Matejczyk, Bartlomiej, Pietschmann, J-F., Wolfram, Marie-Therese and Richardson, G. (2019) Asymptotic models for transport in large aspect ratio nanopores. European Journal of Applied Mathematics, 30 (3). pp. 557-584. doi:10.1017/S0956792518000293 ISSN 0956-7925.

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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-one-dimensional (1D) PNP model, which can be further simplified, in the physically relevant limit of strong pore wall surface charge, to a fully 1D model. Favourable comparison is made to the two-dimensional (2D) 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) 2D 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 2D 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.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics T Technology > TA Engineering (General). Civil engineering (General)
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Nanopores, Ion flow dynamics, Transport theory
Journal or Publication Title:	European Journal of Applied Mathematics
Publisher:	Cambridge University Press
ISSN:	0956-7925
Official Date:	June 2019
Dates:	Date Event June 2019 Published 6 June 2018 Available 23 April 2018 Accepted
Volume:	30
Number:	3
Page Range:	pp. 557-584
DOI:	10.1017/S0956792518000293
Status:	Peer Reviewed
Publication Status:	Published
Reuse Statement (publisher, data, author rights):	This article has been published in a revised form in European Journal of Applied Mathematics http://doi.org/10.1017/S0956792518000293. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder.
Access rights to Published version:	Restricted or Subscription Access
Copyright Holders:	Copyright © Cambridge University Press 2018
Description:
Date of first compliant deposit:	10 May 2018
Date of first compliant Open Access:	6 January 2019
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID 1073/1-2 [DFG] Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659 NST-001 Österreichischen Akademie der Wissenschaften UNSPECIFIED DEC-2013/09/D/ST1/03692 National Science Center UNSPECIFIED
Related URLs:	Publisher
Open Access Version:	ArXiv

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