A Mathematical Framework that Matches Power Density of Nanoporous Membranes with Experimental Literature

In this paper, we develop a mathematical framework to predict ion-transport across thick nanoporous membrane. The framework includes 1) force between the applied voltage and the ion 2) interaction of the ion with the surface charge density of the nanoporous membrane 3) electrostatic force between the applied voltage and the surface charge density of the nanoporous membrane. The framework neglects the ion-ion correlations and treats the ionic correlations as a cumulative sum of ions calculated from a single counter-ion. The mathematical framework matches well with the experimental ion transport I-V results of various published experimental literature with respect to thick nanoporous membranes.