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.     

Simulation of concurrent transport of counterions through a heterogeneous ion-exchange membrane

Numerical solutions of the problem of concurrent transport of two counterions in an ion-exchange membrane are presented and discussed with allowance made for the membranes heterogeneous structure. Densities of fluxes of co-ions and competing counterions are computed as a function of the current density and boundary concentrations on either side of the membrane. The obtain result is viewed as the initial product for solving multilayered problems containing membranes of other nature and diffusion layers surrounding the membrane.Translated from Elektrokhimiya, Vol. 41, No. 3, 2005, pp. 356–366.Original Russian Text Copyright © 2005 by Gnusin.     

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.     

Computer extended series solution for unsteady flow in a contracting or expanding pipe

Unsteady flow in a semi-infinite contracting or expanding pipeis reinvestigated using long series analysis. The proposed seriesmethod is useful in analysing the problem for a moderately largeconstant ( = aa/, where a = a(t), the radius of the pipe isa function of time, a(t) is the velocity of the wall, and iskinematic viscosity). For positive values of (expansion ofthe pipe) accuracy of the series representing shear stress andpressure gradient is increased from = 2.89 to = 6.0 by extractingthe singularity followed by completion of the series. For negativevalues of (contraction of the pipe), we revert the series whichresults into the increase of the region of validity of the transposedseries from = -25.0 to = -2.89. Later we use Padé approximantsfor summing them. Also, the asymptotic solution for large valuesof is obtained and it agrees closely with pure numerical valuesof shear stress at the wall and pressure gradient.     

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.