Analytical solution to the Poisson–Nernst–Planck equations for the charging of a long electrolyte-filled slit pore

Abstract

We study the charging dynamics of a long electrolyte-filled slit pore in response to a suddenly applied potential. In particular, we analytically solve the Poisson–Nernst–Planck (PNP) equations for a pore for which λD≪H≪L, with λD the Debye length and H and L the pore’s width and length. For small applied potentials, we find the time-dependent potential drop between the pore’s surface and its center to be in complete agreement with a prediction of the celebrated transmission line model. For moderate to high applied potentials, prior numerical work showed that charging slows down at late times; Our analytical model reproduces and explains such biexponential charge buildup.