N. P. Gnusin

Method of Model Parameter Calculation of Ion-Exchange Resins

A method for determination of parameters of a three-wire model and Lichtenecker model on the basis of experimental data of conductivity measurement for ion-exchange resins and equilibrium solutions is developed and experimentally tested. This method allows determining the required parameters using experimental points available for measurements on the basis of the minimum root-mean-square deviation. Verification of the method using our own experimental data and data from the literature allowed establishing that the three-wire model in the case of a solid-phase resin is practically devoid of the “solution-only channel“ and can be considered as a two-wire model.

The three-wire model and Lichtenecker’s equation for calculations of the conductivity of ion-exchange columns

The approaches to the evaluation of the conductivity of ion-exchange columns are analyzed. Specifically, the three-wire model and Lichtenecker’s power equation are examined. The problem of how the coefficient of ion-exchange column filling and the parameter characterizing the state of conducting phases with respect to the current flow are related to the parameters involved in the equations of the three-wire model is treated theoretically. The common points and the coincident portions of the functions obtained in each of the approaches and some discrepancies between the functions are found. The discrepancies are determined by the special features of the models under consideration.

Effect of polyaniline on the current passing through structural fragments of ion-exchange sulfonic-cationite resins and membranes

Concentration dependences of the specific electrical conductivity of ion-exchange resin KU-2 and ion-exchange heterogeneous membrane MK-40 made thereof are obtained and compared prior to and after the membrane modification with polyaniline. It is shown that the introducing of the polyaniline to polymer matrices of ionites results in the change of the specific electrical conductivity of both the resin KU-2 and the membrane MK-40, which correlates with the earlier data obtained for the MF-4SK/polyaniline composites. The quantitative evaluation of the polyaniline effect on the mechanism of current passing through structural fragments of initial and modified ionites is carried out. To this purpose, model parameters were used, which reflect the current paths and the conducting phases’ volume fractions and spatial orientation.

Mathematical model of electrodiffusion transfer through three-layer membrane system: Diffusion layer-ion-exchange membrane-diffusion layer

Three-layer combination formed in dialysis systems, which comprises membrane confined between two diffusion layers, can be considered as a single whole (a fragment) included in numerous complicated electrodialysis assemblies. A mathematical model is developed for estimating the electrodiffusion transfer in such a fragment containing four operating salt ions with the allowance for the membrane heterogeneous structure. The method of solving the problem is based on the integrating of the Nernst-Planck transfer differential equations with the corresponding boundary and interfacial conditions.

Modeling of transfer in electrodialysis systems

The mass electrotransfer in an electrodialysis cell that desalinates and concentrates a salt solution is mathematically modeled with consideration of water transfer.

Mathematical Model of Electrodiffusion Transfer through a Diffusion Layer–Heterogeneous Ion-Exchange Membrane System

The kinetics of the charge and ion transport in a two-layer system which comprises a diffusion layer and an ion-exchange membrane in a salt solution and involves hydrogen and hydroxyl ions formed from water is modeled mathematically, making it possible to apply mathematical modeling to solving kinetic problems in complex electrodialysis systems where a two-layer problem is just a fragment.

The conjugation of ionic flows in the diffusion layers of electrodialysis systems

Fundamental regularities of the ion interference in diffusion layers of electrodialysis systems are revealed, as well as their effect on the electrical field strength, through which the ionic flows in their turn affect each other.

Overlimiting Electrodiffusion Transport in the Diffusion Layer as a Function of Rate Constants of Dissociation and Recombination of Water: A Numerical Calculation

A boundary-value problem, which permits discovering the effect the rate constants of dissociation and recombination of water have on the electrical and mass transfer in a diffusion layer at the ion-exchange membrane/solution interface in an overlimiting mode, is solved numerically. According to the calculation, the only value of the rate constant for reactions of dissociation and recombination of pure water determined experimentally and reported in the literature is underrated by several orders of magnitude.

Diffusion of acid and alkaline salt solutions through the Nernst diffusion layer

The behavior of diffusion layer under the conditions of salt transfer with excess of acid or alkali, involving the hydrogen and hydroxyl ions, is studied. The transfer is affected by the applying of current. The method of investigation was mathematical simulation based on the solving of boundary problems by using the Nernst-Planck equation with regard to the corresponding conditions of the transfer.

Thermodynamic Equilibrium between an Ionite's Gel Part and a Simple-Salt Solution with Allowance for Water Dissociation

When solving an ion-exchange equilibrium problem it is usually taken into account that the ionite, according to a two-phased model, comprises microphases of a gel and an equilibrium solution. The question of equilibrium in this case involves the necessity to take into account not only ions of salt contained in an aqueous solution, but ions of hydrogen and hydroxyl, which emerge in the water dissociation process, as well. Setting up such a problem is dictated, for example, by the application of electrodialysis for the production of deeply-desalinated water. In the work, for a solution of a simple salt, relations are established, which allow one to compute complete ionic composition of phases of solution and gel on the basis of specified values of concentrations of cations and anions of salt in solution.