Asymptotic models for transport in large aspect ratio nanopores

TL;DR

This paper develops and analyzes asymptotic models for ion transport in large aspect ratio nanopores, demonstrating that simplified Quasi-1D PNP models outperform standard 1D models in accuracy and computational efficiency.

Contribution

The paper introduces a Quasi-1D PNP model derived from asymptotic analysis, improving upon standard 1D models for nanopore ion transport.

Findings

Quasi-1D PNP model closely matches 2D solutions in typical geometries.

Standard 1D Area Averaged PNP model is inadequate for realistic parameters.

Proposed model offers computational efficiency and better accuracy.

Abstract

Ion flow in charged nanopores is strongly influenced by the ratio of the Debye length to the pore radius. We investigate the asymptotic behaviour of solutions to the Poisson-Nernst-Planck (PNP) system in narrow pore like geometries and study the influence of the pore geometry and surface charge on ion transport. The physical properties of real pores motivate the investigation of distinguished asymptotic limits, in which either the Debye length and pore radius are comparable or the pore length is very much greater than its radius. This results in a Quasi-1D PNP model which can be further simplified, in the physically relevant limit of strong pore wall surface charge, to a fully one-dimensional model. Favourable comparison is made to the two-dimensional PNP equations in typical pore geometries. It is also shown that, for physically realistic parameters, the standard 1D Area Averaged PNP model for ion flow through a pore is a very poor approximation to the (real) two-dimensional solution to the PNP equations. This leads us to propose that the Quasi-1D PNP model derived here, whose computational cost is significantly less than two-dimensional solution of the PNP equations, should replace the use of the 1D Area Averaged PNP equations as a tool to investigate ion and current flows in ion pores.