  Both biological and artificial nanochannels in crooked shape exhibit unusual
transportational characteristics, bringing about a challenge to the traditional
theoretical analysis of nanofluidics, partly due to their complicated boundary
description. In this paper, by developing a curvilinear coordinate system for
crooked nanochannels, we successfully solve the electrostatic Poisson-Boltzmann
equation analytically for a two-dimensional nanochannel, with its effectiveness
confirmed through numerical calculation. The influences of the geometric
profile of the nanochannel on the distribution of electric potential, ionic
concentration, and surface charge on channel walls can be quantitatively
evaluated in a facilitated way in terms of these curvilinear coordinates. Such
a technique can be widely applied to many nanofluidic systems.
