Scientific Journal of KubSAU

This article is devoted to the asymptotic analysis of boundary value problem for a system of equations of Nernst-Planck and Poisson for a singularly perturbed system of ordinary differential equations [1], based on two parameters. This boundary value problem simulates electrodiffusion of four kinds of ions at the same time in the diffusion layer in electro-membrane systems with perfectly selective membrane, taling into consideration the reaction of recombination of two ions. Meanwhile the other two ions represent ions of a binary salt. As a simple example, we consider the transport of ions sodium, chlorine, hydrogen and hydroxide, moreover, hydrogen and hydroxyl ions recombine in the diffusion layer. A more complex case is the transfer of the products of dissociation of the dihydrogen phosphate of sodium, namely, ions of sodium and dihydrogen phosphate, the latter dissociate at the interface, in turn, hydrogen ions and hydrogen phosphate. Thus, in the solution can simultaneously store three different types of ions: sodium, hydrogen, phosphate. During the transfer, hydrogen ions and ions of hydrogen phosphate recombine to produce phosphoric acid. The article has revealed the structure of the Nernst diffusion layer at currents above Harkatsa current. It is shown, that in the diffusion layer, there are two types of boundary layers: the inner (reaction) boundary layer and boundary layer at the interface solution / membrane

The influence of dissociation / recombination of water molecules is important for understanding electroconvection processes, as some authors believe that the emergence of new carriers + H and − OH , and can lead to a reduction in the space-charge and, consequently, to electroconvection disappearance. However, as shown in [5], the dissociation of water molecules, although it reduces the space charge and increases the threshold fall potential jump at which begins electroconvection, yet it persists and effectively mixes the solution. This article is devoted to mathematical modeling of electrodiffusion of four types of ions at the same time (two salt ions as well as + H and − OH ions) in the diffusion layer in electromembrane systems with perfectly selective membrane under the joint influence of violation of electrical neutrality, and the reaction of dissociation / recombination of water molecules, development of mathematical models of these processes, building efficient algorithms asymptotic and numerical analysis for different types of electrolytes. The work proposes a new mathematical model of the process of transfer of salt ions in view of the space charge and the dissociation / recombination of water in the form of a boundary value problem for a system of ordinary differential equations. This system is reduced to a form convenient for numerical solution. We have calculated the required additional boundary conditions for the electric field. Numerical and asymptotic solution of the boundary value problem and physico-chemical analysis of the influence of dissociation / recombination on the transfer of salt ions is expected to devote the next part of the work