Mathematical Modeling of the Influence of Equilibrium Coefficient Variation on the Steady-State Transport of a Binary Electrolyte in the Cross-Section of a Desalination Channel

This paper theoretically investigates the effect of changes in the equilibrium coefficient on the steady-state transport of a binary electrolyte in a desalination channel cross-section of the electrodialysis apparatus using a mathematical model in the form of a bounda-ry-value problem for an extended system of stationary Nernst-Planck-Poisson equations. A numerical solution is obtained using the finite element method and demonstrates that the channel cross-section has a complex structure, specifically, it is divided into seven segments where different processes dominate, and therefore the solution to the bounda-ry-value problem behaves differently in each of them. This paper demonstrates that, un-like existing approaches, the change in the equilibrium coefficient rate is associated not only with the field strength but also with the magnitude of the space charge. In the space-charge region, in the boundary layers near the ion-exchange membranes, intense dissociation of water molecules occurs, and the higher the equilibrium coefficient, the more intense this dissociation is. It is shown that an internal boundary layer (recombina-tion region) arises deep within the solution, associated with the recombination reaction of H+ and OH− ions. It is shown that with an increase in the equilibrium coefficient, the flows increase, and with an increase in flows, the electric field strength decreases propor-tionally, and equilibrium arises. It is shown that by choosing the fitting parameter of the mathematical model it is possible to align the results obtained using the mathematical model and experimental data with arbitrary accuracy. Thus, the proposed model and its numerical solution provide a new understanding of the process of ion transport in electromembrane systems, taking into account the influence of the dissociation/recombination reaction of water molecules.