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

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