Evaluation of the Zn2+ transport properties through a cation-exchange membrane by chronopotentiometry

In this work the effect of zinc concentration, pH, and boric acid concentration on the zinc transport properties through an IONICS 67-HMR-412 cation-exchange membrane was evaluated. The limiting current density and the transport numbers were determined by means of chronopotentiometry. A model between the limiting current density and the bulk zinc concentration was established, assuming a potential relationship between the zinc transport number through the membrane and the bulk zinc concentration together with the Levich equation for the DBL thickness. A decrease in the initial pH value of the solutions causes considerable modifications both in the plateau region and in the overlimiting current density region of the current–membrane potential curves. The results show that the presence of boric acid produces the precipitation of zinc metaborate on the anodic layer of the cation-exchange membrane.     

Flow of Multicomponent Electrolyte Solutions through Narrow Pores of Nanofiltration Membranes

The slow flow of a multicomponent electrolyte solution in a narrow pore of a nanofiltration membrane is considered. The well-known semiempirical method of subdivision of electrical potential into quasi-equilibrium and streaming parts and the definition of streaming concentrations and pressure are discussed. The usefulness of this tool for solving the electrohydrodynamic equations is shown and justified: the use of a small parameter enables a system of electrohydrodynamic partial differential equations to be reduced to a system of ordinary differential equations for streaming functions. Boundary conditions for streaming functions at both the capillary inlet and outlet are derived. The proposed model is developed for the flow of a multicomponent electrolyte solution with an arbitrary number of ions. This is coupled with (i) the introduction of specific interactions between all ions and the pore wall and (ii) the inclusion of the dissociation of water in both conservation and transport equations. Effective distribution coefficients of ions are introduced that are functions of both the specific interaction potentials and the surface potential of the nanofiltration membrane material. The axial dependency of surface potential is expressed by the use of a charge regulation model from which the discontinuity in electric potential and ion pore concentrations at the pore inlet and outlet can be described.A relation between the frequently used capillary and homogeneous models of nanofiltration membranes is developed. An example of application of the homogeneous model for interpretation of experimental data on nanofiltration separation of electrolyte solutions is presented, which shows a reasonable predictive ability for the homogeneous model.     

Ion transfer through solvent polymeric membranes driven by an exponential current flux

General analytical equations which govern ion transfer through liquid membranes with one and two polarized interfaces driven by an exponential current flux are derived. Expressions for the transient and stationary E-t, dt/dE-E and dI/dE-E curves are obtained, and the evolution from transient to steady behaviour has been analyzed in depth. We have also shown mathematically that the voltammetric and stationary chronopotentiometric I(N)-E curves are identical (with E being the applied potential for voltammetric techniques and the measured potential for chronopotentiometric techniques), and hence, their derivatives provide identical information.     

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.     

Decoupling of the nernst-planck and poisson equations. Application to a membrane system at overlimiting currents

This paper deals with one-dimensional stationary Nernst-Planck and Poisson (NPP) equations describing ion electrodiffusion in multicomponent solution/electrode or ion-conductive membrane systems. A general method for resolving ordinary and singularly perturbed problems with these equations is developed. This method is based on the decoupling of NPP equations that results in deduction of an equation containing only the terms with different powers of the electrical field and its derivatives. Then, the solution of this equation, analytical in several cases or numerical, is substituted into the Nernst-Planck equations for calculating the concentration profile for each ion present in the system. Different ionic species are grouped in valency classes that allows one to reduce the dimension of the original set of equations and leads to a relatively easy treatment of multi-ion systems. When applying the method developed, the main attention is paid to ion transfer at limiting and overlimiting currents, where a significant deviation from local electroneutrality occurs. The boundary conditions and different approximations are examined: the local electroneutrality (LEN) assumption and the original assumption of quasi-uniform distribution of the space charge density (QCD). The relations between the ion fluxes at limiting and overlimiting currents are discussed. In particular, attention is paid to the "exaltation" of counterion transfer toward an ion-exchange membrane by co-ion flux leaking through the membrane or generated at the membrane/solution interface. The structure of the multi-ion concentration field in a depleted diffusion boundary layer (DBL) near an ion-exchange membrane at overlimiting currents is analyzed. The presence of salt ions and hydrogen and hydroxyl ions generated in the course of the water "splitting" reaction is considered. The thickness of the DBL and its different zones, as functions of applied current density, are found by fitting experimental current-voltage curves.     

Streaming maxima in the iodine electroreduction at Hg electrodes in DMSO solutions

A current maximum was observed by d.c. polarography during the electroreduction of iodine at Hg electrodes in DMSO solutions. i?t curves during the drop life were performed to characterize the observed maxima. Changes in the cation of the supporting electrolyte do not. appreciably affect the results. The dependence of the streaming with depolarizer and supporting electrolyte concentration, as well as its independence of flux rate confirmed by linear sweep potential experiments at a hanging mercury electrode, permit us to classify the streaming under study as a positive first kind streaming. Regular current fluctuations at a certain depolarizer concentration and low supporting electrolyte concentration are also reported.     

Study on a novel antifouling polyamide–urea reverse osmosis composite membrane (ICIC–MPD): III. Analysis of membrane electrical properties

In this study, the electrical properties of the new polyamide–urea (ICIC–MPD) reverse osmosis composite membrane were analyzed via two self-made test cells. The electrical potential difference across membrane was measured via a perpendicular flow through mode potential difference measurement cell, and the electrical conductivity of membrane was tested by a tangential flow across mode conductivity measurement cell. Both streaming potential coefficient and gap between the upward and downward curves were determined by the plot of electrical potential difference versus up-loading and down-loading external pressure difference at both sides of membrane. It was found that pH of electrolyte solution has strong impact on streaming potential coefficient and electrical conductivity due to the dissociation of COOH group and protonation of NH₂ group of the active layer of ICIC–MPD membrane. It was also observed that both concentration of monomer 5-isocyanato-isophthaloyl chloride (ICIC) in the organic phase and contact time of organic phase with aqueous phase play an important role in salt rejection rate, gap between curves and electrical conductivity of the prepared ICIC–MPD membrane, and experimental results indicate that salt rejection rate of ICIC–MPD membrane is closely correlated to gap between curves at either polymerization condition. In addition, the effects of fouling behaviors on electrical potential difference and electrical conductivity of membrane were also discussed.     

Onset of natural convection in the electrochemical cell with horizontal electrodes under non-steady-state conditions: A numerical study

The disturbance of mechanical equilibrium of stagnant electrolyte containing three types of ions and the onset of natural convection in the electrochemical cell with plane horizontal electrodes under the non-steady-state conditions are studied theoretically. The Navier-Stokes equations in the Boussinesq approximation, the equations of ionic transfer of electrolyte components, which is caused by diffusion, convection, and migration, and the electroneutrality condition were used as the mathematical model of the process. Using the numerical simulation, the regularities of the onset of natural convection of electrolyte solution with the formation of convective cells are studied. The effect of transport properties of solution on the critical time of onset of convection and on the time before the current starts to increase due to the onset of natural convection, on the sizes and shape of convective cells and the mass-transfer rate is investigated by the example of cathodic deposition of metal at the limiting current.     

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.     

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).     

Electrochemistry of capillary systems with narrow pores. I. Overview

In capillary systems with narrow pores the Helmholtz electrochemical double layer located at the pore wall extends over the entire cross section of the pores. It loses its character as the “charge on the wall”. It will be shown that not only the electrokinetic phenomena but also the electrical conductivity and the dialysis potential of membranes with narrow pores can be understood from the same point of view, namely: the electrolyte solution in the pores of a membrane with narrow pores is considered to be an approximately homogeneous solution in contact with immobilised charges located at the pore wall. In this case the electrochemical equations contain the fixed ion concentration as a parameter instead of the ζ potential. This makes it possible to describe quantitatively to a good approximation data on the electroosmosis, the electrical conductivity, the streaming potential and the dialysis potential taken from the literature, as well as results of our own measurements, by using a single membrane constant.     

Electrochemistry of capillary systems with narrow pores V. Streaming potential: Donnan hindrance of electrolyte transport

The electrochemical theory of capillary systems with narrow pores outlined in Part I of this series is applied to the streaming potential and the electrical hindrance of electrolyte transport across ion selective membranes (Donnan hindrance). Both phenomena are related to the fixed ion concentration. Streaming potentials were measured while using collodion membranes of graded porosity and graded fixed ion concentration. The bulk phases consisted of aqueous KCl solutions with a concentration 2×10⁻⁴ n. The streaming potentials were calculated theoretically by using the electrical conductivity data of the membranes given in Part III of this series. The agreement between the experimental results and the predictions of the theory is good. Theory also predicts that a volume flow across the membrane caused by a hydrostatic pressure difference generates a filtration effect the concentration c_s of the electrolyte in the solution leaving the membrane on the low pressure side is lower than the concentration c on the high pressure side. The concentration ratio (c_s/c) is equal to the ratio (κ/κ_i) of the electrical conductivity of the high pressure phase κ and that of the pore fluid κ_i. The hindrance of the electrolyte transport is a transient phenomenon. It disappears slowly if the experiment is continued over a long period of time. This phenomenon, which is of importance in the understanding of ultrafiltration processes using membranes, is discussed in detail. It is compared with the observed changes in the streaming potential as a function of time. The influence of the electrical convection conductivity (electrical surface conductivity) on the streaming potential can be neglected under the chosen experimental conditions. Its influence will be discussed in Part VI of this series.     

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.     

Numerical simulation of natural convection of electrolyte solution with three types of ions in the electrochemical cell with vertical electrodes

The mass transfer in the electrolyte solution with three types of ions in the electrochemical cell of square section with vertical electrodes is studied. The mathematical model of the process involves the Navier-Stokes equations in the Boussinesq approximation, the equations of ionic transfer of electrolyte components, which is caused by diffusion, convection, and migration, and the condition of electroneutrality. It is shown that this problem corresponds to a special case of thermosolutal convection with regard for thermodiffusion (the Soret effect), where the cell boundaries are permeable to an impurity and the flux of impurity through the boundary is proportional to the heat flux. Using the numerical simulation, the distributions of concentration of ions, solution density, local and average mass-transfer rates are studied. The approximate analytical equations for the limiting current are obtained for typical electrochemical systems.     

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.     

Behaviour of a cobalt spinel ultrafiltration membrane during salt filtration with different ionic strengths

The characterisation of the surface charge of a cobalt spinel ultrafiltration membrane was investigated in the presence of electrolyte solutions by means of streaming potential measurements. The selectivity of a membrane towards different salts depends on the electrostatic interactions between the species in solution and the charge of the membrane surface. Firstly, the values of the streaming potential coefficient were measured during the filtration of NaCl, CaCl₂, Na₂SO₄ and CaSO₄ as a function of pH and ionic strength. The iso-electric point was determined for each electrolyte. Secondly, the rejection rates of the electrolytes were measured by ionic chromatography. The rejection was explained by a correlation with the surface charge of the membrane.     

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

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

Electrochemistry of capillary systems with narrow pores V. Streaming potential: Donnan hindrance of electrolyte transport

The electrochemical theory of capillary systems with narrow pores outlined in Part I of this series is applied to the streaming potential and the electrical hindrance of electrolyte transport across ion selective membranes (Donnan hindrance). Both phenomena are related to the fixed ion concentration. Streaming potentials were measured while using collodion membranes of graded porosity and graded fixed ion concentration. The bulk phases consisted of aqueous KCl solutions with a concentration 2×10⁻⁴ n. The streaming potentials were calculated theoretically by using the electrical conductivity data of the membranes given in Part III of this series. The agreement between the experimental results and the predictions of the theory is good. Theory also predicts that a volume flow across the membrane caused by a hydrostatic pressure difference generates a filtration effect the concentration c_s of the electrolyte in the solution leaving the membrane on the low pressure side is lower than the concentration c on the high pressure side. The concentration ratio (c_s/c) is equal to the ratio (κ/κ_i) of the electrical conductivity of the high pressure phase κ and that of the pore fluid κ_i. The hindrance of the electrolyte transport is a transient phenomenon. It disappears slowly if the experiment is continued over a long period of time. This phenomenon, which is of importance in the understanding of ultrafiltration processes using membranes, is discussed in detail. It is compared with the observed changes in the streaming potential as a function of time. The influence of the electrical convection conductivity (electrical surface conductivity) on the streaming potential can be neglected under the chosen experimental conditions. Its influence will be discussed in Part VI of this series.     

Steady-state and transient electrical properties of ion-exchange membrane systems in asymmetric arrangements

The steady-state and transient electrical properties of ion-exchange membranes placed between two solutions with different values of the electrolyte concentration, have been simulated using the network simulation method. The ionic transport processes are theoretically described on the basis of the Nernst-Planck and Poisson equations. The system under study is constituted by a cation-exchange membrane in which the fixed-charge is homogeneously distributed in space and two diffusion boundary layers on both sides of the membrane, the electric double layers at the interfaces being included. The steady-state voltage-current characteristic and the profiles of the ionic concentrations and the electric potential, are analysed. Also, the choronopotentiometric response of the system has been discussed and the time evolution of the electric energy consumption evaluated. In particular, the influence of the ratio of the bathing concentrations on the permselectivity and the chronopotentiometric response of the ion-exchange membrane systems, has been established.     

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.