Water Transport Number Research Articles

Electroosmotic transport of water and aprotic solvent in heterogeneous membranes

Electrosmotic water transport in MK-40, MA-40, and MA-41 electrodialysis membranes before and after their treatment by aprotic solvent solution and electroosmotic permeability of a MK-40/MA-40 membrane couple in water and N,N-dimethyl acetamide were studied for the first time. It is found that N,N-dimethyl acetamide produces practically no effect on the properties of the studied ion-exchange materials and its transport number through the MK-40/MA-40 membrane couple is independent both of the initial lithium chloride concentration in a desalting cell of the concentrator electrodyalizer and its volume fraction in the solution. The initial concentration of lithium chloride in the desalting cell does not affect the transport numbers of water in the studied membrane couple either. However, these depend on the volume fraction of the organic component in the solution and this dependence features an extremum. A method for estimation of electroosmotic permeability of the membrane couple in aqueous-organic solutions of electrolytes is suggested.

Modelling of Soy Sauce Desalting by Electrodialysis

In this work, the main features of electrodialytic (ED) desalting of microfiltered samples of a traditional soy sauce under constant electric current in the range of 1.25 to 6.5 A were quite well reconstructed using a mathematical model based on the Nernst–Planck equation. Amino nitrogen migration was characterised by a small effective transport number (tAN = 0.070 ± 0.01), resulting in an average loss in amino nitrogen of about 30% whatever the electric current tested. The sodium chloride transport number (tB = 0.969 ± 0.05) and diffusion rate (LB ≈ 0), as well as the effective membrane surface area, essentially coincided with those previously established when dealing with concentrated model brines. On the contrary, there was a significant diversity in the water transport number (tW = 8.3 ± 0.1) and diffusion rate [LW = (6.9 ± 0.2) × 10−5 mol m−2 s−1 bar−1], as well as in the anion- and cation-exchange membrane resistances (Ra = Rc ≈ 0.04 Ω). The experimental procedure and mathematical model described in this work may be recommended not only to optimise the ED desalination of soy sauce but also to generate a first-cut design for ED desalting of other natural seasonings.

Electrodialytic desalting of model concentrated NaCl brines as such or enriched with a non-electrolyte osmotic component

The Nernst–Planck approach, previously used to model the electrodialytic recovery of uni- or di-valent electrolytes, was employed to comply with the desalination of concentrated brines with an initial NaCl concentration ( c BD0) ranging from about 1.4 to 3.0 kmol m −3 and to enucleate the contribution of osmosis and electro-osmosis. The experimental procedure formerly developed was simplified and thus shortened in order to determine just the engineering parameters essential to simulate the desalting process under study. This was further checked by performing a few validation tests in quite different operating conditions from those used in the training tests, that is (i) by changing the electric current ( I) step-wisely to simulate the continuous-mode operation of a multistage ED unit, (ii) by reducing the initial salt content of the concentrate by a factor of about 10 and (iii) by spiking the model brine solution with a non-electrolyte osmotic component (i.e., glucose) to enhance water transfer by osmosis. In these tests both membrane resistances were found to be constant and independent of the solute concentration, owing to the fact that the ED desalting process was carried out at electric current densities by far smaller than the limiting one. Either the effective solute ( t B) or water ( t W) transport number was independent of I and c BD0 in the ranges tested. The contribution of solute diffusion was negligible ( L B ≈ 0), while that of osmosis ( L W) across the membranes used here was definitively different from zero and had to be taken into account.

Composite sulfonated cation-exchange membranes modified with polyaniline and applied to salt solution concentration by electrodialysis

A method is developed for obtaining anisotropic composites based on the sulfonated cation-exchange MF-4SK and MK-40 membranes and the electroactive polymer polyaniline (PANI). The kinetics of aniline polymerization by successive diffusion in these membranes is investigated, and differences in the transport characteristics of the resulting MF-4SK/PANI and MK-40/PANI composites are identified. It is established from results of electroosmotic and diffusion experiments that the composite MF-4SK/PANI-1 membrane (after 1 h of aniline polymerization) suppresses electrolyte and water flow the most. Diffusion permeability drops by an order of magnitude, and water transport numbers are reduced by 50–70%. In the process of sodium chloride concentration by electrodialysis, the salt content of the concentrate increases by 50–70% with the composite MF-4SK/PANI-1 membrane compared to the base MF-4SK membrane and by 15–20% compared to the electrodialysis MK-40 membrane. Transport characteristics of the membrane pairs under investigation are calculated from the model of limiting concentration by electrodialysis: current efficiency, water transport numbers, osmotic and diffusion permeability. The dominant influence of the electroosmotic mechanism of water transport on the effect of salt solution concentration is established.

Sodium chloride concentration by electrodialysis with hybrid organic-inorganic ion-exchange membranes: An investigation of the process

This study examines how conditions for modifying homogeneous MF-4SK and heterogeneous MK-40 membranes with tetraethoxysilane affect membrane properties. The microstructure of the bulk membrane and its surface, both before and after exposure to the modifying agent, is examined by scanning electron microscopy, spark spectrophotometry, and standard contact porosimetry. The process of sodium chloride concentration by electrodialysis with hybrid organic-inorganic membranes in cells with noncirculating concentration compartments is investigated, and a mathematical model of the concentration process by electrodialysis is used to determine transport properties: current efficiency, diffusion and osmotic permeabilities, and the salt hydration number. For highly hydrophilic membranes, it is shown that water transport occurs both in ion hydration shells and also as free water. It is established that after modified membranes undergo additional heat treatment, the transport of free water ceases, and the water transport number decreases. This is in accord with an increase in the salt content of the concentrate during concentration by electrodialysis.

Application of the Nernst–Planck approach to model the electrodialytic recovery of disodium itaconate

The Nernst–Planck approach, previously used to model the electrodialytic recovery of univalent electrolytes, was used to comply with the recovery of a diprotic acid (i.e., itaconic acid) once it had been converted into its disodium salt. In this way, by applying sequentially the same experimental procedure formerly developed, it was possible to determine all the engineering parameters (i.e., ion transport numbers in solution and electro-membranes; effective solute and water transport numbers; effective membrane surface area, surface resistances and limiting current intensity) of the electrodialytic process of concern. Whereas the cationic membrane resistance ( R c) was found to be approximately constant (0.16 ± 0.01) and independent of solute concentration, the anionic membrane one ( R a) was generally greater than R c and decreased from about 2 Ω to an asymptotic value of ∼0.6 Ω as the bulk solution electrical conductivity ( κ) ranged from 0.05 to 3 S m −1. Use of all the above engineering parameters yielded a satisfactorily prediction of the voltage applied to the electro-membrane pack in two batch desalination trials carried out under constant electric current of 0.75 and 1.5 A. The electro-membranes used exhibited an almost ideal behaviour and only the itaconate anions carried the electric charge passing through the anionic membrane. The overall performance of this ED process was characterised in terms of a current efficiency (CE) of about 97% and a specific energy consumption ( ɛ) increasing from 0.28 to 0.48 kWh kg −1 for a solute recovery yield of 98% as the current density ( j) was increased from 147 to 294 A m −2.

Ionic transport phenomenon across sol–gel derived organic–inorganic composite mono-valent cation selective membranes

Organic–inorganic composite mono-valent cation selective membranes (MCSMs) were prepared by sol–gel under acidic conditions, in which sulfonic acid groups were introduced at the inorganic segment. Studies on physicochemical and electrochemical properties revealed their excellent mechanical, thermal, and oxidative stabilities, high conductivity, ion-exchange capacity, permselectivity for mono-valent cations, ionic diffusion and water transport number. These properties suggested the suitability of MCSMs, especially Si-65%, for electro-separation of Na + from Ca 2+, Mg 2+, and Fe 3+. The effect of electrolyte solution on the characteristics of the current–voltage ( i – v ) curve in MCSM was studied based on the concentration polarization. Electro-transport of different ions in terms of plateau length and concentration profiles for different ions in the solution phase, diffusion boundary layer and membrane phase were presented. Information obtained from i – v curve analysis were validated by electrodialysis (ED) experiments for individual or mixed electrolyte solutions. Electro-transport efficiency and separation factor of different ions for MCSM and Nafion117 (N117) membranes were compared, which suggested suitability of MCSMs for separating cations.

Water Transport during Ion Conduction in Anion-Exchange and Cation-Exchange Membranes

Water transport during ion conduction through an anion-exchange membrane (AEM) immersed in an aqueous solution of and KOH was investigated. We have developed an apparatus to accurately measure small changes in volumes of the aqueous solution at each side of the membrane by capillary tubes during the passage of an electronic current through the membrane. In contrast to the previously reported apparatus, the present apparatus can be applied to an AEM in various aqueous solutions of electrolytes, and measurements under conditions close to those in actual solid alkaline fuel cells are therefore possible by using alkaline solutions. The water-transport number for AEM in was larger than that in KOH, indicating the importance of selecting the appropriate aqueous solution of electrolytes. It is possible to determine whether anions or cations are conductors in electrolyte membranes with unknown properties.

Model verification of limiting concentration by electrodialysis of an electrolyte solution

The concentration of LiCl in brine and brine volume are obtained as functions of current density by the method of limiting concentration by electrodialysis. These relationships are used for model calculations of current efficiency, the diffusion, osmotic, and electroosmotic permeability of an MK-40/MA-40 membrane pair, and also salt hydration numbers. These theoretical values of water transport numbers and LiCl hydration numbers are compared with corresponding experimental and literature data. It is shown that the model adequately describes the phenomena of the mass electrotransport occurring in electrodialyzers with noncirculating concentration compartments, and it can be successfully applied in calculating the technological parameters of the process, finding the transport properties of ion-exchange membranes, and determining salt hydration numbers in aqueous electrolyte solutions.

The electric transport of proton-bound water in MF-4SK/PAni nanocomposite membranes

Electrochemical characteristics of MF-4SK/PAni nanocomposite membranes prepared at different times of chemical polymerization of aniline are studied. Electroosmotic permeability and conductivity of membranes in solutions of acids and sodium chloride are determined. It is revealed that the conductivity of nanocomposites in the proton form at 30-day synthesis is approximately 3 times as low as that of the base membrane and composite membrane formed at 5-h synthesis. The transport number of water slightly depends on the structural type of membrane and changes from 3.3 to 2 mol H2O/mol H+ with an increase in the concentration of HCl solution from 0.1 to 3 M. The ratio of transport number to the water content rises about twofold in composites as compared to the initial membrane. It is shown that water is transferred with proton as hydronium structures [H5O2]+ and [H9O4]+ by the migration mechanism whose contribution to the total proton transfer in composite membranes increases.

Influence of polyaniline intercalations on the conductivity and permselectivity of perfluorinated cation-exchange membranes

This work describes the effect of polyaniline intercalations, produced by polymerization in situ of aniline in perfluorinated sulfocationic polymer templates, on the electrochemical properties of the resulting composite membrane. During the polymerization in situ process, the color of the template evolves rapidly from white to blue and then to emerald green. After 5 h of aniline polymerization, both pristine and composite membranes exhibit higher protonic conductivity than aqueous sulfuric acid solutions with concentrations lower than 0.1 M. After a polymerization time of 30 days, intercalations made up of a mixture of emeraldine and pernigraniline are formed that reduce the conductivity to one-third of that corresponding to the pristine acid membranes. The electroosmotic water transport number across both the pristine and composite acid membranes is about 3 mol/Faraday, a rather low value explained by the high protonic conductivity of the membranes. Apparent cation transport numbers determined from electromotive forces of concentration cells are little affected by the polyaniline intercalations and their values are rather close to those calculated taking the membranes as reference frame.

Application of chronopotentiometry to determine the thickness of diffusion layer adjacent to an ion-exchange membrane under natural convection

A brief review of the evolution of the diffusion boundary layer (DBL) conception inspired by the works of Nernst, Levich and Amatore is presented. Experimental methods for studying the DBL in electrode and membrane systems are considered. The electrochemical behaviour of a CM2 cation-exchange membrane in NaCl and KCl solutions is studied by chronopotentiometry at constant under-limiting current. Chronopotentiometric curves are described theoretically by applying the Kedem–Katchalsky equations in differential form to a three-layer system including the membrane and two adjoining DBLs. The conductance coefficients entering the equations are found by treating the results of membrane characterisation: the electrical conductivity, transport numbers of ions and water, electrolyte uptake, as functions of the equilibrium electrolyte solution. The two-phase microheterogeneous model is used for this treatment resulting in presentation of the conductance coefficients as functions of (virtual) electrolyte solution concentration in the membrane. The steady-state DBL thickness ( δ) is found by fitting experimental potential drop at sufficiently high times. It is found that δ is proportional to (Δ c) − 0.2 , where Δ c is the difference between the electrolyte concentration in the solution bulk and at the interface. This result differs from the Levich equation, which gives the power equal to − 0.25 for Δ c. This deviation is explained by the fact that the theory of Levich does not take into account microscopic chaotic convection motion recently described by Amatore et al. It is shown that the treatment of experimental chronopotentiometric curves with the model developed allows one to observe the role of streaming potential in the membrane. Different mechanisms of streaming potential and their effect on the shape of chronopotentiograms are discussed. A simple analytical solution of Navier–Stokes equations applied to natural convection near an infinite vertical ion-exchange membrane is found. It is shown that the formation of DBL induced by electric current is quasi-stationary. This fact allows the empirical expression found earlier and linking δ with Δ c under steady-state conditions to be used in transient regimes. The numerical solution of the non-stationary Kedem–Katchalsky equations together with this empirical expression results in quantitative description of the potential difference (pd) and δ as functions of time in chronopotentiometric experiments. The comparison of theoretical and experimental chronopotentiometric curves shows an excellent agreement, especially for the part after switching off the current. The reasons of a small deviation observed just before the curves attain steady state under a constant current applied are discussed.

Transport Number of Water in the Nafion 117 Membrane: Confrontation with the Statistical Mechanics Theory

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O.006 Design and performance of a bioreactor-promoted tissue engineering

The main engineering parameters (i.e. ion transport numbers in solution and electro-membranes; effective solute and water transport numbers; effective membrane surface area, membrane surface resistances, limiting current intensity and mass transfer coefficient) controlling the recovery of sodium propionate from model solutions by electrodialysis were determined in accordance with a sequential experimental procedure. Such parameters allowed a satisfactorily simulation of training and validation tests carried out under constant- or variable-current intensity.The performance of this ED process was characterised in terms of a current efficiency (Ω) of about 98% in constant- and variable-current regions, a water transport number (tW) of about 15, and a specific energy consumption (ε) increasing from 0.22 to 0.35 kW h kg−1 for a solute recovery yield of 95% as the current density (j) was increased from 200 to 400 A m−2. The specific resistance of the cationic or anionic membranes were found to be practically coincident or at least four times greater than that provided by the manufacturer in aqueous solutions of sodium chloride, respectively. These parameters are to be used to design and/or optimise ED stacks involved in the downstream processing of propionic acid fermentation broths.

Studies on electrochemical characterization and performance prediction of cellulose acetate and Zeocarb-225 composite membranes in aqueous NaCl solutions

We have mixed cellulose acetate and Zeocarb-225 in different ratios, leading to the preparations of Membrane-1 and Membrane-2. Membrane potential, water content, and conductance measurements have been carried out to estimate and analyze the data in terms of equilibria and important electrochemical parameters. The Donnan equilibrium has been incorporated to estimate the activity coefficient of counterions, ypM, and solute, y±M in the membrane phase along with the parameter, so called ϕ expressing non-ideality. Dependence of the extent of hydrophilicity of both membranes on mean electrolyte concentrations has been examined. Selectivity in membranes is discussed in terms of dissociation equilibria, Kds and Kdf. It has been found that membrane surface charge density σs increases with increasing of external NaCl concentration. Dependence of water transport number and cationic transport number on electrolyte concentration shows a similar trend of variation. At higher mean concentration of electrolyte, water transport number in Membrane-2 has a negative value. Membrane-2 has a higher value of water transport number than Membrane-1. The entropy production due to solute and water transport has been quantified for both the membranes in the light of nonequilibrium thermodynamics. The various type of interactions such as solute–membrane, solute–water, and water–membrane are analyzed in terms of friction coefficients (fij) of Spiegler's frictional pore model. In our case, an fwm<fsm<fsw-like trend is observed in both membranes. These frictional coefficients show close dependence on external electrolyte concentrations. Pore potential values of Membrane-1 and Membrane-2 have been worked out using the Poisson–Boltzmann equation. In both systems pore potential values increase with increasing mean electrolyte concentrations. The transport through Membrane-1 and Membrane-2 tends to follow diffusion-control criteria, i.e., (D±⋅C⋅d/D±MCM⋅δ)≫2. A slightly higher value of solute rejection is found in Membrane-2.

Modification of cellulose based membranes by γ-radiation: Effect of cellulose content

Electrochemical characterization of three cellophane membranes with different content of regenerated cellulose was carried out by determining salt diffusion and ion transport numbers, which were obtained from diffusion and membrane potential measurements carried out with the membranes in contact with NaCl solutions at different concentrations. Results show a decrease for salt permeability with the increase of cellulose content in the membranes, which can be related with the decrease in the swelling degree of the samples containing higher amount of cellulose, while a slightly increase in the cation transport number was obtained. The effect of γ-irradiation in structural and electrochemical parameters of these membranes was also studied. Two different radiation doses (10 J/kg and 80 J/kg) were used, which were delivered by a 60Co Cobalt Unit. Changes in membrane permeability, cation and water transport numbers were obtained in order to determine structural and electrical modifications in the membrane matrix as a result of irradiation. According to the experimental results, γ-radiation produces: (i) a reduction in salt permeability, which strongly depends on the membrane cellulose content (between 20% and 40% for 10 J/kg dose), but much lower reduction exist when the two different radiation doses for a given sample are compared; (ii) a slight increase in the negative character of cellophane membranes independently of the cellulose content.

Assessment of the main engineering parameters controlling the electrodialytic recovery of sodium propionate from aqueous solutions

The main engineering parameters (i.e. ion transport numbers in solution and electro-membranes; effective solute and water transport numbers; effective membrane surface area, membrane surface resistances, limiting current intensity and mass transfer coefficient) controlling the recovery of sodium propionate from model solutions by electrodialysis were determined in accordance with a sequential experimental procedure. Such parameters allowed a satisfactorily simulation of training and validation tests carried out under constant- or variable-current intensity. The performance of this ED process was characterised in terms of a current efficiency ( Ω) of about 98% in constant- and variable-current regions, a water transport number ( t W) of about 15, and a specific energy consumption ( ε) increasing from 0.22 to 0.35 kW h kg −1 for a solute recovery yield of 95% as the current density ( j) was increased from 200 to 400 A m −2. The specific resistance of the cationic or anionic membranes were found to be practically coincident or at least four times greater than that provided by the manufacturer in aqueous solutions of sodium chloride, respectively. These parameters are to be used to design and/or optimise ED stacks involved in the downstream processing of propionic acid fermentation broths.

Modeling of sodium acetate recovery from aqueous solutions by electrodialysis

The main engineering parameters (i.e., ion transport numbers in solution and electro-membranes; effective solute and water transport numbers; effective membrane surface area, membrane surface resistances, and limiting current intensity) affecting the recovery of sodium acetate from model solutions by electrodialysis (ED) were determined in accordance with a sequential experimental procedure. Such parameters allowed a satisfactory simulation of a few validation tests carried out under constant or step-wisely variable current intensity. The performance of this ED process was characterized in terms of a current efficiency (omega) of about 93% in the constant-current region, a water transport number (t(W)) of about 15, and a specific energy consumption (epsilon) increasing from 0.14 to 0.31 kWh/kg for a solute recovery yield of 95% as the current density (j) was increased from 112 to 337 A/m2. The specific resistance of the anion- or cation-exchange membranes were found to be three or two times greater than those measured in aqueous NaCl solutions and are to be used to design and/or optimize ED stacks involved in the downstream processing of acetic acid fermentation broths.

Water transport in a non-aqueous, polypyrrole electrochemical cell

A conducting polymer based liquid membrane electrochemical cell is presented in which reversible water transport in propylene carbonate (PC) is achieved by applying a dc voltage across the cell. In a cell two electrochemically deposited polypyrrole (PPy) films are utilized together with a porous separator filled with an electrolyte solution to make a sandwich structure, and the water vapor pressure adjacent to each electrode is measured. Under a cycling electrode potential the movement of solvated ions across the cell reversibly transports water. PPy films with different dopant anions (BF 4 −, PF 6 −, DBS −) are tested in PC solutions containing corresponding anions and different cations (Li +, Na +, TBA +). Water activity increases at the cathode and decreases at the anode. Water transport numbers for different liquid membrane systems are estimated and discussed.

Optimal strategy to model the electrodialytic recovery of a strong electrolyte

In this work, mostly Nernst–Planck derived relationships were used to simulate the electrodialytic recovery of a strong electrolyte, namely sodium chloride. To this end, it was set up a five-step experimental procedure consisting of zero-current leaching, osmosis, and dialysis, electro-osmosis, desalination, current–voltage and validation tests. The contribution of leaching and solute diffusion across the electro-membranes was found to be negligible with respect to the electro-migration. On the contrary, solvent diffusion tended to be important as the solute concentration difference at the membrane sides increased or current density was reduced. The electro-osmosis and desalination tests yielded the water and solute transport numbers. By performing several limiting current tests at different solute concentrations and feed flow rates using anionic or cationic membranes, it was possible to determine simultaneously the limiting current intensity, the ratio of the differences between the counter-ion transport numbers in the anion- and cation-exchange membranes and solution, the overall resistance of the electro-membranes, the effective membrane surface area, and the solute mass transfer coefficient. All these process and design parameters allowed the time course of the solute concentration in the concentrating (C) and diluting (D) compartments, as well as the voltage applied to the electrodes, to be reconstructed quite accurately without any further correction factors. The capability of the above parameters to simulate the performance of the electrodialysis (ED) unit was checked by resorting to a few validation tests, that were performed in quite different operating conditions from those used in the training tests, that is by filling tank C with a low feed volume with a low solute concentration and applying a constant current intensity to magnify the effect of electro-osmosis or by changing the current intensity step-wisely to simulate the continuous-mode operation of a multistage ED unit. Finally, a parameter sensitivity analysis made the different contribution of the process and design parameters to be assessed, thus yielding a straightforward procedure for designing or optimising accurately ED desalination units up to a final salt concentration of about 1.7 kmol m −3.