Theoretical Analysis of the Stationary Transport of 1:1 Salt Ions in a Cross-Section of a Desalination Channel, Taking into Account the Non-Catalytic Dissociation/Recombination Reaction of Water Molecules

Abstract

In electromembrane systems, the theoretical study of salt ion transport usually uses mathematical models of salt ion transport in the depleted diffusion layer of ion-exchange membranes. This study uses a one-dimensional mathematical model of salt ion transport in a cross-section of a desalination channel formed by anion-exchange and cation-exchange membranes, taking into account an effect of a dissociation/recombination reaction of water molecules. The reaction on the one hand leads to an overlimiting mass transfer due to the effect of exaltation of the limiting current. On the other hand, an appearance of new electric charge carriers (hydrogen and hydroxyl ions) can reduce the space charge that occurs in membranes and suppress an electroconvective mechanism of overlimiting transport. Thus, there is a problem of studying these phenomena together, taking into account their mutual influence, and this article is devoted to the solution of this problem. Theoretically, using a method of mathematical modeling and numerical research, main regularities are established; in particular, it is shown that the dissociation/recombination reaction of water molecules does not lead to the destruction of the double electric layer at the membranes, but also creates a new double electric layer in the middle of the desalination channel. Thus, the space charge and the dissociation/recombination reaction significantly affect each other and simultaneously the transport of salt ions.

Current distribution along electrodialysis stacks and its influence on the current-voltage curve: behaviour from near-zero current to limiting plateau

“…In the first region of the overall CVC, I1/Itot was up to Future research should focus on the evaluation of the total resistance and all its contributions for a thorough understanding of the stack behaviour, especially in the limiting region. This will make a clear distinction between concentration polarization and phenomena, including those related to water dissociation [81] and to the desalination effect.…”

A simple one-dimensional model for analysis of a bipolar membrane used in electrodialysis desalination

“…R eiss is expressed here as membrane resistance times unit area (Ωm 2 ), often used despite its peculiar dimensions. The mathematical model is based on the equations of dissociation/recombination of water molecules (1) and ( 2), along with a system of stationary onedimensional Nernst -Plank -Poisson equations ( 3) and ( 4), representing the laws of conservation for electric charge and material balance [18]. The current flow condition ( 6) is also set here, indicating that the flow of ions generates the current in the BPM system.…”

“…were I 1 is the firstorder Bessel function, defined as [19]: typically under 20 [19]. Water dissociation constant at E = 0 , k w,0 = 10 -8 mol 2 /m 6 [18].…”

“…The semi-implicit Runge-Kutta method in time and a finite difference scheme in space were used to perform numerical integration of continuum Poisson-Nernst-Planck theory, including source terms and the catalytic Second Wien Effect under the applied electric field [17]. Mathematical modelling environment Comsol Multiphysics, based on the finite element method, was used frequently for various analytical studies regarding bipolar membrane performance [18][19][20]. The main advantage of the COMSOL simulations is related to a facile calculation of concentration and potential profiles across the entire model, splitting the fluxes to diffusion and migration contributions and presenting their coupling even in the absence of electric current [20].…”