The Painlevé equation of the second kind for the binary ionic transport in diffusion boundary layers near ion-exchange membranes at overlimiting current

In ion-exchange membrane systems such as electrodialysis, the overlimiting current phenomenon still remains a difficult topic to study due to the complicated solution method for the Nernst–Planck–Poisson model. In this study, the Nernst–Planck–Poisson equations were prepared to simulate the steady-state binary ionic transport in the diffusion boundary layer near an ion-exchange membrane. The system of differential equations was converted into …