A hydrodynamic theory of desalination by electrodialysis

Abstract

A hydrodynamic theory of demineralization by electrodialysis has been developed for a multichannel system with steady laminar flow between plane, parallel membranes. The modeling of the system is found to be governed by four basic similarity parameters: (i) a dimensionless applied potential, (ii) the product of the channel aspect ratio and the inverse Péclet number, (iii) the ratio of brine and dialysate inlet concentrations, and (iv) a parameter measuring membrane resistance. For sufficiently long channels it is shown that there are two distinct regions: a “developing” region where the concentration diffusion layers are growing, and a “developed” region where the diffusion layers fill the channel. Parabolic and uniform velocity profiles are considered and self-consistent solutions are derived for the distributions of salt concentration, electric field and current density in the system, as well as for the total current. An integral method of solution is used. In the limits of low and high polarization analytic solutions are obtained which when matched at their point of equality closely approximate the complete numerical solutions. It is found that under a wide range of operating conditions, the solution for the total current is represented by the empirical formulaI^=[1−exp(−Ψ^3)]1/3,where Î andΨ^are, respectively, a dimensionless current and potential embodying the four similarity parameters mentioned. Comparison is made of the calculated limiting total current with experiment.