Numerical Investigation of the Effect of Two-Dimensional Surface Waviness on the Current Density of Ion-Selective Membranes for Electrodialysis

Ion-selective membranes are an important component of electrodialysis stacks for desalination. Manufacturing imperfections or slight inhomogeneity of the material can lead to minute membrane surface imperfections. Two-dimensional solutions of the coupled Poisson–Nernst–Planck and Navier–Stokes equations were sought for a perfectly smooth membrane and for membranes with well-defined small-amplitude harmonic surface roughness. The simulations were carried out with the validated rheoEFoam solver by Pimenta and Alves. In the overlimiting regime, the electric field is strong enough for an electrokinetic instability to occur. The instability leads to disturbance growth and the formation of electro-convection cells, which strongly increase the current density. The present simulations show that with an increasing ion concentration and applied voltage, the instability becomes stronger and the overlimiting regime is reached earlier. The limiting current density shows a noticeable dependence on the wavelength of the surface roughness. When the wavelength of the surface roughness is incommensurate with the wavelength of the naturally occurring instability, the limiting current density is increased. Since production membranes will always have some degree of surface roughness, this suggests that membrane surface treatments which favor certain wavelengths may have an effect on the overall membrane performance.