  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 $\lambda_D\ll
H\ll L$, with $\lambda_D$ 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.
