Mathematical modelling of vortex structures in the channel of an electrodialysis cell with ion-exchange membranes of different surface morphology

Abstract

One of the ways to obtain membranes with electroconvection as the dominant mechanism of ion transport is to optimise the surface of known brands of commercial heterogeneous membranes by changing their manufacturing technology. For example, the degree of dispersion of the ion-exchanger or the volume ratio of the ion-exchanger to inert binder can be changed. The aim of this study was to determine and theoretically analyse the fundamental correlations between the intensity of electroconvection and the surface morphology of ion-exchange membranes with different ion-exchanger particle content. Тhe article presents a mathematical model of ion transport across the ion-exchange membrane/solution interface in the channel of an electrodialysis cell. The phenomenon of electroconvection in electromembrane systems (EMS) was modelled by solving two-dimensional Navier-Stokes equations for an incompressible liquid with no-slip boundary conditions and a set distribution of the electric body force. The body force distribution was set taking into account the real size of ionexchanger particles and the distance between them that determine the electrical heterogeneity of the surface of experimental ion-exchange membranes with different mass fractions of ion-exchange resin. It was determined that in the numerical modelling, the most important parameters were the size of the sections of electrical heterogeneity of the membrane surface, the current density, and the length of the space charge region (SCR). Numerical calculations were presented to determine the vortex size depending on the current density and the degree of electrical heterogeneity of the membrane surface. It was shown that an increase in the mass fraction of ion-exchange resin in the production of heterogeneous sulphocationexchange membranes resulted in a decrease in the step of electrical surface heterogeneity and promoted the formation of electroconvective vortices interacting with each other. Within the boundary conditions and approximations of the mathematical model, the vortex sizes reach their maximum value in the middle of the heterogeneity section L0.

Keywords

• mathematical modelling
• electroconvection
• vortex structures
• heterogeneous ion-exchange membrane
• surface morphology
• electrical heterogeneity of surface