Modeling the Conductivity and Diffusion Permeability of a Track-Etched Membrane Taking into Account a Loose Layer.

The microheterogeneous model makes it possible to describe the main transport properties of ion-exchange membranes using a single set of input parameters. This paper describes an adaptation of the microheterogeneous model for describing the electrical conductivity and diffusion permeability of a track-etched membrane (TEM). Usually, the transport parameters of TEMs are evaluated assuming that ion transfer occurs through the solution filling the membrane pores, which are cylindrical and oriented normally to the membrane surface. The version of the microheterogeneous model developed in this paper takes into account the presence of a loose layer, which forms as an intermediate layer between the pore solution and the membrane bulk material during track etching. It is assumed that this layer can be considered as a "gel phase" in the framework of the microheterogeneous model due to the fixed hydroxyl and carboxyl groups, which imparts ion exchange properties to the loose layer. The qualitative and quantitative agreement between the calculated and experimental concentration dependencies of the conductivity and diffusion permeability is discussed. The role of the model input parameters is described in relation to the structural features of the membrane. In particular, the inclination of the pores relative to the surface and their narrowing in the middle part of the membrane can be important for their properties.

Fouling Mitigation by Optimizing Flow Rate and Pulsed Electric Field during Bipolar Membrane Electroacidification of Caseinate Solution.

The efficiency of separation processes using ion exchange membranes (IEMs), especially in the food industry, is significantly limited by the fouling phenomenon, which is the process of the attachment and growth of certain species on the surface and inside the membrane. Pulsed electric field (PEF) mode, which consists in the application of constant current density pulses during a fixed time (Ton) alternated with pause lapses (Toff), has a positive antifouling impact. The aim of this study was to investigate the combined effect of three different relatively high flow rates of feed solution (corresponding to Reynolds numbers of 187, 374 and 560) and various pulse-pause ratios of PEF current regime on protein fouling kinetics during electrodialysis with bipolar membranes (EDBM) of a model caseinate solution. Four different pulse/pause regimes (with Ton/Toff ratios equal to 10 s/10 s, 10 s/20 s, 10 s/33 s and 10 s/50 s) during electrodialysis (ED) treatment were evaluated at a current density of 5 mA/cm2. It was found that increasing the pause duration and caseinate solution flow rate had a positive impact on the minimization of protein fouling occurring on the cationic surface of the bipolar membrane (BPM) during the EDBM. Both a long pause and high flow rate contribute to a more effective decrease in the concentration of protons and caseinate anions at the BPM surface: a very good membrane performance was achieved with 50 s of pause duration of PEF and a flow rate corresponding to Re = 374. A further increase in PEF pause duration (above 50 s) or flow rate (above Re = 374) did not lead to a significant decrease in the amount of fouling.

Evolution with time of hydrophobicity and microrelief of a cation-exchange membrane surface and its impact on overlimiting mass transfer.

Surface properties were measured together with electrochemical characteristics of a CMX (Neosepta, Tokuyama Corp.) cation-exchange membrane. Relative hydrophobicity was controlled by the contact angle; XPS and SEM were used for characterizing chemical composition and microrelief of the surface, respectively. Voltammetry, chronopotentiometry, and mass transfer rate measurements were made as well. A "fresh" membrane and samples after 10, 25, 100, and 150 h of operation in an electrodialysis cell at an overlimiting current equal to 3 theoretical limiting currents, in a 0.02 M NaCl solution, were characterized. Some electrochemical properties were also measured for a Neosepta cation-exchange membrane, aged 2 years, in an industrial food process. It was found that the hydrophobicity of the CMX membrane has increased after the first 10 h of operation; more and more cavities of the dimension of the order of 1 µm have appeared with time testifying electrochemical erosion of the surface. The limiting current density (i(lim)) and the overlimiting transfer rate through the CMX membrane increased with time of its operation under overlimiting current. In the case of new CMX, i(lim) was very close to the theoretical value i(lim)(theor) calculated by the Lévêque equation. After 10 h of operation, i(lim) increased by 5%, and after 25, 100, and 150 h, the increase was by 30%, 70%, and 100%, respectively. Similarly, the mass transfer rate was found to increase up to 5 times (when desalting 0.005 M NaCl under 3 V) in comparison with the theoretical value. The ensemble of data was explained by the hypothesis that the passage of intensive current produces erosion of the ion-exchange polymer forming a continuous phase in CMX. This erosion results in exposure at the surface of the other constituent of CMX: small (about 100 nm) particles of relatively hydrophobic polyvinylchloride. Increasing surface hydrophobicity facilitates the slip of electroconvective vortexes along the surface. Besides, the geometry of the cavities gives rise to appearing tangential electric force applied to the extended space charge density at cavity's walls. As the local limiting current density within a cavity is lower than at the flat surface, electroconvective vortices arise at current densities lower than i(lim)(theor). With time, the number and the size of cavities increase (apparently, due to paired electroconvective vortices occurring inside them) that seems the main reason for overlimiting transfer increase.

Intensive current transfer in membrane systems: modelling, mechanisms and application in electrodialysis.

Usually in electrochemical systems, the direct current densities not exceeding the limiting current density are applied. However, the recent practice of electrodialysis evidences the interest of other current modes where either the imposed direct current is over the limiting one or a non-constant asymmetrical (such as pulsed) current is used. The paper is devoted to make the mechanisms of mass transfer under these current regimes more clear. The theoretical background for mathematical modelling of mass transfer at overlimiting currents is described. Four effects providing overlimiting current conductance are examined. Two of them are related to water splitting: the appearance of additional charge carriers (H(+) and OH(-) ions) and exaltation effect. Two others are due to coupled convection partially destroying the diffusion boundary layer: gravitational convection and electroconvection. These effects result from formation of concentration gradients (known as concentration polarization) caused by the current flowing under conditions where ionic transport numbers are different in the membrane and solution. Similar effects take place not only in electrodialysis membrane systems, but in electrode ones, in electrophoresis and electrokinetic micro- and nanofluidic devices such as micropumps. The relation of these effects to the properties of the membrane surface (the chemical nature of the fixed groups, the degree of heterogeneity and hydrophobicity, and the geometrical shape of the surface) is analyzed. The interaction between the coupled effects is studied, and the conditions under which one or another effect becomes dominant are discussed. The application of intensive current modes in electrodialysis, the state-of-the-art and perspectives, are considered. It is shown that the intensive current modes are compatible with new trends in water treatment oriented towards Zero Liquid Discharge (ZLD) technologies. The main idea of these hybrid schemes including pressure- and electro-driven processes as well as conventional methods is to provide the precipitation of hardness salts before the membrane modules and that of well dissolved salts after.

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.

Effect of anion-exchange membrane surface properties on mechanisms of overlimiting mass transfer.

Four effects providing overlimiting current transfer in ion-exchange membrane systems are examined. Two of them are related to water splitting: the appearance of additional current carriers (H+ and OH- ions) and exaltation effect. Two others are due to coupled convection partially destroying the diffusion boundary layer: gravitational convection and electroconvection. Three anion-exchange membranes, which differ in surface morphology and the nature of ion-exchange sites within a surface layer, are examined. The ion transfer across these membranes in NaCl solutions is studied by voltammetry, chronopotentiometry, and pH-metry. By excluding the effects of water splitting and gravitational convection, it is shown that the main mechanism of overlimiting mass transfer in narrow membrane cells at low salt concentrations is electroconvection. The reasons explaining why water splitting suppresses electroconvection are discussed. The scenario of development of potential oscillations with growing current and time is compared with that described theoretically by Rubinstein and Zaltzman.