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

TL;DR

This paper introduces a new curvilinear coordinate system to analytically solve electrostatic equations in crooked nanochannels, enabling better understanding of their transport properties and potential applications in nanofluidics.

Contribution

Development of a novel curvilinear coordinate system for analytical electrostatic analysis in crooked nanochannels, improving boundary description and computational efficiency.

Findings

Analytical solution of Poisson-Boltzmann equation in crooked nanochannels.

Quantitative evaluation of electric potential and ionic distribution.

Validation through numerical calculations confirming effectiveness.

Abstract

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.