Mathematical modeling of the influence of dissociation/recombination rate constant dependence on salt ion transport in the diffusion layer near an ion-exchange membrane

This study presents a novel theoretical model of steady-state ion transport through cation-exchange membrane systems. Unlike existing theoretical approaches, the proposed model relates modifications in the equilibrium constant not only to the electric potential gradient, but also to spatial charge distribution. Analysis of the Poisson equation confirms the significant dependence of ion dissociation kinetics on local space charge density within the membrane structure.
The developed mathematical model, incorporating this dependence, enables a more accurate description of diffusion-migration processes in cation-exchange membranes. The obtained results provide a more precise description of ion behavior under steady-state transport conditions — a crucial factor for developing advanced membrane materials and technological processes. The proposed model can be applied in various technological fields employing ion-exchange membrane systems, including water treatment processes and energy converters.
A key advantage of the proposed model is its capability for comprehensive consideration of critical ion transport parameters: solution ionic strength, temperature conditions, and membrane structural-functional characteristics. This enables more accurate prediction of membrane system performance in actual technological processes.
In particular, application of this model in membrane water purification systems allows optimization of demineralization processes, thereby enhancing water treatment efficiency while reducing energy consumption in the technological cycle.
Thus, the developed model offers new opportunities for both fundamental research and practical optimization of mass transfer processes in ion-exchange membrane systems.