Criterial numbers describing formation of unstable electroconvective vortices in an electrodialysis desalination channel

Abstract

This work is devoted to the calculation of criterion numbers, corresponding to the emergence of
electroconvective vortices. The analytical expressions to assess the potential jump threshold above which the
vortices are formed under the influence of the external electric field at the surface of the ion exchange membrane,
are not suppressed by the forced flow of liquid. It is shown that with increasing rate of the forced flow, the
threshold potential drop increases. We have compared the values of the threshold potential drops found
analytically and using numerical simulation. We carried out the numerical calculation with a 2D non-stationary
model for the transfer of a binary electrolyte in an electrodialysis desalination channel in overlimiting current
mode. The model is formulated as a boundary value problem for the system of the Nernst-Planck-Poisson
equations and Navier-Stokes equations [1]. It is shown that there are several criteria numbers of unstable
electroconvection onset for an electrodialysis desalination channel with homogeneous perfectly selective ion
exchange membranes. Most of the results can be applied for 3D geometry.