Mathematical modelling of gravitational convection in electrodialysis processes

Two 2D models of non-stationary and non-isothermal transfer of a strong binary electrolyte in a rectangular electrodialysis desalination cell formed by anion- and cation-exchange membranes are developed. Both gravitational and forced convection occurring in underlimiting current mode are taken into account. A boundary problem for the system of equations including Navier–Stokes, Nernst–Planck, Fourier and material balance equations is numerically solved. Results obtained with both models are analyzed and compared. It is shown that the direction of the electric current in the channel is close to perpendicular to the membrane surfaces.

The results of calculations show that the gravitational convection exerts a significant effect on the concentration distribution in an electromembrane desalination channel in the cases where the Grashof number is high and the input flow velocity Fig. 5. Current density distribution calculated with Model B after 60 s from the current switching on; the input flow velocity is 0.01 cm/s. is low. The appearance of vortices causes the diluted solution to be carried from the membrane surfaces to the bulk, thus reducing the concentration in the bulk solution. At the same time the vortices transport the feed solution to the membrane surfaces, thus increasing the mass transfer. The gravitational convection disturbs the uniform distribution of the concentration in the solution bulk, observed when its contribution is negligible. The turbulence caused by spacer in an electrodialysis is not considered in this paper, even the model allows one eventually to make such an analysis. It is shown that at underlimiting currents the direction of the electric current in the channel is close to perpendicular to membrane surfaces that allows the mathematical model to be simplified.