V.I. Zabolotsky

Space charge effect on competitive ion transport through ion-exchange membranes

A mathematical model of the competitive electro-transport of two counter-ions through an ion exchange membrane based on the Nernst-Planck and Poisson equations is developed. A three-layer system is considered: the membrane and two adjacent diffusion layers. Concentration profiles in the three layers, effective transport numbers as functions of the current and current-voltage characteristics are calculated. Deviation from the local electroneutrality in space charge region near the depleted solution/membrane interface is taken into account. It is shown that the space charge region grows with the voltage applied. However the fluxes of the competitive counter-ions at over-limiting currents are determined by their transfer through the electroneutral part of the depleted diffusion layer.

Mathematical description of ion transport in membrane systems

A review of works resulting in development of a hierarchic system of mathematical models is presented. Different scales of ion transport are considered: 1) in the membrane, where two approaches are used, the irreversible thermodynamics and modelling of the membrane material, the last permits to link physicochemical properties with structure-kinetic parameters of the membrane; 2) in a three-layer system composed of a membrane with two adjoining diffusion layers; and 3) in an electrodialysis 2D cell, where the differential equation of convective diffusion is used.

Analysis of electrodialysis water desalination costs by convective-diffusion model

The analysis of electrodialysis water desalination costs was made. Application of the hydrodynamic convective-diffusion model permitted to determine optimum parameters of an “ideal” process in a desalination channel with smooth-wall ion-exchange membranes without a spacer. The method of mathematical simulation based on a regression of experimental data is applied for cost estimation of the process at optimum operating parameters.

Method of electrodialysis stack testing with the feed solution concentration regulation

A technique to test electrodialysis (ED) stacks designed to desalt dilute solutions is developed. The technique permits obtaining reproducible data on laboratory and medium-scale units useful for predicting mass transfer characteristics of large ED stacks. Quasi-steady state of desalination process is the main condition to obtain such data. This state can be attained by applying recycling hydraulic modes and special devices to maintain constant pH, or pH and concentration of the feed solution. To obtain data for scaling, it is necessary to apply a fixed voltage on the stack and to use a constant flow rate of the feed solution during the experiment, the feed solution concentration may vary with the time. Specifications of the stacks studied, rational hydraulic and electrical modes of testing are considered.

Dependence of salt and water ion fluxes through ion-exchange membranes under electrodialysis on the ion-exchange bed composition

Salt and H+(OH−) ion fluxes, the resistivity of desalted solution as well as pH changes are studied in a desalination compartment containing a monolayer of ion-exchange bed (IEB). The influence of anion-exchanger volume fraction in the IEB on the fluxes and the desalted solution characteristics are discussed. The optimum value for the IEB composition is found for the case of Russian commercial ion-exchange membranes and resins.

Prediction of the behavior of long electrodialysis desalination channels through testing short channels

A method to forecast behavior of electrodialyzers with long demineralization channels is suggested. It is based on the data obtained using a laboratory cell or an apparatus with short demineralization channels of similar construction. The results are presented as dimensionless parameters.

Effects of the desalination chamber design on the mass-transfer characteristics of electrodialysis apparatuses at overlimiting current densities

The overlimiting current modes are being increasingly used in electrodialysis (ED) of dilute aqueous solutions. Of great importance is establishing a relationship between the design of ED apparatuses and the character of phenomena observed at overlimiting current densities, primarily, electroconvection and H+ and OH− ion generation during water dissociation at the membrane-solution interface. In this work, we analyze the factors governing the efficiency of dilute solutions using modern theoretical concepts and experimental data obtained in laboratory cells and large-scale electrodialysis apparatuses. We also analyze the relationship between the mechanisms of the overlimiting transfer and the design of the desalinating channel. ED apparatuses of different types are considered, namely, apparatuses with profiled membranes, inert spacers, monolayer of ionite granules, and dipolar fillers of unwoven ionite fibers. The optimum concentration ranges of the desalinated solutions were found, and the operating conditions of membrane stacks, providing maximum overlimiting ion transfer, were determined.

Choosing the electrodialyzer design and hydraulic modes for demineralization of dilute solutions

The purpose of the work presented is the investigation of electrodialysis apparatuses of two types differing by demineralization chambers construction only. These are pilot apparatuses based on Russian membranes: cation exchange MK-40 and anion exchange MA-40.