It was found that the classical result is expressible in differential form from which it followed that the streaming potential over any section of the filter gives a measure of the average surface potential of that section. This is an important result because it shows that the surface potential profile of a filter can be determined from measurements of the streaming potential profile across the filter.     

Role of streaming potential on pulsating mass flow rate control in combined electroosmotic and pressure-driven microfluidic devices

In the present study, we investigate the implications of streaming potential on the mass flow rate control in a microfluidic device actuated by the combined application of a pulsating pressure gradient and a pulsating, externally applied, electric field. We demonstrate that the temporal dynamics due to streaming potential effects may lead to interesting non-trivial aspects of the resultant transport characteristics. Our results highlight the importance of an adequate accounting of the streaming potential effects for temporally tunable mass flow rate control strategies, which may act as a useful design artifice to augment mass flow rates in practical scenarios.     

Transport studies of multielectrolyte solutions across a sintered disc impregnated with cellulose acetate

Experimental results for the measurement of electroosmotic pressure, electroosmotic velocity and streaming potential for different aqueous solutions of ammonium chloride—ammonium nitrate through a sintered disc impregnated with cellulose acetate at 30°C are reported. The data have been analysed in the light of non-equilibrium thermodynamics. The Onsager reciprocity relation has been found to hold good for all the systems. The efficiencies of electrokinetic energy conversion have also been determined. The maximum values of conversion efficiencies for both the modes of conversion, i.e., electroosmotic flow and streaming potential, have been found to be equal to each other and independent of the applied input forces.     

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.     

Stability of Streaming in an Electrified Maxwell Fluid Sheet Influenced by a Vertical Periodic Field in the Absence of Surface Charges

The problem of electroviscoelastic Kelvin-Helmholtz waves of Maxwellian fluids under the influence of a vertical periodic electric field is studied in the absence of surface charges. The system is composed of a streaming dielectric fluid sheet of finite thickness embedded between two different streaming semi-infinite dielectric fluids. Due to the streaming flow and the influence of a periodic force, a mathematical simplification is considered. The weak viscoelastic effects are taken into account so that their contributions are demonstrated in the boundary conditions. The approximate equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion and boundary conditions lead to two simultaneous Mathieu equations of damping terms having complex coefficients. Symmetric or antisymmetric deformation that relaxes the coupled Mathieu equations and yields a single Mathieu equation is considered. Stability criteria are discussed and numerical estimation shows that the increase in the sheet thickness plays a destabilizing effect in the presence or in the absence of the field frequency as well as the field intensity. In the absence of the field frequency the velocity ratio between the upper fluid velocity and the sheet velocity has a destabilizing influence, while that between the velocity of the lower fluid and the velocity of the sheet has a stabilizing influence. Moreover, the viscosity ratios have a damping influence while the elasticity ratios have a destabilizing influence. Furthermore, a range of general deformations of the surface deflections is studied. Moreover, the stability behavior for the resonance cases is studied and discussed. The coupled Mathieu equations are analyzed by the multiple scale method. The numerical examination for stability yields some changes in the stability behavior. The fluid sheet thickness plays a stabilizing role in the presence of a constant field while the damping role is observed for the resonance case. Similar results are found for both the stratified velocities and the stratified relaxation times. The dual role of the stratified viscosities is observed in the presence or the absence of the field frequency. Copyright 2000 Academic Press.     

Transient streaming potential in a finite length microchannel

Pressure-driven flow of an electrolyte solution in a microchannel with charged solid surfaces induces a streaming potential across the microchannel. Such a flow also causes rejection of ions by the microchannel, leading to different concentrations in the feed and permeate reservoirs connecting the capillary, which forms the basis of membrane based separation of electrolytes. Modeling approaches traditionally employed to assess the streaming potential development and ion rejection by capillaries often present a confusing picture of the governing electrochemical transport processes. In this paper, a transient numerical simulation of electrochemical transport process leading to the development of a streaming potential across a finite length circular cylindrical microchannel connecting two infinite reservoirs is presented. The solution based on finite element analysis shows the transient development of ionic concentrations, electric fields, and the streaming potential over the length of the microchannel. The transient analysis presented here resolves several contradictions between the two types of modeling approaches employed in assessing streaming potential development and ion rejection. The simulation results show that the streaming potential across the channel is predominantly set up at the timescale of the developing convective transport, while the equilibrium ion concentrations are developed over a considerably longer duration.     

Streaming potential across cation-exchange membranes in methanol-water electrolyte solutions

Streaming potential measurements across charged membranes separating two equal solutions have been carried out. Two cation-exchange membranes with different cross-linked and swelling properties (Ionics and Nafion membranes) and methanol-water electrolyte solutions of KCl have been used in the experiments. The obtained results show that the streaming potential is higher for the Ionics membrane and that the values depend on the methanol content of the solutions. A different behavior is found in the dependence of the streaming potential on the methanol percentage for each membrane. The study of the relaxation times in the decay of electrokinetic steady states of streaming potential has been carried out from the time dependence of the streaming potential when the pressure difference through the membrane is suppressed. The results show the existence of two different parts or partial relaxations, mechanical and electric. A different behavior of the mechanical relaxation time with the methanol percentage has been found for the two membranes, but any significant difference between their electric relaxation times. These differences have been explained in terms of the different degree of swelling of the membranes used.     

用流动电位法表征纳滤膜的结构及性能

利用测量流动电位的方法考察了纳滤膜的表面电学性能对纳滤膜的截留性能的影响.首先,采用不同功能层材料制备了复合纳滤(NF)膜,考察功能层的交联时间、单体结构等对表面电性能的影响,研究纳滤膜对不同无机盐的选择截留性能与表面电性能的关系.通过流动电位法测定纳滤膜的表面电学参数,如流动电位(ΔE)、zeta电位(ζ)和表面电荷密度(σd).实验表明,这些电学参数的变化与功能层交联时间和纳滤膜截留率的变化一致,在交联时间为45 s时,3种电学参数的绝对值均最大,而纳滤膜对无机盐的截留率也最大.复合纳滤膜zeta电位的绝对值(|ζ|)按照Na2SO4>MgSO4>MgCl2变化,同截留率的变化相同.带侧基单体交联后得到的纳滤膜的表面电性能参数的绝对值小于不带侧基单体的.因此,流动电位法可用于研究复合纳滤膜的截留机理和功能层结构.     

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.     

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).     

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.