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 |
| Re-use Statement: | 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 NST-001 Österreichischen Akademie der Wissenschaften UNSPECIFIED DEC-2013/09/D/ST1/03692 National Science Center UNSPECIFIED |
| Related URLs: | |
| Open Access Version: | |
| URI: | https://wrap.warwick.ac.uk/101523/ |
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