Approximate time-dependent current-voltage relations for currents exceeding the diffusion limit

The time-dependent behavior of one-dimensional ion transport into a permselective medium is theoretically modeled in this work for currents exceeding the diffusion limit. Leveraging the findings of Yariv [E. Yariv, Phys. Rev. E 80, 051201 (2009)10.1103/PhysRevE.80.051201], we derive three separate expressions for the potential drop for short, intermediate, and long times. We show that the potential drop correlates to the time evolution of the space-charge layer adjacent to the permselective interface. Our approximate models show remarkable correspondence to numerical simulations.