Electrostatics in a crooked nanochannel in a newly developed curvilinear coordinate system

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.