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

Although nanochannels in tortuous shape exhibit unusual transportational characteristics, the traditional theoretical analysis of nanofluidics in such kinds of systems remains challenging, partly due to their complicated boundary description. In this paper, by developing a curvilinear coordinate system for such tortuous nanochannels, we 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 on the distribution of electric potential, ionic concentration, and surface charge on channel walls are quantitatively evaluated in a facilitated way in terms of the curvilinear coordinates introduced. Such a technique can be widely applied to many nanofluidic systems in curved channels.