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The model of metal ion permeation through a bulk liquid membrane (BLM), based on the Nernst–Planck equation, was developed. It was satisfactorily tested using the experimental data on the cadmium permeation from Cd(NO 3 ) 2 solution through BLM (D2EHPA in kerosene) to 1 M H 2 SO 4 solution. According to the model simulations, the cadmium permeation was controlled by K eq on the feed side; the knowledge of the exact K eq value on the strip side under the condition c H 2 SO 4 ≫ c Cd was not required. None of the following: an assumed Cd-D2EHPA complex (CdP 2 (HP) 2 , CdP 2 HP), presence of undimerized D2EHPA in BLM, or ion pair formation Cd 2 + · SO 4 2 - in the strip solution, influence the goodness of fit. Assuming the model based on the Fick’s law with the constant cadmium mass transfer coefficient, a large dispersion of its optimal fitting values which depends on the model assumption was found. Thus, that coefficient can only be treated as a fitting parameter.

The electric transport of the H 2 SO 4 and H 3 PO 4 mixture through two types of anion-exchange membranes (strong base: ACM; weak base: AAV) was investigated. The H 2 SO 4 removal efficiency from the mixture and the H 3 PO 4 retention efficiency were calculated. It was found that the effectiveness of the separation process is diminished by the association of phosphoric anions with the fixed charges which reduces the effective charge concentration. The transport of acids was quantitatively described by the model based on the extended Nernst–Planck equation and the Donnan equilibria. It satisfactorily describes the electro-membrane process except its last stage when H 2 SO 4 concentration at the cathode side of a membrane is of a low value. When the association equilibrium between H 2 PO 4 − and the fixed charges of the ACM membrane is introduced into the model, the concentration changes of H 3 PO 4 could be much better described. Assuming the ideal Donnan equilibrium to occur, the transport of the both acids cannot be described by the same parameter related to the membrane porosity, tortuosity and the ion diffusivities. Regarding H 3 PO 4 , different ionic equilibria were taken into account in order to show their effects on the values of optimal model parameters.

The experimental results of the separation of acetic acid (HA) from the sulfuric acid by the electro-electrodialysis (EED) method and the modeling of process have been presented. The Neosepta membranes CMX and ACM have been used. It has been found that the efficiency of retention of HA is high (>0.9) when the process is conducted below the limiting current density with respect to HSO4− or SO42− anions. The observed current efficiency of the H2SO4 removal was rather low (CES = ca. 0.7, when the initial concentration of H2SO4 in the mixture was 1 or 2 M) which was caused by the nonideal selectivity of the anion-exchange membrane. The experimental results have been described by the model based on the extended Nernst-Planck equation and the Donnan equilibrium. Since the efficiency of the process depended mainly on the selectivity of anion-exchange membrane (ACM), the concentration of fixed charges of that membrane, c ¯ m , and the ratio of volume fraction of pores to their squared tortuosity, Vp/θ2, have been chosen as the main fitting parameters. It has been found that the fitting of the EED data depends mainly on c ¯ m , whereas in the modeling of diffusion experiment (or an EED experiment conducted at low current density) both parameters are important. The best fit has been obtained for c ¯ m = 0.5 − 0.6 M , i.e. ca. one order smaller than that determined experimentally. The obtained optimal value of Vp/θ2, equal to 0.013, is consistent with those previously obtained for other Neosepta anion-exchange membrane.

Nowadays the use of synthetic dyes in the food industry is popular. As these compounds can cause the development of various diseases, including the cancer or heart disease, it is a pressure on the technologies of recovery of natural dies from the natural resources (fruits, vegetables, etc.). One of the valuable natural dyes are anthocyanins, which are present in the aronia fruits available in abundant amounts in Poland. In this work the investigations on the concentration of anthocyanins by nanofiltration have been presented. The aronia solutions containing Na 2 SO 3 – one of the most efficient extractants of anthocyanins – have been used. In order to determine its influence on the retention of anthocyanins, the filtration of aronia solution with and without Na 2 SO 4 has been also performed. The retentions of anthocyanins, sodium ions and ionic species have been investigated. It has been found that in the presence of sodium sulfate(IV) anthocyanins are almost completely rejected (>99%). In the case of pure solution or containing sulfate(VI) the retention is lower (91–95%). Thus, sodium sulfate(IV) is not only a good extractant and preserve but also its presence highly increases the efficiency of the filtration process.

The electrodialysis with bipolar membrane (EDB) of organic acid salts is an alternative way of the production of organic acids. In this work a model of the basic EDB cell consisting of three compartments (acid, salt, base) is presented. The transport of ions through monopolar ion-exchange membranes is described by the extended Nernst–Planck equation, assuming the Donnan equilibrium at the boundary solution|membrane. The diffusion of undissociated acid and the electro-osmotic flow of water is taken into account. The model predicts how the efficiency of salt conversion, the resistance of cell, the volumes of acid, salt, and base solutions change with time for a given current density. The simulation results are presented for the acetic acid. The influence of nonideality of membranes and of the acid dissociation constant on the efficiency of acid production is shown.

The transport number of counterions in ion-exchange membranes (Nafion, Neosepta) has been predicted using the homogeneous and capillary models of transport. In the case of capillary model, two distributions of ions — described by the traditional and modified by Gur Boltzmann equations — have been applied. It has been found that the homogeneous model based on the experimental sorption and the capillary model, with the traditional Boltzmann equation, predict the transport number relatively well. The only exception is the anion-exchange membrane Neosepta AM1 in HCl solutions, because of facilitated transport of protons through that membrane. It has been proved that the sorption given by the Boltzmann equation is always higher than that given by the modified Boltzmann equation and than the Donnan sorption. The modified Boltzmann equation, successful in predicting partition coefficient in Nafion 117 membrane equilibrated with H 2 SO 4 solutions and salt mixture solutions, as reported by other authors, failed here.