Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus

A new 3D model of $1 : 1$ salt ion transfer in the desalting channel of an electrodialysis apparatus is presented and investigated in this paper. For the first time a three-dimensional mathematical model of salt ion transfer in the desalting channel taking into account the electroconvection based on the system of Nernst – Planck, Poisson and Navier – Stokes equations with the electric force and the natural boundary conditions is proposed. To solve the boundary value problem, the finite element method is used in the cross-platform numerical analysis software COMSOL Multiphysics in combination with the method of successive approximations, when the electrochemical and hydrodynamic parts of the problem are solved one by one on the current layer. In turn, the electrochemical and hydrodynamic parts of the problem are solved by Newton’s method. As a result of numerical analysis, the fundamental regularities of salt ion transfer in a three-dimensional channel, the emergence and development of electroconvective vortices, including the discovery of new three-dimensional spiral forms of salt ions, are established for the first time. It is shown that electroconvective vortices exist in the form of clusters, within which vortex bifurcations can occur. Thus, the currently existing simplified view of the structure of electroconvective vortices is clarified and developed.