Математическое моделирование влияния основных температурных эффектов на стационарный перенос ионов соли в диффузионном слое

Abstract

This article is devoted to the construction of a new mathematical model, using a mathematical model of the system of Nernst-Planck-Poisson equations for electrodiffusion of four varieties of ions simultaneously (two salt ions, and H+, OH- ions) in the diffusion layer in electromembrane systems with a perfectly selective membrane and the heat equation, taking into account the Joule heating of the solution, endo- and exothermic nature of the reactions of dissociation of water molecules and recombination of ions. In addition, the model takes into account the dependence of the coefficient of equilibrium of the dissociation/recombination reaction on temperature. The mathematical model is a boundary value problem for the system of ordinary differential equations, the study of which allows determining the basic patterns of transport of ions of binary salt and water dissociation products taking into account the space charge, reactions dissociation/recombination of water and the corresponding temperature effects. The paper presents the conclusion of the formula for the amount of heat absorbed/emitted at each point $x$, during the course of the dissociation/recombination reaction of water. A boundary condition is derived at a point $x=\delta $ with allowance for the balance of heat fluxes at this point. The study determines the structure of the diffusion layer from the receiving side of the membrane, and, accordingly, the asymptotic solutions in each of the regions of the diffusion layer, to conduct their splicing. The conditions under which the practically irreversible dissociation of water with the maximum possible constant rate in the expanded space charge region are determined. In addition, the study shows that in the region of electroneutrality a narrow band (the recombination region) arises, where the recombination of water molecules prevails over their dissociation, and that the centers of the recombination and dissociation region, within the diffusion layer, are spaced from each other at a considerable distance.